GGR252H1 Lecture Notes - Lecture 4: Voronoi Diagram, Demand Curve, Distance Decay

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coralcat810

3 Jan 2015

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Opportunities the point at which interaction reduces to zero and high cost of travel (dependent on gravity) Takes into account the gravity of the store and the competition. Diffusion: relocation diffusion (migration, contagious diffusion (diseases, hierarchical diffusion (fashion) In retail: organic growth (contagious) with acquisition and taking over. Considers cost of purchasing on top of transportation and time. Distance decay curve based on convenience and type of goods shopped for. Convenience goods: steep curve, identical, change, low value, frequent visits. Shopping goods: shallow curve (product monopoly), distinctive, high value, infrequent visits. Bottom hierarchy (convenience): closely space, selling basic goods, short travel distance. Top hierarchy (power nodes): small number of large regional shopping centres, higher order goods and travel far distances. Measurements: number of stores, size/centre, order of goods, frequency of consumer visit, distance travel, geographical spacing. Size, space, number of settlements examined to see if the place is large enough for service to be viable and if competition takes over.

Related Questions

A hard rubber ball, not affected by air resistance in its motion, is tossed upward from shoulder height, falls to the sidewalk rebounds to a smaller height, and is caught on its way down again. This motion is represented in Figure OQ2.17, where the successive positions of the ball A through E are not equally spaced in time. At point D the center of the ball is at its lowest point in the motion. The motion of the ball is along a straight, vertical line, but the diagram shows successive positions offset to the right to avoid overlapping. Choose the positive y-direction to be upward. (a) Rank the situations A through E according to the speed of the ball at each point, with the largest speed first. (b) Rank the same situations according to the acceleration of the ball at each point. (In both rankings, remember that zero is greater than a negative value. If two values are equal, show that they are equal in your ranking.)

olivecaribou528

Huygens' principle (first described by the Dutch scientist Christiaan Huygens in 1678) uses geometry to determine the shape of a wavefront at a time t, given some initial wavefront at an earlier time. This can be constructed by imagining that the initial wavefront is a source of wavelets that propagate from each point at the speed of light. From this principle, one can determine the angles of reflection and refraction by considering the speed of light at each point on the wavefront. In this problem, we will explore some of these concepts.

Part A

First, let's look at a plane wave that is incident on a flat piece of material with an index of refraction n. Part of the light is transmitted through the material and part of it is reflected. For the moment, let's just look at the part that is transmitted. At time t=0, the wavefront is a distance d away from the surface of the material. At time t=t₁, the wavefront is at the position of the material interface. Use the Huygens' principle to determine how far into the material (d') the wavefront has propagated by time t=2t₁.

Express your answer in terms of the variables n, t₁, and the speed of light in a vacuum c.

Note that there would be no change in the direction of the wavefront at any point because the wavefront encountered the material interface at the same time at all points. Thus, all of the individual wavefronts all propagated at the same speed, thereby maintaining the flat wavefront.

Now, instead of having a flat wavefront propagating normal to the material interface, we have a flat wavefront propagating toward the material at an angle of 55° to the axis perpendicular to the material interface. In this part, we will look at the relative positions of a few points—A, B, and C—on the wavefront to illustrate Huygens' principle. (Intro 1 figure) Point C touches the vacuum/material interface at time t=0 whereas point B is a distance d and point A is a distance 2d away from the interface.

Part B

What is the time t_B it will take for point B of the wavefront to encounter the vacuum/material interface?

Express your answer numerically to two decimal places in units of t₁ (the time it takes light to travel a distance d in a vacuum).

It should be noted that the accuracy of the method increases the smaller the distance is before making a new wavefront and redoing the wavelets. If you tried to just draw a large wavelet from point B, then it would hit the surface after only traveling a distance d. This large wavelet would make it difficult to visualize how to add up all of the other wavelets to make a coherent wavefront. As a result, one should just draw a line perpendicular to the wavefront at point B until it hits the surface, at which point the wavelets will change owing to the new index of refraction.

Part C

How far did point C go into the material interface in the time t=t_B that it took for point B to get to the interface? For this part we are looking for the distance traversed by the point C in the material (d_C).

Give your answer in terms of the time t_B, c, and n.

Part D

What is the new angle θ at which point C of the wavefront is propagating (relative to a line perpendicular to the vacuum/material interface)? Try to use the fact that you have a spherical wavefront propagating from t=0 at the point where C met the vacuum/material interface until time t_B when the wavefront at point B reached the interface.

Express your answer in terms of inverse trigonometric functions and n.

greenduck607

A coil of wire is connected to a power supply, and a currentruns in the coil. A single loop of wire is located near the coil,with its axis on the same line as the axis of the coil. The radiusof the loop is 2 cm.

At time t1 the magnetic field at the center of the loop, due to thecoil, is 0.4 T, in the direction shown in the diagram; the currentin the coil is constant.

(a) What is the absolute value of the magnetic flux through theloop at time t1?
Î¦ mag = T m2
(b) What approximations or assumptions did you make in calculatingyour answer to part (a)?

Check all that apply.

1.The magnitude of the magnetic field due to the coil is uniformover the area of the loop.
2.The magnetic field outside the loop is zero.
3. The magnetic field due to the coil is uniform in direction overthe area of the loop.

(c) What is the direction of the "curly" electric field inside thewire of the loop at time t1? (Remember that at this time thecurrent in the coil is constant.)
E = 0

At a later time t2, the current in the coil begins todecrease.

(d) Now what is the direction of the "curly" electric field in theloop?
counter-clockwise
At time t2 the rate of change of the magnetic field at the centerof the loop, due to the coil, is -0.36 T/s.
(e) At this time, what is the absolute value of the rate of changeof the magnetic flux through the loop?
|dÎ¦mag/dt| = T m2/s
(f) At this time, what is the absolute value of the emf in theloop?
|emf| = V
(g) What is the magnitude of the electric field at location P,which is inside the wire?
|E| = V/m
(h) Now the wire loop is removed. Everything else remains as it wasat time t2; the magnetic field is still changing at the same rate.What is the magnitude of the electric field at location P?
|E| = V/m

GGR252H1 Lecture Notes - Lecture 4: Voronoi Diagram, Demand Curve, Distance Decay

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