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The albedo of an object is the extent to which it reflects light, defined as the ratio of reflected to incident electromagnetic radiation. It is a unitless measure indicative of a surface's or body's diffuse reflectivity. The word is derived from albus, a Latin word for "white". The albedo of an object is its optical reflectivity, i. ... The reflection of sunlight on water Reflection is the abrupt change in direction of a wave front at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ... In optics, reflectivity is the reflectance (the ratio of reflected power to incident power, generally expressed in decibels or percentage) at the surface of a material so thick that the reflectance does not change with increasing thickness; , the intrinsic reflectance of the surface, irrespective of other parameters such as the... For other uses, see Latin (disambiguation). ...

Percentage of reflected sun light in relation to various surface conditions of the earth

The albedo is an important concept in climatology and astronomy. In climatology it is sometimes expressed as a percentage. Its value depends on the frequency of radiation considered: unqualified, it usually refers to some appropriate average across the spectrum of visible light. In general, the albedo depends on the direction and directional distribution of incoming radiation. Exceptions are Lambertian surfaces, which scatter radiation equally in all directions, so their albedo does not depend on the incoming distribution. In realistic cases, a bidirectional reflectance distribution function (BRDF) is required to characterise the scattering properties of a surface accurately, although albedos are a very useful first approximation. Image File history File links Albedo-e_hg. ... Image File history File links Albedo-e_hg. ... Climatology is the study of climate, scientifically defined as weather conditions averaged over a period of time,[1] and is a branch of the atmospheric sciences. ... For other uses, see Astronomy (disambiguation). ... For other uses, see Frequency (disambiguation). ... The optical spectrum (light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. ... If a surface exhibits Lambertian reflectance, light falling on it is scattered such that the amount of light an observer sees, the surface luminance, is the same regardless of their angle of view. ... A materials bidirectional reflectance distribution function (BRDF) defines the ratio of light reflected from a surface to the incident luminosity. ...

## Terrestrial albedo GA_googleFillSlot("encyclopedia_square");

Sample albedos
Surface Typical
Albedo
Fresh asphalt 0.04[1]
Conifer forest
(Summer)
0.08[2]
Worn asphalt 0.12[1]
Bare soil 0.17[3]
Green grass 0.25[3]
Desert sand 0.40[4]
New concrete 0.55[3]
Fresh snow 0.80–0.90[3]

Albedos of typical materials in visible light range from up to 90% for fresh snow, to about 4% for charcoal, one of the darkest substances. Deeply shadowed cavities can achieve an effective albedo approaching the zero of a blackbody. When seen from a distance, the ocean surface has a low albedo, as do most forests, while desert areas have some of the highest albedos among landforms. Most land areas are in an albedo range of .1 to .4. [5]The average albedo of the Earth is about 30%.[6][7] This is far higher than for the ocean primarily because of the contribution of clouds. As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... This article is about Earth as a planet. ...

Human activities have changed the albedo (via forest clearance and farming, for example) of various areas around the globe. However, quantification of this effect is difficult on the global scale.

The classic example of albedo effect is the snow-temperature feedback. If a snow covered area warms and the snow melts, the albedo decreases, more sunlight is absorbed, and the temperature tends to increase. The converse is true: if snow forms, a cooling cycle happens. The intensity of the albedo effect depends on the size of the change in albedo and the amount of insolation; for this reason it can be potentially very large in the tropics. Not to be confused with insulation. ...

The Earth's surface albedo is regularly estimated via Earth observation satellite sensors such as NASA's MODIS instruments onboard the Terra and Aqua satellites. As the total amount of reflected radiation cannot be directly measured by satellite, a mathematical model of the BRDF is used to translate a sample set of satellite reflectance measurements into estimates of directional-hemispherical reflectance and bi-hemispherical reflectance. Earth Observation refers to the use of sensors onboard artificial satellites to measure properties of the Earth. ... This article is about the American space agency. ... Ash plumes on Kamchatka Peninsula, eastern Russia MODIS (Moderate-resolution Imaging Spectroradiometer) is a payload scientific instrument launched into Earth orbit by NASA in 1999 on board the Terra (EOS AM) Satellite, and in 2002 on board the Aqua (EOS PM) satellite. ... Terra (EOS AM-1) is a multi-national NASA scientific research satellite in orbit around the Earth. ... Aqua (EOS PM-1) is a multi-national NASA scientific research satellite in orbit around the Earth, studying the precipitation, evaporation, and cycling of water. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... Directional-hemispherical reflectance is the reflectance of a surface under direct illumination (with no diffuse component). ...

### White-sky and black-sky albedo

It has been shown that for many applications involving terrestrial albedo, the albedo at a particular solar zenith angle θi can reasonably be approximated by the proportionate sum of two terms: the directional-hemispherical reflectance at that solar zenith angle, ${bar alpha(theta_i)}$, and the bi-hemispherical reflectance, ${bar bar alpha}$ the proportion concerned being defined as the proportion of diffuse illumination D.

Albedo α can then be given as:

${alpha}= (1-D) bar alpha(theta_i) + D bar bar alpha.$

Directional-hemispherical reflectance is sometimes referred to as black-sky albedo and bi-hemispherical reflectance as white sky albedo. These terms are important because they allow the albedo to be calculated for any given illumination conditions from knowledge of intrinsic properties of the surface. Directional-hemispherical reflectance is the reflectance of a surface under direct illumination (with no diffuse component). ... Bi-hemispherical reflectance is the reflectance of a surface under diffuse illumination (with no direct component). ...

## Astronomical albedo

The albedo of planets, satellites and asteroids can be used to infer much about their properties. The study of albedos, their dependence on wavelength, lighting angle ("phase angle"), and variation in time comprises a major part of the astronomical field of photometry. For small and far objects that cannot be resolved by telescopes, much of what we know comes from the study of their albedos. For example, the absolute albedo can indicate the surface ice content of outer solar system objects, the variation of albedo with phase angle gives information about regolith properties, while unusually high radar albedo is indicative of high metallic content in asteroids. This article is about the astronomical term. ... -1... For other uses, see Asteroid (disambiguation). ... Photometry is a technique of astronomy concerned with measuring the flux, or intensity of an astronomical objects electromagnetic radiation. ... Regolith (Greek: blanket rock) is a layer of loose, heterogeneous material covering solid rock. ... For other uses, see Asteroid (disambiguation). ...

Enceladus, a moon of Saturn, has one of the highest known albedos of any body in the solar system, with 99% of EM radiation reflected. Another notable high albedo body is Eris, with an albedo of 86%. Many objects in the outer solar system and asteroid belt have low albedos down to about 5%. Such a dark surface is thought to be indicative of a primitive and heavily space weathered surface containing some organic compounds. Atmosphere Surface pressure: trace, significant spatial variability[8][9] Composition: 91% Water vapour 4% Nitrogen 3. ... Absolute magnitude: âˆ’1. ... For other uses, see Asteroid (disambiguation). ... Please wikify (format) this article as suggested in the Guide to layout and the Manual of Style. ... Benzene is the simplest of the arenes, a family of organic compounds An organic compound is any member of a large class of chemical compounds whose molecules contain carbon. ...

The overall albedo of the Moon is around 12%, but it is strongly directional and non-Lambertian, displaying also a strong opposition effect. [8] While such reflectance properties are different from those of any terrestrial terrains, they are typical of the regolith surfaces of airless solar system bodies. This article is about Earths moon. ... Regolith (Greek: blanket rock) is a layer of loose, heterogeneous material covering solid rock. ...

Two common albedos that are used in astronomy are the geometric albedo (measuring brightness when illumination comes from directly behind the observer) and the Bond albedo (measuring total proportion of electromagnetic energy reflected). Their values can differ significantly, which is a common source of confusion. The geometric albedo of an astronomical body is the ratio of its total brightness at zero phase angle to that of an idealised fully reflecting, diffusively scattering (Lambertian) disk with the same cross-section. ... The Bond albedo is the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space. ...

In detailed studies, the directional reflectance properties of astronomical bodies are often expressed in terms of the five Hapke parameters which semi-empirically describe the variation of albedo with phase angle, including a characterisation of the opposition effect of regolith surfaces. The Hapke parameters are a set of parameters for a quasi-experimental model that are commonly used to describe the directional reflectance properties of the airless regolith surfaces of bodies in the solar system. ... Phase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object. ... It has been suggested that this article or section be merged with Opposition spike. ... Regolith (Greek: blanket rock) is a layer of loose, heterogeneous material covering solid rock. ...

## Other types of albedo

Single scattering albedo - is used to define scattering of electromagnetic waves on small particles. It depends on properties of the material (refractive index), the size of the particle(s), and the wavelength of the incomming radiation. It is proposed that this article be deleted, because of the following concern: This is just a dictionary definition. ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ...

## Some examples of terrestrial albedo effects

### Fairbanks, Alaska

According to the National Climatic Data Center's GHCN 2 data, which is composed of 30-year smoothed climatic means for thousands of weather stations across the world, the college weather station at Fairbanks, Alaska, is about 3 °C (5.4 °F) warmer than the airport at Fairbanks, partly because of air drainage patterns but also largely because of the lower albedo at the college resulting from a higher concentration of spruce trees and therefore less open snowy ground to reflect the heat back into space. The U.S. National Climatic Data Center (NCDC) in Asheville, North Carolina is the worlds largest active archive of weather data. ... Map of temperature station locations with record lengths indicated by coloring. ... For other uses, see Fairbanks (disambiguation). ... Species About 35; see text. ... The coniferous Coast Redwood, the tallest tree species on earth. ...

### The tropics

Although the albedo-temperature effect is most famous in colder regions of Earth, because more snow falls there, it is actually much stronger in tropical regions because in the tropics there is consistently more sunlight. When Brazilian ranchers cut down dark, tropical rainforest trees to replace them with even darker soil in order to grow crops, the average temperature of the area increases up to 3 °C (5.4 °F) year-round,[9][10] although part of the effect is due to changed evaporation (latent heat flux). Snow is a type of precipitation in the form of crystalline water ice, consisting of a multitude of snowflakes that fall from clouds. ... The Daintree Rainforest in Queensland, Australia. ... In thermochemistry, latent heat is the amount of energy in the form of heat released or absorbed by a substance during evaporation. ...

### Small scale effects

Albedo works on a smaller scale, too. People who wear dark clothes in the summertime put themselves at a greater risk of heatstroke than those who wear lighter color clothes.[11] Hyperthermia is an acute condition resulting from excessive exposure to heat, it is also known as heat stroke or sunstroke. ...

### Albedo of various terrains

The albedo of a pine forest at 45°N in the winter in which the trees cover the land surface completely is only about 9%, among the lowest of any naturally occurring land environment. This is partly due to the color of the pines, and partly due to multiple scattering of sunlight within the trees which lowers the overall reflected light level. Due to light penetration, the ocean's albedo is even lower at about 3.5%, though this depends strongly on the angle of the incident radiation. Dense swampland averages between 9% and 14%. Deciduous trees average about 13%. A grassy field usually comes in at about 20%. A barren field will depend on the color of the soil, and can be as low as 5% or as high as 40%, with 15% being about the average for farmland. A desert or large beach usually averages around 25% but varies depending on the color of the sand. For other uses, see Pine (disambiguation). ... This article does not cite any references or sources. ... Deciduous means temporary or tending to fall off (deriving from the Latin word decidere, to fall off). ... For other uses, see Grass (disambiguation). ... This article is about arid terrain. ... For other uses, see Beach (disambiguation). ...

### Urban areas

Urban areas in particular have very unnatural values for albedo because of the many human-built structures which absorb light before the light can reach the surface. In the northern part of the world, cities are relatively dark, and Walker has shown that their average albedo is about 7%, with only a slight increase during the summer. In most tropical countries, cities average around 12%. This is similar to the values found in northern suburban transitional zones. Part of the reason for this is the different natural environment of cities in tropical regions, e.g., there are more very dark trees around; another reason is that portions of the tropics are very poor, and city buildings must be built with different materials. Warmer regions may also choose lighter colored building materials so the structures will remain cooler.

### Trees

Because trees tend to have a low albedo, removing forests would tend to increase albedo and thereby could produce localized climate cooling. Cloud feedbacks further complicate the issue. In seasonally snow-covered zones, winter albedos of treeless areas are 10% to 50% higher than nearby forested areas because snow does not cover the trees as readily. Deciduous trees have an albedo value of about 0.15 to 0.18 while coniferous trees have a value of about 0.09 to 0.15.[12] The difference between decidous and coniferous is because coniferous trees are darker in general and have cone-shape seeds. The pattern of these seeds trap light energy more than deciduous trees. Cloud feedback is the coupling between cloudiness and surface air temperature in which a change in surface temperature could lead to a change in clouds, which could then amplify or diminish the initial temperature perturbation. ... Deciduous means temporary or tending to fall off (deriving from the Latin word decidere, to fall off). ... Orders & Families Cordaitales â€  Pinales   Pinaceae - Pine family   Araucariaceae - Araucaria family   Podocarpaceae - Yellow-wood family   Sciadopityaceae - Umbrella-pine family   Cupressaceae - Cypress family   Cephalotaxaceae - Plum-yew family   Taxaceae - Yew family Vojnovskyales â€  Voltziales â€  Conifer redirects here. ...

Studies by the Hadley Centre have investigated the relative (generally warming) effect of albedo change and (cooling) effect of carbon sequestration on planting forests. They found that new forests in tropical and midlatitude areas tended to cool; new forests in high latitudes (e.g. Siberia) were neutral or perhaps warming.[13] The Hadley Centre for Climate Prediction and Research, which is part of the Met Office, provides a focus in the United Kingdom for the scientific issues associated with climate change. ... Carbon sequestration from a fossil-fuel power station A carbon dioxide sink or CO2 sink is a carbon reservoir that is increasing in size, and is the opposite of a carbon source. The main sinks are the oceans and growing vegetation. ...

### Snow

Snow albedos can be as high as 90%. This is for the ideal example, however: fresh deep snow over a featureless landscape. Over Antarctica they average a little more than 80%.

If a marginally snow-covered area warms, snow tends to melt, lowering the albedo, and hence leading to more snowmelt (the ice-albedo positive feedback). This is the basis for predictions of enhanced warming in the polar and seasonally snow covered regions as a result of global warming. For the superhero, see Feedback (Dark Horse Comics). ...

### Water

Water reflects light much differently from typical terrestrial materials. The reflectivity of a water surface is calculated using the Fresnel equations (see graph). The Fresnel equations, deduced by Augustin-Jean Fresnel, describe the behaviour of light when moving between media of differing refractive indices. ...

Reflectivity of smooth water at 20 C (refractive index=1.333)

At the scale of the wavelength of light even wavy water is always smooth so the light is reflected in a specular manner (not diffusely). The glint of light off water is a commonplace effect of this. At small angles of incident light, waviness results in reduced reflectivity (from as high as 100%) because of the steepness of the reflectivity-vs.-incident-angle curve and a locally increased average incident angle. [14] Image File history File links Size of this preview: 800 Ã— 600 pixelsFull resolution (960 Ã— 720 pixels, file size: 45 KB, MIME type: image/jpeg)Dan Pangburn self File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Size of this preview: 800 Ã— 600 pixelsFull resolution (960 Ã— 720 pixels, file size: 45 KB, MIME type: image/jpeg)Dan Pangburn self File historyClick on a date/time to view the file as it appeared at that time. ... Diagram of specular reflection Specular reflection is the perfect, mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected onto a single outgoing direction. ... Diagram of diffuse reflection Diffuse reflection is the reflection of light from an uneven or granular surface such that an incident ray is seemingly reflected at a number of angles. ...

Although the reflectivity of water is very low at high and medium angles of incident light, it increases tremendously at small angles of incident light such as occur on the illuminated side of the earth near the terminator (early morning, late afternoon and near the poles). However, as mentioned above, waviness causes an appreciable reduction. Since the light specularly reflected from water does not usually reach the viewer, water is usually considered to have a very low albedo in spite of its high reflectivity at low angles of incident light. World map with terminator (April) A composite image showing the terminator dividing night from day, running across Europe and Africa. ...

Note that White caps on waves look white (and have high albedo) because the water is foamed up (not smooth at the scale of the wavelength of light) so the Fresnel equations do not apply. Fresh ‘black’ ice exhibits Fresnel reflection.

### Clouds

Clouds are another source of albedo that play into the global warming equation. Different types of clouds have different albedo values, theoretically ranging from a minimum of near 0% to a maximum in the high 70s. "On any given day, about half of Earth is covered by clouds, which reflect more sunlight than land and water. Clouds keep Earth cool by reflecting sunlight, but they can also serve as blankets to trap warmth." [15]

Albedo and climate in some areas are already affected by artificial clouds, such as those created by the contrails of heavy commercial airliner traffic.[16] A study following the burning of the Kuwaiti oil fields by Saddam Hussein showed that temperatures under the burning oil fires were as much as 10oC colder than temperatures several miles away under clear skies.[17] Contrails are condensation trails (sometimes vapour trails): artificial cirrus clouds made by the exhaust of aircraft engines or wingtip vortices which precipitate a stream of tiny ice crystals in moist, frigid upper air. ... Saddam Hussein Abd al-Majid al-Tikriti (28 April 1937 â€“ 30 December 2006) was the fifth President of Iraq and Chairman of the Iraqi Revolutionary Command Council from 1979 until his overthrow by US forces in 2003. ...

### Aerosol effects

Aerosol (very fine particles/droplets in the atmosphere) has two effects, direct and indirect. The direct (albedo) effect is generally to cool the planet; the indirect effect (the particles act as CCNs and thereby change cloud properties) is less certain.[18] Particulates, alternatively referred to as particulate matter (PM), aerosols or fine particles, are tiny particles of solid or liquid suspended in a gas. ... Aerosol pollution over Northern India and Bangladesh - NASA Cloud condensation nuclei or CCNs (also known as cloud seeds) are small particles (typically 0. ...

### Black carbon

Another albedo-related effect on the climate is from black carbon particles. The size of this effect is difficult to quantify: the IPCC say that their "estimate of the global mean radiative forcing for BC aerosols from fossil fuels is ... +0.2 W m-2 (from +0.1 W m-2 in the SAR) with a range +0.1 to +0.4 W m-2".[19] IPCC is science authority for the UNFCCC The Intergovernmental Panel on Climate Change (IPCC) was established in 1988 by two United Nations organizations, the World Meteorological Organization (WMO) and the United Nations Environment Programme (UNEP) to assess the risk of human-induced climate change. The Panel is open to all... The Second Assessment Report (SAR) of the Intergovernmental Panel on Climate Change was published in 1995. ...

## See also

Global dimming is the gradual reduction in the amount of global direct irradiance at the Earths surface that was observed for several decades after the start of systematic measurements in 1950s. ... Irradiance, radiant emittance, and radiant exitance are radiometry terms for the power of electromagnetic radiation at a surface, per unit area. ... Not to be confused with insulation. ...

## References

1. ^ a b Pon, Brian (June 30, 1999). Pavement Albedo. Heat Island Group. Retrieved on 2007-08-27.
2. ^ Alan K. Betts, John H. Ball (1997). "Albedo over the boreal forest". Journal of Geophysical 102 (D24): 28,901–28,910. Retrieved on 2007-08-27.
3. ^ a b c d Tom Markvart, Luis CastaŁżer (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier. ISBN 1856173909.
4. ^ Tetzlaff, G. (1983). Albedo of the Sahara, pp. 60-63.
5. ^ http://scienceworld.wolfram.com/physics/Albedo.html
6. ^ http://cat.inist.fr/?aModele=afficheN&cpsidt=1034923
7. ^ http://www.agu.org/sci_soc/prrl/prrl0113.html
8. ^ http://jeff.medkeff.com/astro/lunar/obs_tech/albedo.htm A discussion of Lunar albedos
9. ^ Dickinson, R. E., and P. J. Kennedy, 1992: Impacts on regional climate of Amazon deforestation. Geophys. Res. Lett., 19, 1947–1950.
10. ^ http://web.mit.edu/12.000/www/m2006/final/characterization/abiotic_water.html Project Amazonia: Characterization - Abiotic - Water
11. ^ http://www.ranknfile-ue.org/h&s0897.html
12. ^ The Climate System. Manchester Metropolitan University. Retrieved on 2007-11-11.
13. ^ Betts, R.A. (2000) Offset of the potential carbon sink from boreal forestation by decreases in surface albedo, Nature, Volume 408, Issue 6809, pp. 187-190.
14. ^ http://lenah.freeshell.org/pp/01-ONW-St.Petersburg/Fresnel.pdf
15. ^ http://www.livescience.com/environment/060124_earth_albedo.html
16. ^ http://facstaff.uww.edu/travisd/pdf/jetcontrailsrecentresearch.pdf
17. ^ http://adsabs.harvard.edu/abs/1992JGR....9714565C
18. ^ http://www.grida.no/climate/ipcc_tar/wg1/231.htm#671
19. ^ http://www.grida.no/climate/ipcc_tar/wg1/233.htm

Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 239th day of the year (240th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 239th day of the year (240th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 315th day of the year (316th in leap years) in the Gregorian calendar. ...

Results from FactBites:

 Albedo Systems: website content management systems; web design; e-commerce; web-based databases; web site hosting and ... (300 words) Albedo specialises in developing websites that are functional, maintainable, usable and accessible. Albedo Systems can offer everything you need to create and maintain a web presence, large or small, from initial consultancy, through analysis, programming and graphics design, final deployment and promotion - and continuing with systems that will lift the burden of site content management, maintenance and upgrading. We see a website as more than just a set of disjointed pages - to us it is an interconnected system that requires an integrated approach.
 Albedo - Wikipedia, the free encyclopedia (1328 words) Albedo is the measure of reflectivity of a surface or body. The white-sky albedo is the reflectance of a surface illuminated uniformly from all points on a hemisphere (the sky). In this case the albedo depends on the direction of illumination (particularly zenith angle) and is similar to the daytime insolation of the Earth's surface under a clear or cloud-free sky.
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• MEZIANE BRAHIMI

Articles written in Bulletin of Materials Science

• A novel carbon/germanium conic structure: theoretical study using density functional theory

Complete optimization without geometry constraints and calculation of electronic properties of novel conic molecules such as C$_n$H$_n$Ge$_n$H$_n$ and C$_n$Ge$_n$H$_n$, with $n = 3−8$, was carried out with density functional theory using B3LYP and PBE1PBE functionals with 6-31$+$G(d, p) and cc-pVTZ basis sets. Calculations of formation energy showed stable and peculiar geometric and electronic properties. All carbon and germanium atoms for C$_n$H$_n$Ge$_n$H$_n$ compounds, which are sp$^3$-hybridized, were located in the same plane. This finding contradicts the notions of hybridization known to date. For these new molecular compounds, quantum descriptors such as electrochemical potential ($\mu$), chemical hardness ($\eta$), electrophilicity index ($\omega$), dipole moment, energy gap and the shape of the molecular orbital have been calculated in additionto nucleus independent chemical shifts, polarizability and harmonic oscillator model of aromaticity which are important tools for determining the aromaticity of the studied compounds. Thus, the aim of the work is, on the one hand, to propose new stable molecular structures formed of carbon and germanium atoms, and on the other hand, to challenge our understanding of hybridization and aromaticity notion.

• In-silico modelling of fullerene and fullerene adsorbed by nO$_2$ molecules (n(O$_2$)@$C_m$ with n = 1, 2, 4 and m = 48 and 60) as potential SARS-CoV-2 inhibitors

COVID-19 pandemic started more than a year ago and has infected more than 115 million of people from ${\sim}$210 countries and >2.5 million of deaths worldwide being reported without any commercial and effective treatment or vaccine being yet released. However, recent studies on nanomaterials such as fullerenes, carbon nanotubes and graphene showed that they possess anti-inflammatory, antiviral, anti-oxidant and anti-HIV properties. Herein, the interactions which established between the fullerenes $C_m$ (m = 48, 60, 70, 80, 84 and 86) and the spike protein (SP) of SARS-CoV-2 and the human ACE2 receptor have been investigated based on the density functional theory (DFT) method with the CAM-B3LYP functional and the 6-31G* basis. The results of this study show that C48 exhibited as potential inhibitor of SARS-CoV-2. Because of the presence of heteroatoms on the surface of fullerenes which systematically reduce energy gaps, which in turn increase their reactivities. The oxygen adsorbed by fullerenes increases the number of non-covalent contacts and involves a large number of hydrogen bonds, while decreasing the binding energies. Thus, the hACE2-SP-4O$_2$@C60 complex is strongly recommended for inhibiting SARS-CoV-2 in the final phase of contamination.

• # Bulletin of Materials Science

Volume 45, 2022
All articles
Continuous Article Publishing mode

• # Dr Shanti Swarup Bhatnagar for Science and Technology

Posted on October 12, 2020

Prof. Subi Jacob George — Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru
Chemical Sciences 2020

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PREPRINT
C672772D-4157-4ACB-A27E-E7B47B59BB03

# Tidal excitation of autoresonant oscillations in stars with close-by planets

A. F. Lanza
arXiv:2206.14611

Submitted on 29 June 2022

## Abstract

Close-by planets may excite various kinds of oscillations in their host stars through their time-varying tidal potential. Magnetostrophic oscillations with a frequency much smaller than the stellar rotation frequency have recently been proposed to account for the spin-orbit commensurability observed in several planet-hosting stars. In principle, they can be resonantly excited in an isolated slender magnetic flux tube by a Fourier component of the time-varying tidal potential with a very low frequency in the reference frame rotating with the host. However, due to the weakness of such high-order tidal components, a mechanism is required to lock the oscillations in phase with the forcing for long time intervals (${10}^{3}-{10}^{7}$ years) in order to allow the oscillation amplitude to grow. We propose that the locking mechanism is an autoresonance produced by the non-linear dependence of the oscillation frequency on its amplitude. We suggest that the angular momentum loss rate is remarkably reduced in hosts entering autoresonance that contributes to maintain those systems in that regime for a long time. We apply our model to a sample of ten systems showing spin-orbit commensurability and estimate the maximum drifts of the relevant tidal potential frequencies that allow them to enter the autoresonant regime. Such drifts are compared with the expected drifts owing to the tidal evolution of the planetary orbits and the stellar angular momentum loss in the magnetized winds finding that autoresonance is a viable mechanism in eight systems, at least in our idealized model. The duration of the autoresonant regime and the associated spin-orbit commensurability may be comparable with the main-sequence lifetimes of the host stars, indicating that gyrochronology may not be applicable to those hosts.

## Preprint

Comment: 21 pages, 7 figures, 5 tables, 2 appendixes; accepted by Astronomy & Astrophysics

Subjects: Astrophysics - Earth and Planetary Astrophysics; Astrophysics - Solar and Stellar Astrophysics


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# RBSE Solutions for Class 12 Maths Chapter 12 Differential Equation Ex 12.2

## Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Ex 12.2

Find the differential equation of the following groups :

Question 1.
y = ax + $$\frac { b }{ x }$$
Solution:

Question 2.
x2 + y2 = a2.
Solution:
Differentiating given equation w.r.t. x, we get

Question 3.
y = Ae3x + Be5x.
Solution:
y = Ae3x + Be5x
Differentiating w.r.t. x, we get

Question 4.
y = ex [a cos x + B sin x] …..(1)
Solution:

Question 5.
y = a cos (x + b), where ‘a’ and ‘b’ are arbitrary constant.
Solution:
y = a cos (x + b)
Differentiating w.r.t. x,


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Why the weight vector is a linear combination of the inputs and the outputs in the Perceptron

I was studying Support Vector Machines and I've got stuck with this relation regarding the weight vector of the hyperplane.

$$w=\sum\limits_{i\in I}^{} y_i x_i$$

For reference, I'm studying from the Alex Smola slides and this relation is not justified.

That particular slide is about Perceptron algorithm, where initially $$w$$ is $$0$$ and you update it for each misclassified sample with the following update rule (there are slightly changed versions of this, but sticking with the slides): $$w\leftarrow w+y_ix_i$$ Because we start from $$0$$ and every update made is in terms of $$y_ix_i$$, the final version of the weights will be a linear combination of the input samples, i.e. something like $$w=\sum m_i y_i x_i$$
where $$m_i$$ is the number of times in the learning loop we updated for sample $$i$$. The concept of linear combination is correct, but the equation provided is wrong. If it were, we could have solved for $$w$$ directly, without the need of iterating until convergence: $$w=\sum y_i x_i=\sum_{y_i=1} x_i-\sum_{y_i=-1} x_i$$