Conditions Definition and 978 Threads

I'm modelling a system with a nanosized semiconductor in 1d, inside which I want to find the electrostatic potential. Having found this I am unsure what boundary conditions to put on this, when it is connected to a metal on one side and to vacuum on the other. So far I have put that it is...

Homework Statement The scenario is a pendulum of length l and mass m2 attached to a mass of m1 which is allowed to slide along the horizontal with no friction. The support mass moves along in the X direction and the pendulum swings through the x-y plane with an angle θ with the vertical. After...

Let H be a real-valued function of two real variables with continuous first partial derivatives. If h(z)=h(x+i y)= u(x,y)+iv(x,y)is holomorphic in a region V, and H(u,v)=0. Find a condition on H under which one can conclude that h is a constant . Of, course H is the zero function can do the job...

Sorry about the title, had a hard time trying to fit the question on the given space. The question is quite simple : If F = F(x_1,...,x_n,t) , Under what conditions is \frac{d }{dt} \frac{\partial F }{\partial xi} = \frac{\partial }{\partial xi} \frac{dF }{dt} true?

Homework Statement Given 9 good light bulbs and 4 defective light bulbs, how many ways can you select 3 such that you get exactly 1 defective bulb? Homework Equations C(n,r) The Attempt at a Solution I understand total ways to select is C(13,3)=286, and that total ways to select only good...

Currently in my C++ program I have something like if (A){ do thing 1; } if (A && B){ do things 1 and 2; } if (A && B && C){ do things 1 and 2 and 3; } and so on. Unfortunately this has to be done for a very large sample and it takes quite a long time. I was just wondering if it's more...

Homework Statement A redox titration is carried out by adding Purple KMnO4 solution from a burette to a solution of H2O2 in a flask. Which of the following would occur in the flask before the equivalence point is reached? The answer is: The solution is colorless and O2 is formed. The other...

A mass is tied to a rope, that rope is attatched to a pole coming out of the screen. The pole is being moved by a person to cause the mass to rotate in a verticle circle at constant speed. A second pole coming out of the screen is introduced within the radius. The second pole interacts with the...

I know that an atom can become excited in one of two ways: by absorbing some energy from a source of electromagnetic radiation or by colliding with some other particle—another atom, for example, but my question is about the second part. So I want to know how and in what conditions (pressure...

Homework Statement Find parametric equations for the line through P1 and P2 and also for the line segment joining those points. Also find the conditions for the parametric equations. a) P1(0, 2) and P2(-4,-4) b) P1(7,-3,9) and P2(7, -3, 1)Homework Equations Equation of a line (Vector...

My question is about Force Free fields in the study of plasma stability (in MHD regime): Consider an isolated ideal plasma in an equilibrium state (where the effect of selfgravity is negligible), from the Navier-Stokes equation we get that: $$\vec{\nabla} P = \frac{1}{c} \vec{J} \times...

Homework Statement Consider the homogeneous Neumann conditions for the wave equation: U_tt = c^2*U_xx, for 0 < x < l U_x(0,t) = 0 = U_x(l, t) U(x,0) = f(x), U_t(x,0) = g(x) Using the separation of variables, find a nontrivial solution of (1). Homework Equations Separation of variables The...

Hi there, I'm solving the equation for the transverse vibrations of a Euler-Bernoulli beam fixed at both ends and subject to axial loading. It's a similar problem to that described by Rao on page 355 of his book "Vibration of Continuous Systems" (Google books link), except the example he uses...

Hello guys, I'd just like to ask how can I formulate transfer function of second order differential system when I don't have zero initial conditions? the equation is = y''(t) + B/m*y'(t) + k/m*y(t) = g y(0)= -L don't care what parameters mean .. it's supposed to be solved in general Thank...

The ODE is $y'' + 4y' - 12y = 0$, I get $y = C_1e^{-6x} + C_2e^{2} $ The initial conditions are y(0) = 1, y(1)=2 - which gives me $C_1 = 1-C_2$ and $C_2 = \frac{2e^{6}-1}{e^{8}-1} $ This just looks more messy than book exercises normally are, and when I laboriously substitute back into the...

I know that an atom can become excited in one of two ways: by absorbing some energy from a source of electromagnetic radiation or by colliding with some other particle—another atom, for example, but my question is about the second part. So I want to know how and in what conditions (pressure...

Hello. I'm trying to wrap my head around how Lagrangians work in classical field theory. I have a book that is talking about the gauge invariance of the Lagrangian: \mathscr{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-J^\mu A_\mu. It shows that we can replace A^\mu with A^\mu+\partial^\mu\chi for...

Firstly, my main question boils down to speaking about the initial conditions and boundary conditions. I was given: $$ u(0,y,t) = u(\pi,y,t) = u(x,0,t) = u(x,\pi,t) = 0 $$ but then the initial condition was: $$ u(x,y,0) = 1 $$ Aren't the initial and boundary conditions inconsistent in such...

The Euler-Lagrange equations give a necessary condition for the action be extremal given some lagrangian which depends on some function to be varied over. The basic form assumes fixed endpoints for the function to be varied over, but we can extend to cases in which one or both endpoints are free...

Homework Statement Nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if (e) Hal or Ida (but not both) are in the picture? (f) Ed and Gail are in the picture, standing...

Homework Statement Complete a free body diagram for the truss structure with a weight attached to node 2 (this is known as 151N) Homework EquationsThe Attempt at a Solution I have attached my Free Body Diagram The diagram is to display what is know at the start of the problem before working...

I am trying to solve the differential equation ##\frac{d^{2}y}{dr^2}+(\frac{1}{r}+1)y=0## with the boundary conditions ##y(r) \rightarrow r \frac{dy}{dr}(0)## as ##r \rightarrow 0## and ##y(r) \rightarrow \sin(kr+\delta)## as ##r \rightarrow \infty##. I know that the shooting method is the...

Hi! I can't understand how to implement boundary conditions in a 2D axisymmetrical model. How should be the value of pressure, x-velocity and y-velocity at the axis of symmetry? Thank you!

I want to model the diffusion-controlled combustion of a small carbon particle. The system I want to model is similar to this one However, I'm not going to use the stagnant gas film model as shown in the figure, since I lack data for the film thickness, and I want to evaluate the problem...

Right now I think there's 118 elements. If somewhere in space it was a certain temperature, with certain pressure, and other certain factors, could there be more elements. Let's say these conditions are too extreme to be made on Earth like a Trillion degrees Celsius. So if there were there...

Hello, Can anyone help me find the boundary conditions of the below given beam please. Its a clamped-free beam but the overhanging sectiona and the mass makes it confusing. Actually I am puzzled about finding the initial conditions.

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 7.1 Chain Conditions (for modules) ... I need some help in order to gain a full understanding of some remarks made in AMA on page 526 on modules in the context of chain conditions and...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 7.1 Chain Conditions (for modules) ... I need some help in order to gain a full understanding of some remarks made in AMA on page 526 on modules in the context of chain conditions and...

1. The problem statement, all variables and given/know In rural communities where landowners have their own water wells, large tanks are used to store water, which is pressurized by a sealed “air cushion”. Water is pumped intermittently from the well to restore the tank supply when the level is...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help with understanding a feature of the Theorem...

It is known that f"x>0,f(x)=f(-x),then which is correct? f(0)<f(1); f(4)-f(3)<f(6)-f(5); f(-2)<(f(-3)+f(-1))/2 Can I simply use y=x^2 to conclude that only the third is incorrect? Thx!

I have a horizontally supported cylindrical tube that is fixed at both ends. I modeled half of it to run the simulation on in Abaqus. The only load that it has is its weight. What I get confused at with cylindrical geometry is applying the load. How should I apply the gravitational load and at...

Hello, PF! Recently, while reading chapter 10 (microscopic energy balances) of the second edition of BSL, I found a minor discrepancy which is confusing me, especially when considering the mathematical analogies of heat and mass transfer. In section 10.1, the authors introduce Newton's law of...

I want to know how this integral will equal zero? I know that Ψ will fall to zero as x goes to infinity and i know that Ψ must fall to zero very quickly , Ψ must fall to zero faster than 1/√|x| all of this will help evaluating this integral i tried to solve it as follows The first term...

How to find value of integration constant?I know with the help of boundary conditions,but How boundary conditions help in finding integration constant?

I want to verify whether I am correct .As the title suggests It is about point where potential is zero (point other than infinity) Note:x is distance of neutral point from charges Firstly,I would like to ask Is coordinate system necessarily be there 1) If there are two positive charges for the...

Homework Statement Under what conditions is \left\langle{{\mathbf{x} \cdot \mathbf{p}}}\right\rangle a constant. A proof of the quantum virial theorem starts with the computation of the commutator of \left[{\mathbf{x} \cdot \mathbf{p}},{H}\right] . Using that one can show for Heisenberg...

Hello, I have a question regarding the solution to a second order 'mass-spring-damper' system. Over the years, I have gotten familiar with the idea of system damping in the sense of under damped, over damped, and critically damped systems. However, I've began looking closer at the solution to...

Suppose y is a positive vector. Let p and x be two positive matrices with N rows, where ##p_j## and ##x_j## denotes the j:th row in these matrices, so that j = 1,…,N. Does the following hold: \inf_{k=1,...,N} [\sup_{l=1,...,N} [p_k(y-x_k)]] = \inf_{k=1,...,N} [p_k(y-x_k)] where ##p_k(y-x_k)##...

Mod note: Fixed the broken LaTeX in the following, and edited the difference quotient definition of f'(z). The following is from a mathematical introduction to a physics book: "The real part u and the imaginary part v of w=u+i v are functions of the two variables x and y. Nevertheless, two...

Hi, We normally use a simple symmetry argument to show that the probability of each outcome of a throw of a fair, cube-shaped die is 1/6. However, is it possible to actually model the physics of the throw and show that the probabilities are 1/6? Since this is classical physics, the outcome can...

I am reading Jackson Electrodynamics (section 1.10 in 3rd edition) and he is discussing the Poisson eqn $$\nabla^2 \Phi = -\rho / \epsilon_0$$ defined on some finite volume V, the solution using Greens theorem is $$\Phi (x) = \frac{1}{4 \pi \epsilon_0} \int_V G(x,x') \rho(x')d^3x' +\frac{1}{4...

I've forgotten a lot of field theory so I've been rereading it in a couple of electric field theory textbooks. What seems like a simple problem falls between the cracks. I hope some readers can help - it will be appreciated. My application seems simple (solution will require numerical FEA but...

Hi Everyone, I had a quick question. If you have an IVP ODE and you solve for the general solution first and you had fractions in it, could you multiply by a number to make it "easier" (whole number, rather than involving fractions) without violating the initial conditions? Thanks

I am working with a fixed fixed bar with a distributed axial load to the right as w(x)=CX/L. I am having a hard time determining the force boundary conditions. I know that U(0)=0 and U(L)=0. However, I need to come up with something in regards to U'(Value). Any help would be appreciated.

Hi, I have two coupled differential equations d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2) d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda) where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions...

Consider the heat equation dT/dt - aΔT + v⋅∇T = S where S is a source term dependent of the radiation intensity I and the temperature T. The fluid velocity v is prescribed. We also consider the radiative transfer equation describing the radiative intensity I(x,ω,t) where ω is the ray direction...

1) Are there any ways to control the impulse in an collision in a lab condition? I.e. if I set an object connected to a spring and try to hit a ball using the object, are there any ways to control the impulse of the collision? 2) How to detect the change from slipping to pure rolling...

I'm currently a mechanical engineering student and many courses that I take involve topics that have multiple conditions. For instance if event "A" happens then apply Table "a" or Equation "aa". It becomes difficult to solve problems when topics have multiple conditions especially when similar...

Shouldn't the ΔG° partial pressure of the components be based on the K? Where ΔG°=-RTlnK such that K is based on the partial pressures of the gas involved? If we were to set the partial pressure to be 1bar each then every reaction having the same stoichiometric proportion of reactants and...