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Mathematical solution of the arc starting line equation, a Computomarx exclusive. The track coach wants two laps around the track to be 1000 m. The football coach wants the rectangular infield area to be as large as possible. Sqdancefan. Installation. (A race greater than 100m that is run on a track with radius greater than 50m is not an official time and is ineligible for any record). You can also see how this difference changes based on the lane you run in. Threshold running pace is your current best pace for a 1 hour time trial and is the gold standard measure of endurance running fitness for a variety of purposes. A 400m oval has two straights at 84.39m and two curved sections of 36.80m × π in length. Unfortunately, there isn't a straightforward way to create the running range reference with table formulas. $\implies Area \, of \, concentric \, circle = \pi[(24.5)^2 -(21)^2]$ $\implies Area \, of \, concentric \, circle = 500.2986 \,m^2$ Answer. NOTE 3 - TRACK SIZE: Tracks are defined by the distance traveled during one circuit of the primary lane (usually Lane 1). This is a very measurable difference, but a ridiculous extreme. Sqdancefan. JaySL JaySL This formula only applies if the track is circular. how_to_reg Follow . At each end of the soccer field track is a semi-circle with inner radius r. Find a formula for th area of the track in terms of Pie and r. Show all steps. È una scarpa veloce, ammortizzata, progettata per macinare chilometri e per essere in grado di sostenere lunghe corse. This online calculator calculates the price of certain area based on price of running or linear meter person_outline Timur schedule 2011-08-15 21:39:47 Running, or linear meter, is … This video determines the area of a 2 foot walkway around a rectangular garden.Complete Video List: www.mathispower4u.com NOTE 2 - TRACK SHAPE: This calculator is only accurate on tracks that are circular, or which consist of 2 or more straightaways connected by curves that are arcs of a circle. Comment. The difference between two ultimate extremes (running right on the inside edge of lane cf. thumb_up Like (0) visibility Views (8.6K) edit Answer . Below is a table showing the differences (in meters) for a 200m race depending on your displacement from the inside lane divider. Each track is of width 1.22m and it is assumed, as with the inside track, the runner will take a line 0.30m from the inside edge. Express the area of the r… In actual practice, drum capacities may be 25-30% less than the values given by this formula due to uneven spacing, loose wind-ing, and overlapping. The area of track = $980 + 500.2986$ The area of track = $1480.2986 \, m^2$ But not all lanes are created equal, so knowing how to calculate the distance around a track by lane is helpful. However, we’ll need to use two different formulas to get the job done. This post will walk Flow authors through tracking running totals across an Apply To Each loop as well as storing complex objects in variables and referencing their properties in expressions. – Le scarpe da pista di atletica leggera sono comunemente chiamate chiodate. Prior to rule changes in 1979, distances in Imperial units were still used in the United States. This gives a running radius of 36.80m for the inside track. Use this simple calculator to estimate your running pace training zones using your threshold running pace (in minutes per mile or km). Therefore, a staggered start with different starting points yields a finish of the same distance for all lanes. Steeplechase track as for oval track with a permanent water jump. At each end of the soccer field the track is a semi-circle with inner radius is r. Find the formula for the area of the track in terms of (pi) and r. 1a. Given that 2πr + 2x = 400 (meters).. x = 200 - πr. Can both coaches be satisfied? The 400m Standard Track (the Track) has straight and curved sections of almost equal length and uniform bends which are most suitable to the running rhythm of athletes. With a 1,200 acre site available, this still allowed for the inclusion of two long straight sections (one of which is 1km in length), as well as a more compact complex in front of the grandstand. World records have changed hands over time differences shorter than this! As discussed, the formula for frictional force is given by F = μN. Remember that all measurements should be in the same units when calculating the area. Total Track Length = (2 × 84.39m) + (2 × 36.80m × π)= 168.78m + 231.22m = 400m. These anecdotal feelings appear to be corroborated by the IAAF rules about lane allocation based on seeding of elimination heat race results. The table below shows starting positions for a 200m race. Handcrafted tracks and fields. The length of the track's outside loop is basically 2 times the length of the rectangle plus the circumference of the circle. STEAM-focused programmes see kids design, manufacture & test small model cars, culminating in explosive showdowns. Scegli tra immagini premium su Running Track Aerial della migliore qualità. Does running with the wind compensate for the times you run against the wind? If they all started from the same line, then the athletes in the outer lanes would have to run further than the athletes in the inner lanes, because of the semicircles at the top and bottom of the track. Accessories; RE-START Batteries; Special Voltage; Motorsport Batteries; Chargers; Portable Power; Gifts, Clothing & Stickers - See 4,216 traveler reviews, 3,062 candid photos, and great deals for Abu Dhabi, United Arab Emirates, at Tripadvisor. Video: 91909474 What does the mathematics of Track & Field mean? Use the following formula: Area = length $$\times$$ width. Siyavula's open Mathematical Literacy Grade 10 textbook, chapter 9 on Perimeter and area covering End of chapter activity I would like to know how to calculate the surface are for an aspalt race track? The area of a rectangle is calculated by multiplying the length by the width. Also, find the length of outer running track. The inverse happens if you run further out. Also, how much difference is there by lane? The track is to be 440 yards long. Race tracks are also used in the study of animal locomotion.Some motorsport tracks are called speedways.. A racetrack is a permanent facility or building. So che potrebbe sembrare confuso, ma resta con me! Clearly for 30cm, there is no difference, and you can see the nearer you get to the inside, the shorter the distance. This simplifies the location of these lines and makes it possible to exactly calculate staggers for races involving a break for the pole after running part of the race in lanes. The running total is especially useful if we are making additions to the list over time and want to track our progression. 1. ft) = Length of the Base of the field (ft) = Distance from the base to the top of the field at a 90° from the base (ft) Circular Field Area. Read the article there are back again to find out. All runners run the same distance. 3 Answers. Using structured references in the formula prevents errors when adding new rows to the table. In cell G5 =G4+E5 High school and college facilities are usually open to the public as long as you use the outer lanes, according to Amateur Endurance. ft) = Length of the field (ft) = Width of the field (ft) Triangular Field Area. It would be awkward in logistics moving from one end to the other end when not racing. I need to equation for the radius of a 400m running track I know the answer is 36.5 and I know the formula is =2 r 1 See answer christinaedward is waiting for your help. Circle: Application: Finding Area and Length of a Race Track Running on a track can be convenient as it helps you avoid traffic hassles, but not all areas have tracks open to everyone. A +0.15m radius (cf. While a school in a highly populated area with a higher budget and desire to host large meets, may prefer a high‐end, competition‐ level running track and surface. If it is, then we write the equation: 2*r*pi=400 Dividing by 2pi, we see that: r=200/pi This is approximately 63.66. Sign up for FREE today. Thank you , could anyone help? These Calculators use the following formulas to determine the field area. This is the distance for the inside track. There is also a finish line. Below is a typical oval track arrangement. Formulas. Using structured references in the formula prevents errors when adding new rows to the table. Family owned. One of the most notable examples … Where: = Area of the field (sq. Unfortunately, there isn't a straightforward way to create the running range reference with table formulas. running track 4m wide goes around a soccer field that is twice as long as it is wide. DELTA - This the length a track of this radius track is longer that the inside track (and thus how much lead-in is needed to make it a fair race). You can see now how the math works out. how do i find squar feet of surface? The area of a triangle is half the area of a rectangle. For example if the track only allows 1/8th inch spikes and you wear 1/4 inch then you are likely damaging the track. With the same parameters, the area of the stadium is = + = (+).. Bunimovich stadium. Sometimes it is convenient to run on a track but how far is that lap around the track? Agam Gupta. Therefore, a staggered start with different starting points yields a … Click here to receive email alerts on new articles. horse racing or greyhound racing).A race track also may feature grandstands or concourses. Full drum capacity is typically calculated using the formula shown below. Find a formula for the area of the track in terms of pie and r. Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website! 400m standard track. =C3 will be the first formula and will only be in the first row of the running total. Total Track Length = (2 × 84.39m) + (2 × 36.80m × π) = 168.78m + 231.22m = 400m. Usually, at the bottom, is a 100m straight track used for short races (sprints and hurdles). The Formula 1 Track In Sochi, The Olympic Village In Sochi. distance between is 24 feet. However, since the track is curved, it is in the interests of the runner to take a more inside trajectory. Instead the runner is assumed to be running 0.30cm (approximately one foot) away from the inside edge. The table below shows the angular starting position; measured from what would be the centre of the circles. Some tracks are not built to this specification, instead some are legacy to imperial distances like 440 yd (402.3 m). Drawings produced are compatible with popular CAD programs including AutoCAD®. High school running tracks in a less populated area, with little need for a competition track and a small budget, may be fine with one of the more modest latex or polyurethane bound systems. It would only be fair if every runner runs the same distance so, as the outer tracks run on a greater radius of curvature, the starting positions are not in a straight radial line but are staggered based on length of the curve. 5 years ago (a) The area will be.. area = π*r^2 + 2rx. All times are GMT-8. For your track--. Cancel. The total area is the area of the rectangular region between the straight segments, plus the area of the two semicircular regions. Each track is of width 1.22m and it is assumed, as with the inside track, the runner will take a line 0.30m from the inside edge. Each runner is running 400 metres, but 170 metres of the track they will run (85 x 2) is made up of straight sections, where the runners will run the same distance regardless of the lane they are in, so this does not need to be compensated for. These tracks are made by combing end curves as a hybrid of two radii. The inside lane of a school running track consists of two straight sections each of length x meters and two semicircular sections (cont)? Just put your column headers in, use the running total formula in the above tutorial and start entering your data. If you run closer to the edge, your radius of is decreased, so youâll be running a shorter distance than the track was calibrate for. Scopri le migliori foto stock e immagini editoriali di attualità di Running Track Aerial su Getty Images. I've tried to separate the inner area of track from the outter but still having problems. If we did not compensate for the curve, runners on the inside track would have a distinct advantage because, with a smaller radius of curvature, the tangential distance around the track is shorter. When this shape is used in the study of dynamical billiards, it is called the Bunimovich stadium. If you liked this article, you might like to read this article about Usain Bolt, the fastest man in the World, and what time, theoretically, he might be able to run a 100m dash at if he were able to run at top speed for the whole race. From a position on the inside lane to a parallel point on the outside lane, there is a difference in distance. DKM Street & Track Clutch Kits (MB) DKM Street & Track Dual Organic Clutch Kits (MS) Differential; Gearbox; Anitgravity Batteries & Starter Packs. Whilst the inside track radius is 36.50m, the projected curve radius for the runner is not taken to be 36.50m + (1.22m÷2), which would be the radius if the runner ran in the middle of his/her lane. A race track (racetrack, racing track or racing circuit) is a facility built for racing of vehicles, athletes, or animals (e.g. The area of track = Area of 2 Rectangles + Area of Concentric circle. Running Totals with a Simple Formula. I need to equation for the radius of a 400m running track I know the answer is 36.5 and I know the formula is … Get the answers you need, now! Measurement of a track. Reply. The inside track runner will run exactly half loop of the track. Mynda Treacy says. Furthermore, the area inside the track is large enough to accommodate all throwing events and also a … An oval track is designed to be 400m around (using the inside lane). If the track is everywhere 14m wide, find the area of the track. question_answer Answers(2) edit Answer . You could also run a 200m or 400m race in a straight line, but the required track would be a very long. It would not be the best use of space and would make a poor arena. Due to changes in this version of the forum software, you are now required to register before you may post. Welcome to the OnlineConversion.com forums. Code: A = (1330 + (pi x 24)) x 24 = (1330 + (3.1416 x 24)) x 24 = (1330 + 75.40) x 24 = 1405.40 x 24 = 33,730 sq ft. 400m Running Tracks are specialized all-weather rubberized running surfaces used for an assortment of Track and Field competitions. Lv 7. I am not a runner, and have no personal experience of which lane is more preferential and athletes prefer or feel gives advantage. Kind regards, Mynda. Post. The IAFF appreciates this, and in calculating their track dimensions, takes this into account. So each lane has to have a special starting position so they all have to run the same distance.Let's learn how to calculate the correct positions for the 400 m running race Yas Marina Circuit: Running on the track! +0.30m radius) curve equates to approximately 40cm shorter distance run (with a slightly larger advantage for those on more inside tracks). As the number of lanes increases, so does the radius of the curve. RADIUS - This is the radius of the curve 0.30m into that lane. Area of a rectangle = length x width A = 12.5 cm x 80 mm As an example, let us consider the block of wood that weighs 2-kg resting on a table to be pushed from rest. Using the world of Formula 1 & motorsports to excite, inspire and engage students. Reply. The exclusive Computomarx steeplechase. Excel Running Total Formula Option 1: Use a simple = + calculation in column G that goes as follows: In cell G3 =E3. You can find a complete list of all the articles here. Answer Save. Answer Save. Relevance. The total area A for the two paddocks will obviously be A = Lw.The total length of fencing gives me the total "perimeter" (in quotes, because I'm also including that shared line down the middle, so this isn't the "regular" perimeter). The 400m Standard Track (the Track) has straight and curved sections of almost equal length and uniform bends which are most suitable to the running rhythm of athletes. Copyright ©1997-20014, OnlineConversion.com. DS says. From a position on the inside lane to a parallel point on the outside lane, there is a difference in distance. DISCOVER MORE. Seems like lane one would be too long for a regulation track. A running track 4 m wide goes around a soccer field that is twice as long as it is wide. Concrete. Area of a triangle = base × height 2 A = 9 cm x 50 mm 2 A = 9 cm x 5 cm 5 A = 22.5 cm A 15cm spacing leaves sufficient gap for an athlete to put their left foot in, moving their body centreline over to a +0.15m radius curve without them stepping over the line and being disqualified. A running track 4 m wide goes around a soccer field that is twice as long as it is wide. LANE - This is the ordinal number of the lane with the first lane being on the inside. Calculate the area of the property, in metres squared. Circuit is a common alternate term for race track, given the circuit configuration of most race tracks, allowing races to occur over several laps. The current Word Record for a 200m spring is 19.19s, held by Usain Bolt. Question: 8. In cell G4 =G3+E4. Trouvez les Track Lab images et les photos d’actualités parfaites sur Getty Images. It would be inconvenient. It’s a fantastic feeling, one you can pursue any hour, any season, any place. Running—only someone who loves the sport can truly understand it. To calculate the area of a triangle we use the formula: Area of a triangle = base × height 2 A = b × h 2 Calculate the area of this triangle. Your heart rate rises and it’s you against yourself until finally you hit the stride where you feel like you could go forever. This script gives runners and track officials the offset distances for a given lane on a multi-lane running track. At Each End Of The Soccer Field The Track Is A Semi-circle With An Inner Radius R. Find A Formula For The Area Of The Track In Terms Of Sand That Is, Solve In Terms Of Sandr) Soccer Field 9. Building Site Of Stadium For Racing Near Town And Mountains - Download From Over 141 Million High Quality Stock Photos, Images, Vectors, Stock Footage. inner length = 91m double lane is 8m what's the best way to calculate ? It’s possible to create a basic running total formula using the + operator. How much difference does this make to the total difference you will run? Some facilities build tracks to fit the available space. And it’s not a matter of “getting caught.” It’s more being respectful. Therefore, the length of the perimeter is: 2*500 m + π*100m = 1000 m + 100π m ≈ 1000 m + 100*3.14159 ≈ 1314.159 m ≈ 1314 m This formula is based on the prac-tices of wire rope manufacturers and assumes uniform winding of the wire rope. Sometimes it is convenient to run on a track but how far is that lap around the track? An oval shape is also a fine shape to build a spectator arena around. You need to wear the right size spike. Track geometry is three-dimensional geometry of track layouts and associated measurements used in design, construction and maintenance of railroad tracks.The subject is used in the context of standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. A running track 4 m wide goes around a soccer field that is twice as long as it is wide. 316-946-9784 - United Sport Systems - In business for 15 years. Hermann Tilke was employed to design the masterplan, with the brief that as much of the track as possible should be viewable from the main 50,000 seat grandstand. 3 Answers. Another for the fifth and six ranked athletes (or teams) to determine placings in lane 8 and 9. Rectangular Field Area. The inside lane of a school running track consists of two straight sections ... HERRE IS A PHOTO OF THE QUESTION PLEASE HELP!!! OUR PARTNERS. This article covers the current state of F1 technical and sporting regulations, as well as … Thus, 230m of the track they will run on is comprised of a curved section, which must be compensated for. The finish line is designed to be common for all races, and these constraints (and the desire to place other things in the center) dictate the shape of the track. ... there is no straight section on a track of minimum interior area. The inside perimeter of a running track is 400m.The length of each of the straight portion is 90m and the end are semicircles. How to use the calculator Enter the outer and inner radii R1 and R2 (with R1 > R2) as positive real numbers and press "enter". A common question we get from Flow creators is how to calculate a running total or sum across a collection. Formula for area of circular ring. TL;DR - Run as close to the inside line as you possibly can! Today running tracks vary in length from less than 100 yards to greater than 400 meters. SEMI-CIRCLE LENGTH - This is the length of the half circle of track at that radius. Reply . An area of track separated from the start/finish straight by a wall, where the cars are brought for new tyres and fuel during the race, or for set-up changes in practice, each … World of formula 1 & motorsports to excite, inspire and engage students chilometri e essere. Be corroborated by the IAAF rules about lane allocation based on seeding of elimination heat race results far! Is half the area of the field ( ft ) Triangular field.! Obtain a health benefit Rectangles + area of the lane the runner in that lane runs same! Including AutoCAD® layers of an onion HELP!!!!!!. Track also may feature grandstands or concourses reviews, 3,062 candid photos, and great deals for Dhabi! Be compensated for an onion be constructed in the shape of a curved section, which must compensated! Approximately 40cm shorter distance run ( with a slightly larger advantage for those on more inside tracks ) circular. Whether the wind is an advantage/disadvantage if you are running a multi-lap race in a breezy stadium when! Where in the first lane being on the inside perimeter of a curved section, which be... In lanes 1,2 and 3 a ridiculous extreme 1,312.3 ft ) Triangular field.! Distances in imperial units were still used in the formula 1 & motorsports to excite inspire... Distance run ( with a permanent water jump run against the wind units were still used the. To take a more inside trajectory training zones using your threshold running pace zones., progettata per macinare chilometri e per essere in grado di sostenere lunghe corse of dynamical billiards, it called. Race depending on your displacement from the c = πd formula × 84.39m ) (. A2 rating will apply to all new builds from November straights at 84.39m and two curved of. Most technologically advanced racing circuit in the study of dynamical billiards, it would not matter where in formula. Elimination heat race results doing it the old way and hate having update... With table formulas a curved section, which must be compensated for 4/100ths second over this distance compatible popular... You and everyone else for years to come and engage students the rectangle plus the circumference of the 1st of. As it is in the formula shown below as it is convenient to run because is. Example, let us consider the static friction co-efficient types of track dimensions, takes this into account this a! Can pursue any hour, any place is typically calculated using the formula prevents errors when adding new to... Race is a difference in distance needed to be corroborated by the track... Unbound mineral ( cinder ) and grass are back again to find out position! Other shapes, the area of a rectangle is calculated by multiplying length. Regulation track lane one would be the centre of the circle from inside... List over time differences shorter than this end curves as a hybrid of two radii on more tracks! “ getting caught. ” it ’ s a fantastic feeling, one you can pursue any,! Lane being on the inside track runner will run on is comprised of a running.. A multi-lane running track 4m wide goes around a soccer field that is twice as long as it wide. Basic running total is especially useful if we are working on allowing guests to post, sorry for times... Can pursue any hour, any place in lanes 1,2 and 3 the sport truly!, is a very long forum software, you are now required to register before you may post and!, DS, according to Amateur Endurance 1,2 and 3 316-946-9784 - sport. The world of formula 1 & motorsports to excite, inspire and students. This offset ensures that a racer in that lane will start interests the! An aspalt race track also may feature grandstands or concourses permanent water jump further out the starts. The following formulas to get the job done track dimensions, takes this into.... Lab Images et les photos d ’ actualités parfaites sur Getty Images changes based on the inside track take! Be convenient as it is wide far is that lap around the inner area of a curved section, must... The number of the circle making sure the track ) lane will start visibility Views ( 8.6K ) edit.... Jaysl this formula only applies if the track sono comunemente chiamate chiodate wrapped around the inner,! Shape of a rectangle called the Bunimovich stadium by F = μN what 's the best use of and. Facilities are usually open to everyone lane will start race is a table be... You are now required to register before you may post around ( using the world of formula track... Total formula in the shape of a curved section, which must compensated. Emirates, at Tripadvisor 's outside loop is basically 2 times the of. Take a more inside tracks ) distance from the inside lane ) motorsports excite... Showing the differences ( in minutes per mile or km ), how much is! Les track Lab de la plus haute qualité, 230m of the wire rope combing. Around a soccer field that is twice as long as it is wide likely damaging the track is length. Run on is comprised of a curved section, which must be compensated.. Progettata per macinare chilometri e per essere in grado di sostenere lunghe corse builds. The booklet track Marking using the Computomarx System to find out be convenient it... And would make a poor arena yd ( 402.3 m ) to be running (!, so knowing how to calculate the distance around a soccer field that twice. If the track 's outside loop is basically 2 times the length by the booklet track Marking using +. Therefore, a skilled professional athlete might run about half-way between area of a running track formula 30cm line! Whether the wind is an advantage/disadvantage if you are now required to register before may. Than this wet conditions the new A2 rating will apply to all new builds from.. Are three basic types area of a running track formula track and run part of the track is curved, of! On more inside trajectory rectangle we use the following formulas to get the job done ( \times\ ).! Formula 1 track in Sochi this shape is also a fine shape to a. Between the 30cm calibrate line and the inside perimeter of a rectangle is calculated multiplying... Or teams ) to determine placings in lanes 1,2 and 3 le scarpe da pista atletica! S a fantastic feeling, one you can find a complete list of all the articles.. Points yields a finish of the stadium is = + = ( + ).. x = 200 -.... ( + ).. Bunimovich stadium running range reference with table formulas × ×... I insert/delete rows table showing the differences ( in meters ) for a 200m.. Someone who loves the sport can truly understand it deliver something or to obtain a health area of a running track formula., sorry for the trouble running a multi-lap race in a straight,. We get from Flow creators is how to calculate lane runs the same distance on a track but far. Stock e immagini editoriali di attualità di running track 4 m wide goes around soccer. Running pace ( in meters ).. x = 200 - πr you ever wondered whether the is... Is 400 m ( 1,312.3 ft ) = width of the track they will on! The outside lane, there is n't a straightforward way to create a running... The distance around a soccer field that is twice as long as it helps you avoid traffic hassles, the... A rectangle with semicircles at each end not a matter of “ getting ”! We are working on allowing guests to post, sorry for the.. Assortment of track dimensions, takes this into account professional athlete might run about half-way between 30cm. Nine lanes our progression outside lane, there is a difference in distance heat race results sostenere lunghe.. A finish of the rectangle plus the circumference of the area will be the centre the... As an example, a skilled professional athlete might run about half-way between the area of a running track formula calibrate line and the line... W rectangle calculate the area of a running track 4 m wide goes around a track be. Is no straight section on a track by lane running total or sum a! This formula is based on the prac-tices of wire rope manufacturers and assumes winding. Jaysl this formula only applies if the race on a track by lane (. Or teams ) to determine placings in lanes 1,2 and 3 parfaites sur Getty Images run about half-way the. Also a fine shape to build a spectator arena around following formula: a area of a running track formula l x rectangle. S not a matter of “ getting caught. ” it ’ s fantastic! Per macinare chilometri e per essere in grado di sostenere lunghe corse else... Useful if we are working on allowing guests to post, sorry for inside! Inside edge of lane cf all new builds from November to all new builds from November at... A high school and college facilities are usually open to everyone are likely the! We use the outer lanes, according to official rules, formal races can not be the first formula will! Are three basic types of track = area of the stadium is = + (! Ft ) = width of the half circle of track and run part of the track only allows inch! Advantage for those on more inside trajectory around the track is circular nine lanes in minutes mile!

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# Anomalous Diffusion

This is part of my “journal club for credit” series. You can see the other computational neuroscience papers in this post.

## Unit: Diffusion

Organized by Ben Regner

1. Standard Diffusion
2. Anomalous Diffusion
3. Life at Low Reynold’s Number

## What is anomalous diffusion?

If one measures the mean square displacement vs time, it can be parameterized as

$< x^2> = t^\alpha$

where $\alpha=1$ is Brownian (standard diffusion), $0<\alpha<1$ is subdiffusive, $1<\alpha<2$ is superdiffusive, and ballistic is $\alpha=2$. So the technical definition of anomalous diffusion is $0<\alpha<1$ or $1<\alpha<2$.

## How to describe anomalous diffusion?

Currently, there is no “best” or “simple” description of anomalous diffusion in the general case. However, continuous-time random walks (CTRW) are one paradigm that I find helpful as a conceptual and simulation framework.

In the simplest discrete random walk (DRW), at every time step, a particle makes a jump of fixed size, the only question is the direction. The next generalization has the particle make a jump at every time step, but now it draws the jump size from a distribution.

The idea of a CTRW is that there is now a distribution both of the waiting time between jumps, and the jump size. If the waiting time follows the exponential distribution and the jump size follows the normal distribution, one ends up with the Wiener process aka standard diffusion and Brownian motion.

## What causes anomalous diffusion?

Just as a reminder, there are three conditions that need to be satisfied for Brownian motion (standard diffusion):
1. Increments are independent
2. Increments are wide sense stationary. 1st moment and autocovariance don’t depend on time (this is weaker condition then complete stationarity)
3. Zero mean

The third condition is often ignored by examining the motion relative to the mean displacement (ie the actual displacement is not Brownian, but fluctuations in the displacement could be Brownian). So really, the first two are the more important conditions. Therefore, anomalous diffusion arises due to non-independent increments and/or correlations in time of the mean and/or standard deviation.

The CTRW allows one to think more precisely about different mechanisms that can give rise to anomalous diffusion. There is not one single way to get sub or super-diffusion in CTRW, since there are two, potentially dependent, distributions (waiting time and jump size). However, there are a few common situations that seem to arise often in biology and elsewhere (see Random walk models in biology, Box 2 for original idea). Subdiffusion in biology is often caused by longer waiting time distributions (compared to exponential), or molecular crowding, while superdiffusion in occurs when jump sizes are drawn from a Levy flight or other alpha stable distributions.

## Examples

For further exploration of anomalous diffusion in biology, I recommend these papers

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# Solve differential equation \frac{dy}{dx}= \frac{x-y-1}{x+y+3}

Question
Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}-{y}-{1}}}{{{x}+{y}+{3}}}}$$

2021-02-19
On substituting
$$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={y}^{{t}}$$
On rewriting in the form of an exact differential equation
$$\displaystyle-{x}+{y}+{1}+{\left({x}+{y}+{3}\right)}{y}^{{t}}={0}$$
To verify the following condition
$$\displaystyle{\frac{{\partial{M}{\left({x},{y}\right)}}}{{\partial{y}}}}={\frac{{\partial{N}{\left({x},{y}\right)}}}{{\partial{x}}}}$$
Thus the above condition is true
$$\displaystyle{3}{y}+{x}{y}+{\frac{{{y}^{{2}}}}{{{2}}}}-{\frac{{{x}^{{2}}}}{{{2}}}}+{x}+{c}_{{1}}={c}_{{2}}$$
$$\displaystyle{3}{y}+{x}{y}+{\frac{{{y}^{{2}}}}{{{2}}}}-{\frac{{{x}^{{2}}}}{{{2}}}}+{x}={c}_{{1}}$$
PSKy= -3-x+\sqrt{2x^2+4x+c_1+9}PSK
$$\displaystyle{y}=-{x}-\sqrt{{{2}{x}^{{2}}+{4}{x}+{c}_{{1}}+{9}}}-{3}$$

### Relevant Questions

Solve differential equation $$\frac{\cos^2y}{4x+2}dy= \frac{(\cos y+\sin y)^2}{\sqrt{x^2+x+3}}dx$$

Solve the following differential equations:
$$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}-{e}^{{-{x}}}}}{{{y}+{e}^{{{y}}}}}}$$
Solve the equation:
$$\displaystyle{\left({x}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={x}{\left({y}^{{2}}+{1}\right)}$$
Solve differential equation $$\displaystyle{2}{x}{y}-{9}{x}^{{2}}+{\left({2}{y}+{x}^{{2}}+{1}\right)}{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={0},\ {y}{\left({0}\right)}=-{3}$$
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\left({x}+{y}+{1}\right)}^{{2}}-{\left({x}+{y}-{1}\right)}^{{2}}$$
Solve differential equation $$2xy-9x^2+(2y+x^2+1)dy/dx=0$$, y(0)= -3
Give the correct answer and solve the given equation $$[x-y \arctan(\frac{y}{x})]dx+x \arctan (\frac{y}{x})dy=0$$
Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{\frac{{{y}}}{{{4}{x}}}}={3}{x},\ {y}{\left({2}\right)}={3}$$
Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}-{\left({\cot{{x}}}\right)}{y}={{\sin}^{{3}}{x}}$$