text:
# American Institute of Mathematical Sciences

June  2017, 22(4): 1525-1546. doi: 10.3934/dcdsb.2017073

## An almost periodic malaria transmission model with time-delayed input of vector

 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

* Corresponding author:Bin-Guo Wang

Received  April 2016 Revised  December 2016 Published  February 2017

An almost periodic malaria transmission model with the time-delayed input of vector is considered. It is shown that the disease is uniformly persistent when the basic reproduction ratio $R_{0}>1$, and it will die out when $R_{0} < 1$ under the assumption that there exists a small invasion. Furthermore, the global stability of the disease-free almost periodic state is obtained provided that the disease-induced death rate is null. Finally, we illustrate the above results by numerical simulations and show that the periodic epidemic models may overestimate or underestimate the malaria risk.

Citation: Lizhong Qiang, Bin-Guo Wang. An almost periodic malaria transmission model with time-delayed input of vector. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1525-1546. doi: 10.3934/dcdsb.2017073
##### References:
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Metz, On the definition and the computation of the basic reproduction ratio $R_{0}$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382. doi: 10.1007/BF00178324. Google Scholar [11] A. M. Fink, Almost Periodic Differential Equations Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1974. Google Scholar [12] D. Gao, Y. Lou and S. Ruan, A periodic ross-macdonald model in a patchy environment, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 3133-3145. doi: 10.3934/dcdsb.2014.19.3133. Google Scholar [13] H. -W. Gao, L. -P. Wang, S. Liang, Y. -X. Liu, S. -L. Tong, J. -J. Wang, Y. -P. Li, X. -F. Wang, H. Yang and J. -Q. Ma, et al. , Change in rainfall drives malaria re-emergence in anhui province china, PLoS ONE, 7 (2012), e43686. doi: 10.1371/journal.pone.0043686. Google Scholar [14] J. K. Hale, Asymptotic Behavior of Dissipative Systems Math. Surveys and Monographs 25, Amer. Math. Soc. , Providence, RI, 1988. Google Scholar [15] M. B. Hoshen and A. P. Morse, A weather-driven model of malaria transmission, Malar. J., 3 (2004), 32-46. doi: 10.1186/1475-2875-3-32. Google Scholar [16] W. Jepson, A. Moutia and C. Courtois, The malaria problem in mauritius: The bionomics of mauritian anophelines, Bulletin of entomological research, 38 (1947), 177-208. doi: 10.1017/S0007485300030273. Google Scholar [17] Y. Lou and X.-Q. Zhao, Threshold dynamics in a time-delayed periodic SIS epidemic model, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 169-186. doi: 10.3934/dcdsb.2009.12.169. Google Scholar [18] Y. Lou and X.-Q. Zhao, A climate-based malaria transmission model with structured vector population, SIAM J. Appl. Math., 70 (2010), 2023-2044. doi: 10.1137/080744438. Google Scholar [19] G. Macdonald et al, The Epidemiology and Control of Malaria Oxford University Press, Oxford, UK, 1957.Google Scholar [20] P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275. doi: 10.1137/S0036141003439173. Google Scholar [21] J. Nedelman, Introductory review some new thoughts about some old malaria models, Math. Biosci., 73 (1985), 159-182. doi: 10.1016/0025-5564(85)90010-0. Google Scholar [22] E. Ngarakana-Gwasira, C. Bhunu and E. Mashonjowa, Assessing the impact of temperature on malaria transmission dynamics, Afr. Mat., 25 (2014), 1095-1112. doi: 10.1007/s13370-013-0178-y. Google Scholar [23] G. Ngwa, Modelling the dynamics of endemic malaria in growing populations, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), 1173-1202. doi: 10.3934/dcdsb.2004.4.1173. Google Scholar [24] G. A. Ngwa and W. S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations, Math. Comput. Modelling, 32 (2000), 747-763. doi: 10.1016/S0895-7177(00)00169-2. Google Scholar [25] P. Reiter, Climate change and mosquito-borne disease, Envir. Hlth. Perspect., 109 (2001), 141-161. doi: 10.2307/3434853. Google Scholar [26] R. Ross, The Prevention of Malaria John Murray, London, 1911.Google Scholar [27] S. Ruan, D. Xiao and J. C. Beier, On the delayed ross-macdonald model for malaria transmission, Bull. Math. Biol., 70 (2008), 1098-1114. doi: 10.1007/s11538-007-9292-z. Google Scholar [28] G. Sell, Topological Dynamics and Ordinary Differential Equations Van Nostrand Reinhold, London, 1971. Google Scholar [29] M. Service, Mosquito Ecology: Field Sampling Methods Springer Netherlands, 1993.Google Scholar [30] H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative systems Math. Surveys and Monographs, 41, Amer. Math. Soc. , Providence, RI, 1995. Google Scholar [31] H. L. Smith and P. Waltman, The Theory of the Chemostat Cambridge University Press, Cambridge, 1995. doi: 10.1017/CBO9780511530043. Google Scholar [32] P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar [33] H. Wan and H. Zhu, The impact of resource and temperature on malaria transmission, Journal of Biological Systems, 20 (2012), 285-302. doi: 10.1142/S0218339012500118. Google Scholar [34] B. G. Wang, W. T. Li and L. Zhang, An almost periodic epidemic model with age structure in a patchy environment, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), 291-311. doi: 10.3934/dcdsb.2016.21.291. Google Scholar [35] B.-G. Wang and X.-Q. Zhao, Basic reproduction ratios for almost periodic compartmental epidemic models, J. Dyn. Diff. Equ., 25 (2013), 535-562. doi: 10.1007/s10884-013-9304-7. Google Scholar [36] W. Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dynam. Differential Equations, 20 (2008), 699-717. doi: 10.1007/s10884-008-9111-8. Google Scholar [37] The world health report, 2014. Available from: http://www.who.int/malaria/media/en/.Google Scholar [38] X. -Q. Zhao, Dynamical Systems in Population Biology Springer-Verlag, New York, 2003. doi: 10.1007/978-0-387-21761-1. Google Scholar [39] X.-Q. Zhao, Global attractivity in monotone and subhomogeneous almost periodic systems, J. Differential Equations, 187 (2003), 494-509. doi: 10.1016/S0022-0396(02)00054-2. Google Scholar

show all references

##### References:
 [1] S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual and P. Rohani, Seasonality and the dynamics of infectious diseases, Ecology Letters, 9 (2006), 467-484. doi: 10.1111/j.1461-0248.2005.00879.x. Google Scholar [2] J. L. Aron, Mathematical modeling of immunity to malaria, Math. Biosci., 90 (1988), 385-396. doi: 10.1016/0025-5564(88)90076-4. Google Scholar [3] A. Bomblies, Modeling the role of rainfall patterns in seasonal malaria transmission, Climatic Change, 112 (2012), 673-685. doi: 10.1007/s10584-011-0230-6. Google Scholar [4] N. Chitnis and J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math., 67 (2006), 24-45. doi: 10.1137/050638941. Google Scholar [5] N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272-1296. doi: 10.1007/s11538-008-9299-0. Google Scholar [6] C. Chiyaka, W. Garira and S. Dube, Transmission model of endemic human malaria in a partially immune population, Math. Comput. Modelling, 46 (2007), 806-822. doi: 10.1016/j.mcm.2006.12.010. Google Scholar [7] C. Chiyaka, J. M. Tchuenche, W. Garira and S. Dube, A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Appl. Math. Comput., 195 (2008), 641-662. doi: 10.1016/j.amc.2007.05.016. Google Scholar [8] C. Corduneanu, Almost Periodic Functions Chelsea Publishing Company New York, N. Y. , 1989.Google Scholar [9] M. Craig, I. Kleinschmidt, J. Nawn, D. Le Sueur and B. Sharp, Exploring 30 years of malaria case data in kwazulu-natal, south africa: part Ⅰ. the impact of climatic factors, Trop. Med. Int. Health, 9 (2004), 1247-1257. doi: 10.1111/j.1365-3156.2004.01340.x. Google Scholar [10] O. Diekmann, J. A. P. Heesterbeek and J. A. Metz, On the definition and the computation of the basic reproduction ratio $R_{0}$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382. doi: 10.1007/BF00178324. Google Scholar [11] A. M. Fink, Almost Periodic Differential Equations Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1974. Google Scholar [12] D. Gao, Y. Lou and S. Ruan, A periodic ross-macdonald model in a patchy environment, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 3133-3145. doi: 10.3934/dcdsb.2014.19.3133. Google Scholar [13] H. -W. Gao, L. -P. Wang, S. Liang, Y. -X. Liu, S. -L. Tong, J. -J. Wang, Y. -P. Li, X. -F. Wang, H. Yang and J. -Q. Ma, et al. , Change in rainfall drives malaria re-emergence in anhui province china, PLoS ONE, 7 (2012), e43686. doi: 10.1371/journal.pone.0043686. Google Scholar [14] J. K. Hale, Asymptotic Behavior of Dissipative Systems Math. Surveys and Monographs 25, Amer. Math. Soc. , Providence, RI, 1988. Google Scholar [15] M. B. Hoshen and A. P. Morse, A weather-driven model of malaria transmission, Malar. J., 3 (2004), 32-46. doi: 10.1186/1475-2875-3-32. Google Scholar [16] W. Jepson, A. Moutia and C. Courtois, The malaria problem in mauritius: The bionomics of mauritian anophelines, Bulletin of entomological research, 38 (1947), 177-208. doi: 10.1017/S0007485300030273. Google Scholar [17] Y. Lou and X.-Q. Zhao, Threshold dynamics in a time-delayed periodic SIS epidemic model, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 169-186. doi: 10.3934/dcdsb.2009.12.169. Google Scholar [18] Y. Lou and X.-Q. Zhao, A climate-based malaria transmission model with structured vector population, SIAM J. Appl. Math., 70 (2010), 2023-2044. doi: 10.1137/080744438. Google Scholar [19] G. Macdonald et al, The Epidemiology and Control of Malaria Oxford University Press, Oxford, UK, 1957.Google Scholar [20] P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275. doi: 10.1137/S0036141003439173. Google Scholar [21] J. Nedelman, Introductory review some new thoughts about some old malaria models, Math. Biosci., 73 (1985), 159-182. doi: 10.1016/0025-5564(85)90010-0. Google Scholar [22] E. Ngarakana-Gwasira, C. Bhunu and E. Mashonjowa, Assessing the impact of temperature on malaria transmission dynamics, Afr. Mat., 25 (2014), 1095-1112. doi: 10.1007/s13370-013-0178-y. Google Scholar [23] G. Ngwa, Modelling the dynamics of endemic malaria in growing populations, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), 1173-1202. doi: 10.3934/dcdsb.2004.4.1173. Google Scholar [24] G. A. Ngwa and W. S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations, Math. Comput. Modelling, 32 (2000), 747-763. doi: 10.1016/S0895-7177(00)00169-2. Google Scholar [25] P. Reiter, Climate change and mosquito-borne disease, Envir. Hlth. Perspect., 109 (2001), 141-161. doi: 10.2307/3434853. Google Scholar [26] R. Ross, The Prevention of Malaria John Murray, London, 1911.Google Scholar [27] S. Ruan, D. Xiao and J. C. Beier, On the delayed ross-macdonald model for malaria transmission, Bull. Math. Biol., 70 (2008), 1098-1114. doi: 10.1007/s11538-007-9292-z. Google Scholar [28] G. Sell, Topological Dynamics and Ordinary Differential Equations Van Nostrand Reinhold, London, 1971. Google Scholar [29] M. Service, Mosquito Ecology: Field Sampling Methods Springer Netherlands, 1993.Google Scholar [30] H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative systems Math. Surveys and Monographs, 41, Amer. Math. Soc. , Providence, RI, 1995. Google Scholar [31] H. L. Smith and P. Waltman, The Theory of the Chemostat Cambridge University Press, Cambridge, 1995. doi: 10.1017/CBO9780511530043. Google Scholar [32] P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar [33] H. Wan and H. Zhu, The impact of resource and temperature on malaria transmission, Journal of Biological Systems, 20 (2012), 285-302. doi: 10.1142/S0218339012500118. Google Scholar [34] B. G. Wang, W. T. Li and L. Zhang, An almost periodic epidemic model with age structure in a patchy environment, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), 291-311. doi: 10.3934/dcdsb.2016.21.291. Google Scholar [35] B.-G. Wang and X.-Q. Zhao, Basic reproduction ratios for almost periodic compartmental epidemic models, J. Dyn. Diff. Equ., 25 (2013), 535-562. doi: 10.1007/s10884-013-9304-7. Google Scholar [36] W. Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dynam. Differential Equations, 20 (2008), 699-717. doi: 10.1007/s10884-008-9111-8. Google Scholar [37] The world health report, 2014. Available from: http://www.who.int/malaria/media/en/.Google Scholar [38] X. -Q. Zhao, Dynamical Systems in Population Biology Springer-Verlag, New York, 2003. doi: 10.1007/978-0-387-21761-1. Google Scholar [39] X.-Q. Zhao, Global attractivity in monotone and subhomogeneous almost periodic systems, J. Differential Equations, 187 (2003), 494-509. doi: 10.1016/S0022-0396(02)00054-2. Google Scholar
Compartmental model for malaria.
The total number of vector.
The graph of $\|u(t)\|$ and $\ln\|u(t)\|$ of (26) when $k=2.5$.
The long-term behavior of vector and human populations when $R_{0}<1$.
The graph of $\|u(t)\|$ and $\ln\|u(t)\|$ of (26) when $k=5$.
The long-term behavior of vector and human populations when $R_{0}>1$.
Relationship between $\widehat{p}$ and $R_{0}$.
The long-term trend of $\ln\|u(t)\|$ of (27) with $m=2.4$ and $m=2.5$.
The parameters of model and their means.
 Parameters Meaning $a$ Infection probability from infective humans to susceptible mosquitoes. $\eta$ Transfer rate of mosquitoes from the exposed class to the infectious class. $\lambda$ The proportion between the probability of transmission from recovered humans to susceptible vectors and the probability of transmission from infectious humans. $\gamma_{R}$ Per capita loss rate of immunity for humans. $\gamma_{E}$ Transfer ratio of humans from the exposed class to the infectious class. $\gamma_{I}$ Human recovery rate. $c$ Infection probability from infectious mosquitoes to susceptible humans. $d_{h}$ Death rate of humans. $\sigma_{h}$ The diseased-induced rate of humans. $\Lambda_{h}$ Supplement rate of humans.
 Parameters Meaning $a$ Infection probability from infective humans to susceptible mosquitoes. $\eta$ Transfer rate of mosquitoes from the exposed class to the infectious class. $\lambda$ The proportion between the probability of transmission from recovered humans to susceptible vectors and the probability of transmission from infectious humans. $\gamma_{R}$ Per capita loss rate of immunity for humans. $\gamma_{E}$ Transfer ratio of humans from the exposed class to the infectious class. $\gamma_{I}$ Human recovery rate. $c$ Infection probability from infectious mosquitoes to susceptible humans. $d_{h}$ Death rate of humans. $\sigma_{h}$ The diseased-induced rate of humans. $\Lambda_{h}$ Supplement rate of humans.
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# High Contrast Far-Field Radiative Thermal Diode

## Abstract

We propose a theoretical concept of a far-field radiative thermal rectification device that uses a phase change material to achieve a high degree of asymmetry in radiative heat transfer. The proposed device has a multilayer structure on one side and a blackbody on other side. The multilayer structure consists of transparent thin film of KBr sandwiched between a thin film of VO2 and a reflecting layer of gold. When VO2 is in its insulating phase, the structure is highly reflective due to the two transparent layers on highly reflective gold. When VO2 is in the metallic phase, Fabry-Perot type of resonance occurs and the tri-layer structure acts like a wide-angle antireflection coating achieved by destructive interference of partially reflected waves making it highly absorptive for majority of spectral range of thermal radiation. The proposed structure forms the active part of configuration that acts like a far-field radiative thermal diode. Thermal rectification greater than 11 is obtained for a temperature bias of 20 K, which is the highest rectification ever predicted for far-field radiative diode configurations.

## Introduction

Thermal diode1, thermal transistors2, thermal memory element3 and similar thermal analogues of electronic devices have been topic of theoretical as well as experimental works. While earlier research has been on conduction (phonon) based devices4,5,6,7,8, more recent studies have been focusing on radiation (photon) based thermal rectifiers9,10,11,12. Thermal rectification has numerous applications in thermal management, thermal logic gates13,14,15 and information processing16.

Analogous to electrical diode, thermal diode is a rectification device wherein magnitude of heat flux strongly depends on the sign of applied temperature bias. To quantify rectification, we employ the widely used definition of rectification ratio, i.e., R = (Q f  − Q r )/Q r where Q f and Q r refer to forward and reverse heat flux, respectively17. Alternatively, rectification coefficient can be defined as η = (Q f  − Q r )/max(Q r , Q f ). There are numerous studies pertaining to near-field and far-field thermal radiation based rectification devices that exploit temperature dependent properties of a phase change materials such as vanadium dioxide (VO2) and La0.7Ca0.15Sr0.15MnO3 (LCSMO)11, 18, 19. A number of studies deal with far-field thermal radiation20, 21 while several others focus on modulation of radiative heat transfer in the near-field regime18, 19, 22,23,24,25,26. Ben-Abdallah and Biehs introduced a VO2 based simple far-field radiative thermal diode, while Prod’homme et al.27, proposed a far-field thermal transistor that uses a VO2 base between a blackbody collector and a blackbody emitter. Zhu et al.28, showed that temperature dependent optical properties of SiC can be used to attain negative differential conductance. Van Zwol et al.22, proposed that one can take advantage of the phase transition from crystalline to amorphous state in AIST (an alloy of Ag, In, Sb, and Te) driven by a current pulse to obtain a large contrast in heat flux. In far-field limit, rectification is due to the change in emissive properties of a phase change material. In near-field limit, the difference in the coupling strength of polaritons or tunneling of surface waves between structures leads to thermal rectification. In general, it is observed that a higher rectification can be achieved in the near-field regime than in the far-field. However, it is challenging to develop such devices operating on the principle of near-field radiative transfer.

Spectral control has been studied to affect radiative heat transfer in both the far-field as well as near-field. Customization of absorption/emission spectra is often achieved by the use of multilayer thin film structures29, nanoparticles30, 31, dielectric mixtures32, 33, photonic crystals34, 35, 1-D/2-D gratings36 and metamaterials37, 38. Absorbers that utilize Fabry-Perot cavities39, 40, Salibury screens41 and Jaumann absorbers42 and ultra-thin lossy thin films bounded by transparent substrate and superstate43,44,45 have been investigated for decades. Quite notably, Nefzaoui et al.46, proposed using multilayer structures consisting of thin films (e.g., Si, HDSi and gold) to obtain thermal rectification. Kats et al.47, have theoretically and experimentally demonstrated that a thin-film of VO2 on sapphire shows strong modulation of absorbance upon phase transition, particularly, at wavelength of 11.6 μm. Taylor et al.48, recently proposed an emitter consisting a dielectric spacer between VO2 film and a reflecting substrate to achieve dynamic radiative cooling upon phase transition of VO2. Fabry-Perot resonance was achieved at 10 μm wavelength. As discussed later, we show that, by tuning the resonance at right wavelength, maximum rectification can be achieved in the proposed design.

VO2 has often been used in thermal rectification devices, because its phase-change from an insulator to a metal can be switched reversibly within a short time (~100 fs)49. The common devices use either a bulk VO2 solid or its thin-film form. In this work, we present a VO2 based far-field thermal rectification device with a simple multilayer structure. We predict a record rectification factor of greater than 11 (η > 0.91).

A typical far-field thermal diode has two planar components separated by a distance much larger than thermal wavelength. The active component is made of a phase-change solid, whereas the passive component stays inert. Figure 1 illustrates the vertical structure of our proposed thermal diode. The active component contains a tri-layer structure consisting of VO2, potassium bromide (KBr) and gold thin films on a substrate. Thicknesses of VO2 and KBr layers can be tuned to maximize rectification. The thickness of gold layer is fixed at 1 μm to block radiation from the substrate. For a given temperature bias, maximum (far-field) radiative heat transfer would be possible when both sides are blackbodies, while minimum heat transfer would take place when at least one side is a highly reflective mirror. Ideally, the active component should exhibit a transition from blackbody to reflective surface upon the reversal of a temperature bias which induces the phase change. This is exactly our design attempts to achieve. Therefore, the passive component is chosen to be a blackbody. Any material other than a blackbody would not yield the maximum rectification. Structure 1 and 2 are at temperature T 1 = T C  + ΔT and T 2 = T C  − ΔT, respectively. The mean temperature is chosen to be the phase transition temperature of VO2 (T C  = 341 K). When T 1 > T 2 (referred to as forward bias), VO2 layer is in its metallic phase; and when T 1 < T 2 (reverse bias), VO2 layer becomes insulating with its optical axis aligned along the vertical direction, i.e., z-axis.

Phase transition of VO2 is not abrupt49, 50 and a complete insulator-metal transition does not occur until 350 K26. Rectification ratio depends on temperature bias as the temperature dependence of radiative heat transfer is essentially nonlinear. We calculate rectification values at a minimal temperature bias of 20 K i.e., ΔT = ±10 K. Although transition of VO2 exhibits a thermal hysteresis of about 8 K as presented in refs 49, 51, the phase transition is reversible. As we are concerned with heat flux values at 10 K above and below the critical temperature of VO2, hysteresis behavior is beyond the scope of this study.

## Results and Discussion

A multilayer structure can be designed to attain high absorbance or reflectance based on its dimensions and material properties. Multilayers with constituent thicknesses much smaller than the incident wavelength of light have been studied before52. We show that in a VO2 based multilayer structure, the dramatic change in the optical property of VO2 upon phase-change facilitates an extensive variation in the surface reflectivity.

Concept shown in Fig. 1 has variable dimensions of VO2 (L 1) and KBr (L 2) layer. These dimensions were optimized by running Genetic Algorithm to maximize rectification ratio. Matlab’s optimization toolbox was used to run Genetic Algorithm to perform optimization. Default values of population size (50), fitness scaling (rank), crossover fraction (0.8), stopping criteria (100 generations) were selected in the optimization toolbox. No tuning of optimization parameters was required as number of variables was only two. Lower and upper bounds on both L 1 and L 2 were kept at 25 nm and 2 μm, respectively. Optimal dimensions were found to be L 1 = 25 nm and L 2 = 880 nm, both are practical values. Further discussion will be focused on the design with these dimensions.

Figure 2 shows spectral heat flux (dq/) of the proposed thermal diode in forward and reverse direction with temperature bias 20 K (ΔT = 10 K). Forward heat flux is significantly higher than reverse flux as is clear from Fig. 2. A comparison is shown for heat flux across blackbodies at temperatures 331 K and 351 K, respectively. Inset in Fig. 2 displays angle-averaged emissivity of the active component in both scenarios. When VO2 is metallic, the structure on the active component has high emissivity near the thermal wavelength (λ th  = 1.27ħc/k B T = 8.5 μm for 341 K). As a significant portion of blackbody radiation falls within this range, this gives rise to a high heat flux in forward bias. However, when VO2 is insulating, the structure has very low emissivity in the broad spectrum. The tri-layer structure behaves like a highly reflecting mirror resulting in very low heat flux. Consequently, high contrast in heat flow is achieved leading to a high rectification ratio of 11.3 (η = 0.918). In order to highlight the diode-like characteristics, heat flux across the device has been plotted against themeprature difference in Fig. 3. For comparison, simple case of bulk VO2 is also shown, it has a rectification coeffcient of η = 0.49. Note that, effect of thermal hystersis is not considered here for simplicity. Angle dependent spectral reflectivity of the active component of the thermal diode is plotted in Fig. 4 for the forward and reverse bias cases. When VO2 is metallic, the tri-layer structure acts like a wide-angle antireflection coating for wavelengths between 4 μm to 10 μm. The dark spot in Fig. 4 corresponds to Fabry-Perot type of resonance that occurs around λ = 4n KBr (λ)L 2 = 5.3 μm47. High absorption/emission in this wavelength region favors radiative heat transfer as thermal wavelength falls within this range. In reverse bias, the structure is highly reflective in a broad range of wavelengths giving rise to a very low absorption. Note that for thermal wavelength of 8.5 μm, Fabry-Perot resonance occurs (for metallic VO2) when thickness of KBr layer is L 2 = λ th /4n KBr (λ th ) = 1.4 μm. This configuration however, would not necessarily achieve maximum rectification as the structure may not be purely reflecting when VO2 is its insulating phase.

Contrasting reflective properties of the structure are due to constructive and destructive interferences of electromagnetic waves generated by partial reflections at interfaces. As an electromagnetic wave travels through the media, it is partially reflected at each interface leading to multiple reflections from each layer. This causes interference of electromagnetic waves due to each partial reflection. Effective reflection coefficient of the structure is the phasor sum of these reflection coefficients due to (an infinite number of) individual reflections. When VO2 is metallic, phasor sum of partial reflections results in destructive interference in the wavelength range of 4 μm to 10 μm. As a result, the structure is highly absorptive in the range. When VO2 is insulating, individual reflections add up to a large value making the structure highly reflective for a broad range of the spectrum.

Figure 5 shows phasor diagram of partial reflections at air-VO2 interface and VO2-KBr interface for TE polarized incident ray of wavelength λ th  = 8.5 μm and angle of incidence 10°. $${\tilde{R}}_{\mathrm{1,2}}$$ is the effective reflection coefficient at air-VO2 interface and $${\tilde{R}}_{\mathrm{2,3}}$$ is the effective reflection coefficient at VO2-KBr interface due to multiple reflections within KBr layer. They can be expressed as geometric series whose terms are relative amplitudes of partial waves due to first, second and third reflection and so on. For both metallic as well as insulating VO2, the magnitude of $${\tilde{R}}_{\mathrm{2,3}}$$, $$|{\tilde{R}}_{\mathrm{2,3}}|$$, is large. However, when VO2 is in metallic phase, each partial reflection results in a phase-shift such that partial waves add up destructively leading to a small value of $$|{\tilde{R}}_{\mathrm{1,2}}|$$ and low reflectivity, especially in the wavelength range centered around thermal wavelength. On the other hand, in reverse bias (insulating VO2) phasors add constructively, giving rise to highly reflective surface properties for a broad range of wavelengths. A similar phenomenon can be observed for TM polarization as well. As KBr is transparent and has a negligible extinction coefficient for most of infrared region, much of the absorption takes place within the VO2 layer. Transparent layer of KBr mainly influences the reflective properties by altering the phase of the light propagating through the media. Potentially, any other material transparent to infrared light such as magnesium fluoride or intrinsic silicon can be used in this concept. However, optimal dimensions of such a device might be different.

In summary, we present a VO2 based far-field radiative thermal diode structure with a high rectification ratio of 11.3. The active component of the proposed device has a tri-layer structure consisting thin films of VO2, KBr and gold. As VO2 undergoes phase change around 341 K, reflecting properties of the surface are dramatically changed in the spectral region that contributes to significant amount of thermal radiation. Facilitated by Fabry-Perot type of resonance around 5.3 μm, metallic VO2 makes the structure behave like a wide-angle antireflection coating while insulating VO2 makes it highly reflecting. As a result, high degree of asymmetry in radiative heat transfer is predicted across the tri-layer structure and a blackbody. Contrasting reflecting properties of the structure can be explained using constructive and destructive interference of partial reflections across the interfaces. We optimized layer thicknesses to maximize rectification. Thermal rectification greater than 11 is predicted for temperature difference of 20 K and it is highest among far-field radiative diodes that have been studied. Possibility of attaining higher rectification could be investigated in future by using alternate transparent materials, thinner films of VO2 and/or using more number of alternating VO2/dielectric layers. Such devices can find numerous applications such as thermal logic devices and thermal management systems.

## Methods

To calculate heat flux in forward and reverse bias across our far-field thermal diode, we use the well known expression of radiative transfer obtained through dyadic Green’s function formalism53. Radiative transfer between two planar objects is given by

$${Q}_{1\to 2}({T}_{1},{T}_{2},L)={\int }_{0}^{\infty }\frac{d\omega }{2\pi }[{\rm{\Theta }}(\omega ,{T}_{1})-{\rm{\Theta }}(\omega ,{T}_{2})]{T}_{1\to 2}(\omega ,L)$$
(1)

where Θ(ω, T) = (ħω/2)coth(ħω/2k B T) is the energy of a harmonic oscillator at frequency ω and temperature T, ħ is the reduced Planck constant, and k B is the Boltzmann constant. The function T 1→2(ω, L) corresponds to the spectral transmissivity in radiative transfer between media 1 and 2 with a separation of L and is expressed as53

$${T}_{1\to 2}(\omega ,L)={\int }_{0}^{\omega /c}\frac{{k}_{\rho }d{k}_{\rho }}{2\pi }\sum _{\begin{array}{c}\mu =TE,\\ TM\end{array}}\frac{(1-{|{\tilde{R}}_{h1}^{(\mu )}|}^{2})(1-{|{\tilde{R}}_{h2}^{(\mu )}|}^{2})}{{|1-{\tilde{R}}_{h1}^{(\mu )}{\tilde{R}}_{h2}^{(\mu )}{e}^{2j{k}_{hz}L}|}^{2}}$$
(2)

where $${\tilde{R}}_{h1}^{(\mu )}$$ and $${\tilde{R}}_{h2}^{(\mu )}$$ are polarized effective reflection coefficients of the two half spaces (calculated in the absence of other half space), μ = TE (or TM) refers to transverse electric (or magnetic) polarization and k hz is the z-component of wavevector in vacuum. Here, j is the imaginary unit. For a structure having N-layer media having (N − 1) interfaces, by solving the boundary conditions at the interfaces, one can obtain the expression for the generalized reflection coefficient at the interface between regions i and i + 154,

$${\tilde{R}}_{i,i+1}^{(\mu )}=\frac{{R}_{i,i+1}^{(\mu )}+{\tilde{R}}_{i+\mathrm{1,}i+2}^{(\mu )}{e}^{2j{k}_{i+\mathrm{1,}z}({d}_{i+1}-{d}_{i})}}{1+{R}_{i,i+1}^{(\mu )}{\tilde{R}}_{i+\mathrm{1,}i+2}^{(\mu )}{e}^{2j{k}_{i+\mathrm{1,}z}({d}_{i+1}-{d}_{i})}}$$
(3)

where $${R}_{i,i+1}^{(\mu )}$$ is the Fresnel reflection coefficient at the interface between the layers i and i + 1, and $${\tilde{R}}_{i+\mathrm{1,}i+2}^{(\mu )}$$ is the generalized reflection coefficient at the interface between the layers i + 1 and i + 2, z = −d i is the location of the ith interface. $${k}_{i,z}=\sqrt{{\varepsilon }_{i}(\omega ){\omega }^{2}/{c}^{2}-{k}_{\rho }^{2}}$$ is the normal z-component of the wave vector in medium i, wherein ε i (ω) is the relative permittivity of the medium i as a function of angular frequency ω, c is the speed of light in vacuum and k ρ is the magnitude of the in-plane wave vector. With $${\tilde{R}}_{N,N+1}^{(\mu )}=0$$, the above equation provides a recursive relation to calculate the reflection coefficients $${\tilde{R}}_{i,i+1}^{(\mu )}$$ in all regions. Note that Eq. 2 has only one integral corresponding to propagating waves. The terms due to evanescent waves are ignored as separation between the two half spaces is much larger than the thermal wavelength ($$L\gg {\lambda }_{th}$$). The hemispherical emissivity of the active component can be expressed as32

$$e(\omega )=\frac{{c}^{2}}{{\omega }^{2}}{\int }_{0}^{\omega /c}d{k}_{\rho }{k}_{\rho }\sum _{\mu =s,p}(1-{|{\tilde{R}}_{h}^{(\mu )}|}^{2})$$
(4)

Note that the term for tranmissivity has been omitted as a layer of gold makes the structure opaque.

Insulating VO 2 (below 341 K) is anisotropic. In a plane (x − y plane in Fig. 1) perpendicular to optical axis known as the ordinary mode, its dielectric function is ε O and it is ε E along the optical axis (extraordinary mode). Both ε O and ε E can be calculated using the classical oscillator formula $$\varepsilon (\omega )={\varepsilon }_{\infty }+{\sum }_{i=1}^{N}\frac{{S}_{i}{\omega }_{i}^{2}}{{\omega }_{i}^{2}-j{\gamma }_{i}\omega -{\omega }^{2}}$$. Values of high-frequency constant ε , phonon frequency ω i , scattering rate γ i and oscillator strength S i are taken from ref. 55. There are eight phonon modes for ordinary and nine phonon modes for extraordinary dielectric function. In the metallic state, VO2 is isotropic and Drude model55 is used to describe the dielectric function i.e., $$\varepsilon (\omega )=\frac{-{\omega }_{p}^{2}{\varepsilon }_{\infty }}{{\omega }^{2}-j\omega {\rm{\Gamma }}}$$. Refractive indices of KBr are taken from ref. 56, while dielectric properties of gold can be found in ref. 57. Blackbody is assumed to have a constant dielectric function ε = 1 + 0.001j.

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## Acknowledgements

This project was supported in part by an Institutional Development Award (IDeA) Network for Biomedical Research Excellence from the National Institute of General Medical Sciences of the National Institutes of Health under grant number P20GM103430, the National Center for Research Resources/Center of Biological Research Excellence of the National Institutes of Health under grant number 5P30GM110759, Rhode Island STAC Research Grant number AWD05085, and Rhode Island Fundation Research Grant number 20164342. Work at Brown University was supported by National Science Foundation through Grant number DMR-1307056.

## Author information

Authors

### Contributions

A.G. did the calculations for far-field thermal diode. G.X. provided technical insights of physical phenomena. Y.Z. supervised the project. All authors discussed the results and commented on the manuscript.

### Corresponding author

Correspondence to Yi Zheng.

## Ethics declarations

### Competing Interests

The authors declare that they have no competing interests.

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Ghanekar, A., Xiao, G. & Zheng, Y. High Contrast Far-Field Radiative Thermal Diode. Sci Rep 7, 6339 (2017). https://doi.org/10.1038/s41598-017-06804-w

• Accepted:

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You’ll be installing programs to use with Photoshop and manipulating your images in other applications. Photoshop is an essential tool, but you can never rely on it to do everything for you. You will need to learn other programs and to be able to work with the different features and capabilities of each.

Although you are learning a powerful application, you are always learning and will have to keep up with new tutorials and techniques. At the end of the book, you will learn how to share and publish your finished images online.

Once you have started working with Photoshop, it can be a bit intimidating, but by the end of this book, you’ll be ready to edit your images in Photoshop and create your own version of the cover of this book.

This book is intended to be a guided introduction to using Photoshop for professional-level work. It’s meant to be a continuing reference that you can turn to throughout your time with Photoshop.

This book is for the beginner and advanced user who has had a little experience with Photoshop. It assumes that you are familiar with the features of Photoshop and that you are ready to begin learning how to edit your own photographs.

This book is not intended to train you in how to use Photoshop. Instead, it’s intended to teach you how to do the things you want to do in Photoshop and more.

While you will encounter many concepts and techniques that you’ve learned about in other books or online courses, the main focus of this book is

In this Photoshop download tutorial, we’ll show you how to use this powerful image editing software to edit any image that you want. We’ll also show you how to add text to your images.

The following tutorial is different from the other eHow tutorials in that you can go through the tutorial step by step without reading them. This tutorial covers Photoshop version 13.1 and Elements version 12.

You can also see a list of 15 Photoshop tips and tricks

STEP 1: Open the Original Photo In Photoshop

Open the image you want to edit. Click on Image > Open or press Ctrl + O or CMD + O.

If the image is in one of the.jpeg,.jpg,.tif, or.tiff file formats, just double-click on the file.

The picture should open in Photoshop.

If it opens in Photoshop, you can move and resize the image if you want. For the rest of this tutorial, we’re assuming that you want to be able to see all of your edits at once in Photoshop.

STEP 2: Go to the Appearance tab

Go to the Image menu and click the Appearance tab.

The Image menu is usually in the top or bottom of the screen, depending on where you have your images.

You’ll see that there are many options in this tab. By default, most of these options are turned on. To open any of these options, just click on that option and it will turn on.

The Background Color, Anti-aliasing, Sharpen, Soften, Image Size, Lighting Effects, and Spot Healing Brush options are all on by default.

All of the rest of these options are turned off by default. Clicking on them will turn them on.

STEP 3: Change the Background Color

Click on the Background Color option and change it to black.

Click on the button that says Color Fill.

Then click on the Color box in the color picker.

Choose black, navy blue or any other color that you want for your background.

If you want to see a different shade of the background color, click on the color box in the color picker.

Then click on the
05a79cecff

epsilon} \le 2}} \| \alpha \|_{H^k_{\epsilon}(\Omega)} \| \alpha \|_{H^{k}_{\epsilon}(\Omega)}
\\
& \le c_{\epsilon,k,\Omega} \| \alpha \|_{H^k_{\epsilon}(\Omega)}^2
\le c_{\epsilon,k,\Omega} c_{\epsilon} \| \alpha \|_{H^k_{\epsilon}(\Omega)}^2.\end{aligned}$$This concludes the proof. $Rem-2-1$ For simplicity, for the above result, we have not considered the case where the boundary is also rough. Rough boundary means \partial \Omega can be divided into many smooth boundary strips (see the figure below). $Hmap$ [(Hmap)]{} (0,0) rectangle (6,5); (2.5,3) – (6.5,3); (6.5,0.5) – (2.5,0.5); (3.5,0.5) node$above$[\partial\Omega]{}; (4,0) – (4,5); (4.5,3) – (4.5,5); (4.5,0.5) node$above$[\partial\Omega]{}; (1,0) – (1,5); (0.5,3) – (0.5,5); (0.5,3.1) node$right$[\partial\Omega]{}; (2,1) node$right$[\Omega]{}; There exist functions \Gamma_j such that \Gamma_j(x) \in T_x(\partial \Omega), such that$$\partial \Omega = \bigcup_{j=1}^{\infty} \{ x \in \Omega : x_n \le \Gamma_j(x) \}.

The function $\Gamma_j$ is called a $j$-th layer.

Q:

Changing original caption of axis in d3

I have a plunker:

I need to add a real caption on my x-axis. I am using a custom label above the axis, but it does not change caption of axis…
Is there any options for that?
EDIT:
I’ve created another plunker and it seems that in version v3.12.0 of d3 scales have an option for including a custom tick text. Is it possible to add a custom label to the ticks?
EDIT2:
I’ve just found another post from 3 years ago that sounds like it can help. But there is no “correct” answer for it.

A:

For the chart “Running”
So i dont know the reason why d3axis font-size on window resize has different size. But i have solved the issue by adding this CSS style
.axis path,.axis line {
fill: #99b5cd;
}
.axis.domain {
stroke: #ccc;
font-size: 9px;
}
.axis.axis line {
stroke-width: 0;
}

then adding a few lines inside chart method
var xAxisScale = d3.time.scale();
var myScale = d3.scaleTime()
.domain([new Date(0), new Date(d3.time.hour(d3.time.minutes()) + d3.time.day())]).range([0, 720]);
xAxisScale.domain(myScale.domain());
xAxisScale.tickFormat(function (d) {
return ’19’+ d3.time.format(‘%Y-%m-%d %H:%M:%S’)(new Date(d)) ;
});

and it will work fine for me.

Re: [UK] [NHS] GPs’ top concerns on vaccine failure

## System Requirements:

Windows 7 and above
Mac OS X 10.6 and above
New version of NVidia 3D Vision family of software is required (see below)
Linux
Minimum 1280×1024 display resolution
Minimum 300 MHz CPU with 64 MB RAM.
Minimum 5 GB of free space
About the new NVidia 3D Vision family of software (Windows only):
(NVidia 3D Vision Surround SDK
NVidia 3D Vision Surround)
This version provides the following new features:
(New


text:
# Silver is the best conductor of heat and electricity.(a) True(b) False

Verified
202.2k+ views
Hint: The specific resistance of Silver at 293 K is $1.59 × 10^{−8}$ Ωm at $20^oC$ which is the lowest of all metals. Think of what this would imply in terms of the conductivity of heat and electricity.

Complete step-by-Step Solution:
Let us first understand what the conductivity of an element is before we look at the specific case of Silver.
Conductivity is the measure of the ease at which an electric charge or heat can pass through a material. A conductor is a material which gives very little resistance to the flow of an electric current or thermal energy.
In other words, conductivity refers to the ability of a material to transmit energy. There are different types of conductivity, including electrical, thermal, and acoustical conductivity. The most electrically conductive element is silver, followed by copper and gold. Silver also has the highest thermal conductivity of any element and the highest light reflectance.
Silver is the best conductor because its electrons are freer to move than those of the other elements, thereby making it more suitable for the conduction of electricity and heat than any other element.
Therefore, the correct answer to this question is “Silver is the best conductor of heat and electricity” is a true statement.

Note: Although it is the best conductor, copper and gold are used more often in electrical applications because copper is less expensive and gold has a much higher corrosion resistance. Because silver tarnishes, it is less desirable for high frequencies because the exterior surface becomes less conductive.


text:
# Connect Frontend to Kernel Started by JVM via JLink

I have a MathKernel started and controlled via JLink from a JVM. The $CommandLine for this kernel is:$CommandLine

I can open a Frontend from this kernel by sending it the following string for evaluation:

Needs["JLink"];
FrontEndLaunchCommand = mmaFrontEndPath;
ConnectToFrontEnd[]

and this string to actually open a window with a notebook

UseFrontEnd[
nbObj = CreateWindow[
DocumentNotebook[
{TextCell["Launched by JVM Kernel", "Title"]}],
Visible -> True ]
]

I'd like to be able to set this notebook to use the JVM's kernel for evaluation (rather than its own) so I can use the notebook for easier debugging of the JVM launched kernel.

I've tried creating a link on the JVM's kernel using

and then attempting to connect to this in the Notebook using

I've also tried just setting the Notebook's evaluation kernel to "feMathLink" using

but this also just hangs.

Apologies in advance if this really is in the manual but it is not obvious.

This all comes from a small test program here that seemed too large to post.

Update - Clarification

As suggested by halirutan, I've simplified the question by taking Java/Groovy out of the question and focusing just on the kernel to frontend connection issue.

If you run the following code from a kernel (call it kernel A) in "terminal mode" then it will launch a frontend which is connected to this kernel but has its own kernel (call it kernel B) for evaluation. That is, kernel A can send commands to the frontend via UseFrontEnd[] but this frontend doesn't use kernel A for evaluation.

(* this is the program the JLink will use to launch a FrontEnd *)
$FrontEndLaunchCommand = FileNameJoin[{$InstallationDirectory, "Mathematica.exe"}]
(* this connects the kernel to a FrontEnd launched via JLink *)
ConnectToFrontEnd[]
(* at this point, FrontEnd is not visible, it is available only for processing some commands via UseFrontEnd[] *)
(* this uses UseFrontEnd[] to open a new Notebook in a Window making the FrontEnd visible *)
UseFrontEnd[
nbObj = CreateWindow[
DocumentNotebook[{TextCell["Launched by JVM Kernel", "Title"]}],
Visible -> True ]
]
(* you should now see an unnamed notebook with first cell as a Title "Launched by JVM Kernel" *)

I'd like to set the evaluation kernel (currently Kernel B) to be Kernel A, the initializing kernel. The objective is to use the frontend as a debugging tool for a kernel launch via JVM (or terminal in this case).

As noted above, I've tried creating a math link in Kernel A using:

and setting the frontend's evaluation kernel to this link using:

I've also tried reading and writing from this link but it always hangs on me.

I've put a windows batch file and a simple .m file with all of this here. This should enable you to replicate the issue on any standard windows setup without much effort, none if you have version 10 installed in the standard place - just run the runIt.bat in a cmd or Powershell terminal.

Many thanks again to halirutan for suggestions to clarify the question. It really isn't a JVM question at all, although UseFrontEnd[] is a JLink function.

• As I understood it until now, UseFrontEnd in the JLink package was not meant to create a user interface, but for certain things (like image rasterization) that usually needs a front end. I tried it from the command-line and I wasn't even able to create a notebook windows. With your CreateWindow command, I get an icon in the task-bar without an actual window. I cannot raise this window. It's like having a symbol for something that is not there. That being said, would it be possible for your to edit your question and first try to do this from command line? I guess this will attract.. Jul 25, 2014 at 4:26
• ..more people, because they can easily try the code on their own without having knowledge of Groovy. Jul 25, 2014 at 4:27
• @halirutan Good point, thanks. The whole JVM thing I think is irrelevant to the issue I am actually having. I'll work on rephrasing the question using a kernel started from the cmd line as you suggest. Jul 25, 2014 at 18:59

I was able to get a satisfactory answer to my question by using a very good article by David Wagner, "MathLink Mode" available here.

I'll leave all the JVM stuff out of the answer but the approach does work just as well for a kernel launched by some external program as it does for the direct launch explained here.

I'll explain it for Windows but there isn't much that is platform specific; it is mostly Wolfram code.

Step 1: Launch a kernel direct from the command line:

%MathematicaInstallationDirectory%\MathKernel.exe

where %MathematicaInstallationDirectory%\ is the $InstallationDirectory. This will launch a standalone kernel with a terminal interface. This emulates the kernel we want to be able to inspect and work with during debugging. (In my case this emulates the kernel I launch and use from the JVM.) We'll refer to this kernel as the remote kernel. As a simple test, set symbol a to be something like this. We will later read this symbol from a Mathematica Frontend. a = "This was set in the remote kernel" Step 3: Create a Mathlink in this kernel and set it ready to be connected to by putting it in Listen mode: (* this is all in the remote kernel terminal interface 8) linkName = "5000" remoteLinkObj = LinkOpen[linkName, LinkMode -> Listen] LinkWrite[remoteLinkObj, "Hello from remote"] linkName can be any string on Windows but needs to be a port number on Linux or OSX. This will block the remote kernel (at line 2) until we connect to the mathlink named "5000" from the frontend. It will then immediately write back on the link the string "Hello from remote" and block again until the frontend reads this string. Step 4: Launch Mathematica and open a new notebook and a fresh kernel. Step 5: Create the following functions to make it easier to work with remote kernel and its link. (* this is in the frontend notebook (and thus evaluated in the frontend's kernel) *) drainLink[link_LinkObject] := Reap[While[LinkReadyQ[link], Sow[LinkRead[link]]]] remoteEval[link_LinkObject, expr_] := ( LinkWrite[link, Unevaluated[expr]]; LinkRead[link] ) SetAttributes[remoteEval, HoldRest] drainLink[] is a useful function to use if the link appears frozen. The remote kernel will block until everything it wrote to the link is read off the link by the frontend. drainLink does that for us. remoteEval[] sends unevaluated expressions to the remote kernel for evaluation and reads the results of the remote evaluation off the link. Step 6: Connect the frontend to remote kernel via the mathlink named "5000" and read whatever is on the link (which should be the string "Hello from remote". Enter the following into the frontend's notebook. (* frontend notebook *) linkName = "5000" (* this should match the linkName used in remote kernel *) (* this connects to linkName *) feLinkObject = LinkOpen[linkName, LinkMode -> Connect] (* this will read everything off the link, if anything is there *) drainLink[feLinkObject] (* this should return the string "Hello from remote" *) Step 7: return to the remote kernels terminal interface and set it into a read, evaluation and write loop so it will act as an evaluation server for the frontend. Define the following function on the remote kernel: (* this is entered into the remote kernel's terminal *) evalLoop[link_LinkObject] := Module[ {resultOfEval, exprIn, exprOut, evalMessages}, (* this collects any messages *) evalMessages = {}; collectMessages[m_] := AppendTo[evalMessages, m]; InternalAddHandler["Message", collectMessages]; (* this is the actual loop until Break[] *) While[True, (* reset messages *) evalMessages = {}; (* read incoming expr off the link and wrap in Hold[] *) exprIn = LinkRead[link, Hold]; (* release Hold and evaluate expr checking for messages *) resultOfEval = Check[exprOut = ReleaseHold[exprIn],$Failed ];
Which[
(* messages generated by evaluation so return everything *)
resultOfEval === $Failed, LinkWrite[link, EvalError["In" -> exprIn, "Out" -> exprOut, "Messages" -> evalMessages]], (* no messages, assume OK and just return result of evaluation *) True, LinkWrite[link, exprOut] ] ]; (* loop ended by sending Break[] so clean up *) (* turn off message handler *) InternalRemoveHandler["Message", collectMessages]; (* write back message that evaluation loop is off *) LinkWrite[link, "Evaluation loop is off"] ] and run it with evalLoop[remoteLinkObj] this blocks the remote kernel in the While loop above until it gets a Break[] from the frontend. It will read, eval and write until stopped by Break[]. step 8: Switch back to frontend notebook and test remote kernel evaluation. remoteEval[feLinkObject, a] (* should return the string "This was set in the remote kernel" *) This sends the symbol a unevaluated back to the remote kernal where the evalLoop[] reads it, evaluates a (to the string "This was set in the remote kernel") and returns this result on the link where it is read off by the frontend in remoteEval. In this way remoteEval and evalLoop can be used to inspect and change the remote kernel's state in an interactive environment to debug code and data sent to a kernel by some other program (in my case a JVM app). This approach is a direct lift from the Wagner article referenced above. There is probably a better way to connect the frontend to the remote kernel using the$ParentLink of the remote kernel and creating a new kernel connection under the Evaluation menu of the frontend (see page 55 of Wagner) but I couldn't get it to work and as I had all I needed for now I let it go.

I wrapped this into a small package that I can load and use as required without too much work on the keyboard to manually connect and disconnect.

You can debug JLink apps by adding link listeners and the like but the frontend is such a powerful interactive tool I wanted to figure out a way to use it instead.

This question and answer from pjc42 promises to be helpful for my own question re .NET.

Going through the question it was surprisingly difficult to replicate the OP's code:

UseFrontEnd[
nbObj = CreateWindow[
DocumentNotebook[{TextCell["Launched by JVM Kernel", "Title"]}],
Visible -> True
]

(halirutan has also commented that he couldn't get it to work.)

In .NET the notebook would not appear until a SelectionEvaluate was performed.

MathKernel kernel = new MathKernel();
kernel.Compute("$FrontEndLaunchCommand = FileNameJoin[{$InstallationDirectory, \"Mathematica.exe\"}]");


text:
# Standard for typesetting mathematical objects other than variables

Is there a standard in mathematics for typesetting the textual (not symbolic) identifiers of mathematical objects other than variables?

Textual identifiers of mathematical objects other than variables are typically

• function names (\sin, \log);
• constant names (\textnormal{e}, \textnormal{i});
• variable specifiers (n_\textnormal{water}, \rho_\textnormal{air}).

For constant names and variable specifiers, I use \textnormal, according to egreg's great post which seems to me the most logical choice.

However function names are already defined by the American Mathematical Society in their amsopn package and they use \mathrm instead of \textnormal (in \operatorname and \DeclareMathOperator). Because my question is not about the font style, let us assume that we are comparing \mathrm and \textrm (rather than \textnormal).

Why does the American Mathematical Society use \mathrm instead of \textrm for function names?

Because that […] wouldn't obey to \boldmath, for one thing

In classic LaTeX (not Unicode LaTeX) both use the same text font (so kerning and ligatures are activated), and indeed, the only difference is that

• \mathrm stays in math mode, so is affected by \boldmath;
• \textrm switches to text mode, so is not affected by \boldmath.

But is there other reasons not to use \textrm in function names? Because \textrm has some serious advantages over \mathrm:

• it doesn't need the mathcode modifications of \operatorname and \DeclareMathOperator to prevent hyphens and stars from being converted to binary operators, and apostrophes from being converted to primes;
• spaces are not gobbled.
• I think the problem here is the fact that euler is not a typical font, it has its singularities (so the choice for text font in \log would be just because of euler font). In a more general sense: \sin is maths, e is maths, air is not maths. So, it's okey to have \log with \mathrm, it's acceptable (depending on the choice if you prefer upright math constants) to have \mathrm{e}, but air is not maths (altough I write it usually with \mathrm{air} may be \textnormal is the most correct way). – Manuel May 23 '15 at 12:54
• Besides the purely logical reasons, there is also a reason of efficiency: \textnormal makes use of \mathchoice and therefore typesets its argument four times (one for each of the four math styles), whereas \mathrm simply stores the characters that appear inside its argument directly in the math list, as characters of the appropriate family (whose size will be decided only when the math list is dismantled and converted to an horizontal list). – GuM May 23 '15 at 15:24

There are in fact very few standards for such things. There is ISO 80000-2 which is an ISO standard "Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural sciences and technology" this is the standard referenced by the rather unfortunately named isomath package and mathstyle=iso option to unicode-math. (I say unfortunate as there is no generic ISO view on math styling, just that one particular style guide has been promoted through the ISO process does not imply other styles are wrong, or should not also go through ISO, just as ODF being standardised as an Office format as ISO/IEC 26300:2006 did not prevent a separate standard being defined for Open (Micorosoft) Office formats ISO/IEC 29500:2008 (although it does complicate the process slightly). The ISO 80000-2 style guides are fairly universally not followed by journals of mathematics.

The choice of using Roman or italic or bold letters for such things as the differential d or vectors etc, is not something set by global standards but just part of the style choice set by a particular publication.

However mostly your question seems not to be asking about the output (which is what is addressed by ISO 8000-2 and publishing style guides, but by the technical details of the TeX construct used to obtain that style, and there are no standards for that at all, other than the general LaTeX2e documentation on the font mechanism.

The question that you reference in your question, and egreg's answer, are not (mostly) comparing \textrm and \mathrm but comparing using a text font designed for multi-letter identifiers with using the math italic font designed with large sidebearings separating individual letters used as the default math font.

It is clear that multi-letter identifiers should always be set in a "font" that does not have the wide side-bearings and lack of ligatures that is typically used for single letter variables in traditional math settings. I say "font" as traditional TeX necessarily needs different fonts for these different uses, but with large opentype fonts, the different usage may be accommodated by different ranges within the same physical font.

So it is perfectly natural (and consistent with the quoted text) to use \mathrm for \log and friends. Generally I would use \mathxx settings for any identifier that is naming a mathematical object (in its widest sense, such as computer language identifiers if using math setting for pseudocode) and would use \textxx settings for fragments of natural language that for reasons related to technicalities of the markup end up inside a math region. Examples include if and otherwise clauses inside multi-line displays.

Unicode 3.1 introduced the mathematical alphabets in the range starting from U+1D400, but the use of these is still evolving, and especially their mapping to typesetting requirements. Unicode does not distinguish a text italic style (using ligatures) from a math italic style, but just provides a range that distinguishes italic text in mathematics, exactly how that is typeset is out of scope for Unicode and left up to the designers of the font and typesetting systems. Currently with unicode-math the \mathxx commands do not change fonts but just translate the characters into the 1d400 range, however currently OpenType math fonts do not style the characters in those ranges in a way suitable for multi-letter identifiers so it doesn't really work.

In classic TeX where you are restricted to 16 families in a single math expression the choice between using the \mathrm or \textrm mechanism is complicated by the extra consideration that using \text... (ie, a hidden \mathchoice construct around a text font \hbox setting) allows you to add additional fonts without eating into the 16 math font limit, thus often it makes sense to use that mechanism for additional, rarely used fonts even if a \mathxx mechanism would be logically more natural. This is less of an issue in Unicode TeX extensions where there are more families available and vastly more characters in each family.

With a Unicode TeX there are three mechanisms for getting a different visual style for letters in math mode,

• Translating the character to the math alphabet range, eg replace A by U+1D400 to get a bold A

• allocating a roman font to a new math family and selecting a in that family (the traditional definition of \mathrm not so easily available in unicode-math currently, although indirectly available by specifying a different font for the \mathup range with \setmathfont)

• using \hbox{...}and selecting a font using the text font mechanisms, \textbf{A} to get a bold A.

All of these mechanisms have a place, although it isn't clear yet how best to map them to TeX markup, and default styling behaviour.

• Thank you for this great answer! I think my question was too vague so I improved it. – Maggyero May 24 '15 at 18:11


text:
# Nitric oxide (Zero) maintains cardiovascular health by activating soluble guanylate cyclase

Nitric oxide (Zero) maintains cardiovascular health by activating soluble guanylate cyclase (sGC) to improve mobile cGMP levels. that homo- and heterodimerization may control activity which inactive homodimer private pools may regulate the forming of energetic and activatable heterodimers inside the cell (Zabel et al., 1999; Zhou et al., 2008). Mammals possess two different isoforms of every sGC subunit. The 11 sGC heterodimer may be the greatest characterized and may be the predominant form in the heart (Gupta et al., 1997; Mergia et al., 2003). The regulatory N-terminal site from the subunit harbors a heme prosthetic group this is the principal NO binding site from the enzyme (Gerzer et al., 1981). The high-resolution 3d framework of sGC is certainly unidentified but crystal buildings of specific domains or area homologs have already been motivated for the HNOX area (Nioche et al., 2004; Pellicena et al., 2004; Ma et al., 2007; Olea et al., 2008; Erbil et al., 2009; Martin et al., 2010; Olea et al., 2010; Weinert et al., 2010, 2011; Wintertime et al., 2011), the HNOXA area (Ma et al., 2008; Purohit et al., 2013), the CC area (Ma et al., 2010), as well as the GC area (Rauch et al., 2008; Winger et al., 2008; Allerston et al., 2013; Seeger Rabbit Polyclonal to SEC22B et al., Cediranib 2014). Latest studies recommend how these domains put together in space to create the full-length enzyme. Winger et al., initial recommended that HNOX straight binds to and inhibits the cyclase domains (Winger and Marletta, 2005). Afterwards studies backed this hypothesis, and additional showed close closeness from the HNOX and cyclase domains (Haase et al., 2010; Underbakke et al., 2013; Busker et al., 2014). Latest studies also confirmed that HNOX and HNOXA keep up with the HNOX within an inhibited declare that is certainly released upon NO/activator binding hence resulting in cyclase activation (Fritz et al., 2013; Purohit et al., 2014). Complementing this style of auto-inhibition, a thorough regulation system was recently suggested whereby the experience of sGC is certainly fine-tuned by distinctive area connections that either inhibit or promote an optimum conformation from the energetic middle (Seeger et al., 2014). Low-resolution electron microscopy (EM) data on rat sGC confirm most prior observations about the area agreement of sGC (Campbell et al., 2014). The EM envelope displays two distinctive lobes composed of the HNOX and HNOXA domains on the N-terminus Cediranib as well as the GC domains on the C-terminus. Both of these lobes are linked with a parallel CC area linker. The reconstruction shows that the full-length enzyme is certainly highly flexible throughout the HNOXA-CC and CC-GC area edges and explore an array of conformational space. Substrate and/or NO binding towards the enzyme usually do not appear to stabilize particular conformations or restrict the motion seen in the apo enzyme. Having less observation of unique conformations that may match the basal and triggered state from the enzyme prospects to the final outcome that domain-domain relationships aswell as little intra-molecular changes take into account the transition between your two activity says of sGC (Campbell et al., 2014; Seeger et al., 2014). Despite these significant improvements, the exact system where sGC propagates the NO activation transmission from your regulatory N-terminus towards the catalytic C-terminus from the proteins continues to be elusive (examined in Derbyshire and Marletta, 2012; Fritz et Cediranib al., 2013; Underbakke et al., 2013). sGC activation by NO When NO binds towards the subunit heme of sGC, a complicated is usually formed where both NO and -His105 axially ligate the Fe2+ atom (Rock et al., 1995; Rock and Marletta, 1996; Zhao et al., 1999; Goodrich et al., 2010). This NO binding event prospects to elongation and perhaps breakage from the Fe-His105 relationship and formation from the NO-bound sGC varieties (Dierks et al., 1997). Following structural rearrangements in the enzyme result in a 100C200 fold upsurge in enzyme activity (Wedel et al., 1994; Russwurm and Koesling, 2004; Cary et al., 2005; Pal and Kitagawa, 2010). The 1st NO binding event is usually instantaneous (Rock and Marletta, 1996). Following decay from the NO-sGC-His105 complicated can develop two catalytically unique varieties: a high- and a low-activity Cediranib NO-sGC (Russwurm and Koesling, 2004; Cary et al., 2005; Derbyshire et al., 2008). In circumstances of extra NO or stoichiometric NO in the current presence of substrate or item, the fully energetic NO-sGC varieties is usually created (Russwurm and Koesling, 2004; Cary et al., 2005; Tsai et al.,.