Conditions Definition and 1000 Threads

Hi, I am a bit confused about the terminology used for the boundary conditions describing open and closed strings. For the open string, Ramond case: \psi^+(\sigma = \pi, t) = \psi^-(\sigma = \pi, t) Neveu-Schwarz case: \psi^+(\sigma = \pi, t) = -\psi^-(\sigma = \pi, t) Question 1: Is it...

I'm given a probability measure ##\mathbb P## on ##\Omega = \{f\in C([0,1],\mathbb R): \enspace f(0)=0\}## and told that ##\mathbb P## satisfies i.i.d. increments. I'm interested in the weakest additional conditions that will ensure that ##\mathbb P## describes a Brownian motion, i.e. that...

For a project in my 3rd year hydraulics course we have to design a water distribution network for a residential area using EPANET and optimizing it using GAWUP (GANEO). I have the entire network set up with all the peak flow demands set for each of the required nodes. Using GANEO I can easily...

Homework Statement I have an infinite plate of which two electrodes are attached at a distance ##2a## and the electric potential between them is ##U##. Now I have to find a function ##\phi (x,y)## that satisfies Laplace's equation ##\nabla ^2 \phi =0## and is equal to ##0## at all possible...

Hello, I am at present analyzing the electromagnetic interaction of a layer of paritcles in air when illuminated by an electromagnetic wave. This can be done by considering the layer of particles as an interface with surface current (as opposed to a 'normal' interface with Fresnel...

Hi, I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth. For example for...

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

Hi there Can anyone tell what is the meaning of boundary conditions for temperature distribution in a flowing viscous fluid in a pipe ? for example I need some one explane for me this: T = T1 at r = R, x<0 T = T0 at x = 0, r<R where T1 is a temperature of well and T0 is a temperature...

Hi everyone, first time post here. Sorry if this isn't the place to ask, but I'm looking to settle disagreement and thought someone here might have the knowledge to set me straight. This is a slightly off color question to start with, and my lack of expertise in any science is not helping the...

Hi all. Say we have a background inflaton field ##\varphi## and that we've integrated the background equation for ##\varphi##, ##H(\eta)##, and ##a(\eta)## up to the number of e-folds of inflation corresponding to ##\epsilon = 1## in the slow-roll parameter. We then wish to solve for the ##k##...

My A level Chemistry textbook defines Lattice Energy as "the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions"; a definition which I can't fully grasp because of the "standard conditions" part. How can gaseous ions exist under standard...

Hello, I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate. Question: How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$ Thanks.

Homework Statement Let ##f## be an entire function such that there exist ##z_0,z_1 \in \mathbb C##, ##\mathbb R##-linearly independent, with ##f(z+z_0)=f(z)## and#f(z+z_1)=f(z)## for all ##z \in \mathbb C##. Show that ##f## is constant. The attempt at a solution From the hypothesis, I know...

Hello! This is my first post to this excellent forum! I would like some help with this exercise: u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...

Hİ. How can we sure that the initial conditions , say, for a second-order linear equation must be unique which is also the uniqueness of the solution.

I need some help figuring out a problem dealing with lattices. The problem is this: Prove that any lower-bounded lattice satisfying the maximal condition is a complete lattice. I've been able to figure out some things so far. I know that a lattice is a meet- and join-semilattice, which...

Hi, Can anybody help me withg the following problem: A rectangular plate with points starting from top left corner and going clockwise:: A B C D. Sides CD and DA are simply supported, and a point force F is applied anywhere on the surface. I am looking for the bending stress distribution...

Hi, there Today, a friend came to me and asked the following questions and they made me confused. If the source is strong, the light has to be considered as wave, and the double-slit interference (DSI) can be interpreted, and the conditions for the DSI is (1) same frequencies, (2) parallel...

I was wondering about Earth and it's gravity and I came up with these 2 questions... 1.) What would Earth's gravity be if the Earth stopped spining? 2.) What would Earth's gravity be if the Earth stopped spining and there was no other stars or planets that interfered with there gravity...

Homework Statement Find B and C such that \emptyset \in C B \in C B \subset C The Attempt at a Solution B=\emptyset C=\{B\} It just does not look right. Any feedback?

I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases. Thank you.

hi pf! i was reading a sample problem in a text on ode's and came across a boundary condition that didnt really make sense to me. the physical scenario is: a liquid ##L## measured in moles/cubic meter (##mol / m^3##) is injected into a stream of water. ##L## is being injected at a rate...

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that is not grounded, then there will be (as long as I am dealing with static problems) no electric...

Homework Statement Part (a): List the boundary conditions Part (b): Show the relation for potential is: Part (c): Find Potential everywhere. Part (d): With a surface charge, where does the Electric field disappear? Homework Equations The Attempt at a Solution Part (a) Boundary conditions...

The Laplace of 1 is: $$\int_{0}^{\infty} 1 \exp(-st) dt = \left[ \frac{\exp(-st)}{-s} \right]_{0}^{\infty} = \frac{\exp(-s \infty) - \exp(-s 0)}{-s} = \frac{0 - 1}{-s} = \frac{1}{s}$$ It's result known, however, for this be true is assumed that s>0, because 0 = exp(-∞) = exp(-s∞). But we...

I don't really understand boundary conditions and I've been trying to research it for ages now but to no real avail. I understand what boundary conditions are, I think. You need them along with the initial conditions of a wire/string in order to describe the shape of motion of the string. I...

the boundary conditions on p are homogenous dirichlet on this equation where q(0,τ)=0 and q(l,t)=0 for all τ>0. the initial condition p(x,0)=p_o(x) also translates to an initial condition on p. how do i show what the new initial condition is on q

Homework Statement Let a,b,c be distinct real numbers satisfying a^3+b^3+6abc = 8c^3 then which of the following may be correct? A) a,c,b are in Arithmetic Progression B) a,c,b are in Harmonic Progression C) a+bω-2cω^2 =0 D) a+bω^2-2cω=0 The Attempt at a Solution I could prove...

Homework Statement A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by y(x, t). It is attached to a boundary at x = 0. The condition at the boundary is y+\alpha \frac{\partial y}{\partial x} =0 where \alpha is a constant. Write the...

Homework Statement I have been given a complex function I have been given a complex function \widetilde{U}(x,t)=X(x)e(i\omega t) Where X(x) may be complex I have also been told that it obeys the heat equation...

Questions about Green's functions for ODEs, jump conditions I'm having a hard time understanding Green's functions which have been introduced quite early on in the course, and which I think hasn't been well motivated. I can't find any other resource which explains this at this level (have only...

Homework Statement "The lift gradient of a wing under actual flight conditions is 0.1179 per degree. Calculate the lift-drag ratio of the wing with an angle of attak of 3 degrees?" Given is: altitude=5000 m velocity=225 m/s wing area S=149 m2 wing span b=34.5 m span efficiency factor e1=0.82...

Homework Statement Hello, I have to demonstrate that multiplying a differential equation: -d/dx[a(x)*d/dx{u(x)}]=f(x), 0<x<1 subject to u(0)=0 and u(1)=0. by some function v(x) and integrating over an interval [0,1], I get a new equation that can be used in an optimisation problem, that...

Hello all, I am currently in possession of two chemistry textbooks, Changs and Atkins, which I believe are both fairly new versions. Changs defines STP at 25 degrees Celsius and 1 atm, and Atkins defines STP at 25 degrees Celsius and 1 bar; I understand that numerically it would not make a...

The positive integers $a_1,\,a_2,\,\cdots,a_7$ satisfy the conditions $a_6=144$, $a_{n+3}=a_{n+2}(a_{n+1}+a_n)$, where $n=1,\,2,\,3,\,4$. Determine $a_7$.

Homework Statement How fast would a electric arc be when it ionizes through normal, unpressured air between say, two electrodes? Not the same as lightning as it is hypothetically from an artificial source. Homework Equations How would one calculate (please include your formula's and which...

Homework Statement Verify that diamond becomes more stable than graphite at approximately 15 kbars Homework Equations The Attempt at a Solution So, I understand that to show one substance is more stable than another at particular environmental conditions, I just have to show...

Homework Statement I am trying to extract the constant of integration after integrating the following stress equation (I got this by solving a system of ODEs for the upper and lower tablets (attached), quite tedious to paste it all here): σ = β * sinh(λx/2) * cosh( λ(L-x)/2 ) Where σ...

This is my first post so I hope this in the right place. I am fairly sure this is quite a straight forward question but I having trouble working out the details of it. "State the boundary conditions for an inviscid fluid at an impermeable fixed boundary x_3-h(x_1,x_3)=0 where we do...

How to solve this question. Please explain step by step.

Homework Statement Consider the RL circuit shown in the figure. Assume that the current ##i(t)## has reached a steady state with the switch at position ##A##. At time ##t = 0##, the switch is moved from position ##A## to position ##B##. http://imgur.com/dRIOrp0 If I use the image button...

Hi, it is easy solving these PDEs with the idealized homogeneous BCs they throw out in class, but I am having some difficulty solving the transient problem posed in the images below. I have tried working through it, but I don't have confidence in the result. I overlook the solution when the...

Homework Statement Let ##a>0## and y(x)=\left\{\begin{matrix} -x ;& x<-a\\ Cx^2+D;& -a<x<a\\ x;& x>a \end{matrix}\right. a) Find ##C## and ##D## so that ##y\in C^1(\mathbb{R})## b) For A>a calculate ##\int_{-A}^{A}(1-({y}')^2)dx## c) Is it possible to find ##C## and ##D## so that ##y\in...

Homework Statement Find the volume of an object bounded by x2 + y2 ≤ 1, x2 + z2 ≤ 1 and y2 + z2 ≤ 1. Homework Equations The Attempt at a Solution This stuff is very new to me (multiple integrals to find volume) so I am not entirely familiar with it. My first thought was to put...

How to show in details that the function |x| satisfies Dirichlet's conditions on [-\pi \pi].; I know the Dirichlet's conditions, but facing problems to apply it on the given function.

Hi I am tutoring a pupil in high-school out of necessity (no other teachers avail), while I am not so acquainted anymore with chemistry. The pupil showed me a question concerning the calculation of the reaction enthalpy which looked somewhat as follows: 1. Problem statement, all variables...

Burgers Equation Question -- cannot satisfy initial conditions Homework Statement Use characteristics to solve u_t+uu_x=0 on half line x≥0 with u(x,0)=x^2 Homework Equations NA The Attempt at a Solution I think I have an issue with the initial condition. So solving via...

Hi! :o Given then following problem: $$ \min [-x_1 - (x_2 -9)^2]$$ subject to $$4x_1^2+x_2^2 \leq 400$$ I have to find the solution using the KKT conditions. I have found that the solution is $(0,9)$. Is my result correct?

I'm working on a student design project building a multirotor UAV to host a sensor array. The airframe supports arm beams with motors producing thrust at the end, a battery, a flight controller, payload, ESC's and needs to be custom made so that it is of a size that can support large blades and...

Hello, I am looking to solve the 3D equation in spherical coordinates \nabla \cdot \vec{J} = 0 using the Ohm's law \vec{J} = \sigma \cdot (\vec{E} + \vec{U} \times \vec{B}) where \sigma is a given 3x3 nonsymmetric conductivity matrix and U,B are given vector fields. I desire the...