Conditions Definition and 1000 Threads

In calculus of variations, extremizing functionals is usually done with Dirichlet boundary conditions. But how will the calculations go on if Neumann boundary conditions are given? Can someone give a reference where this is discussed thoroughly? I searched but found nothing! Thanks

The Schwarzschild equation of motion, where coordinate length is differentiated by proper time is as far as I know r''(t) = -\frac{G\cdot M}{r(t)^2} + r(t)\cdot{\theta}'(t)^2 - \frac{3\cdot G\cdot M\cdot{\theta}'(t)^2}{c^2} {\theta}''(t) = -2\cdot r'(t)/r(t)\cdot{\theta}'(t) Now the question...

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] I know dV=1/C∫idt and that we integrate the voltage from V to V0. What I don't get are the boundary conditions for t - How do we get what we get in the parenthesis? My closest assumption is that the t/T values refer to the...

I'd like to read some articles, papers, or whatever scientific there is about the prospects and impacts of climate change for professional ground based astronomy and observatory sites. In particular, which locations which are now among the most suitable sites for observatories - especially...

Suppose we are solving a diffusion equation. ##\frac{\partial}{\partial t} T = k\frac{\partial^2}{\partial x^2} T## On the domain ##0 < x < L## Subject to the conditions ##T(x,0) = f(x) ## and ##T = 0 ## at the end points. My question is: Suppose we solve this with some integration scheme...

For the case of a particle attached to an inextensible string which is hanging at rest and then provided an impulse horizontally, what conditions must the system meet in order to allow for COMPLETE circular motion. I am well aware the tension at the apex of the motion must be satisfy one of the...

If I am doing a simple, static analysis on something like a table, or tripod with a vertical force acting on it, what support condition do I assign to the base at which the legs contact the ground? I feel like it is incorrect to specify this as "fixed," since that would be like saying the legs...

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law essentially uses the fact that, if ##\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3##, ##\boldsymbol{J}\in C_c^2(\mathbb{R}^3)##, is a compactly supported twice continuously differentiable field...

Mathematically, what conditions must a B-field that obeys the Biot-Savart Law satisfy before it will obey Ampere's Law? Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?

Homework Statement Find the Green's function $G(t,\tau)$ that satisfies $$\frac{\text{d}^2G(t,\tau)}{\text{d}t^2}+\alpha\frac{\text{d}G(t,\tau)}{\text{d}t}=\delta(t-\tau)$$ under the boundary conditions $$G(0,\tau)=0~~~\text{ and }~~~\frac{\text{d}G(t,\tau)}{\text{d}t}=0\big|_{t=0}$$ Then...

Homework Statement Derive the basic relationship that the Antoine equation represents. Most importantly, explain the underlying condition when the Antoine equation applies and the underlying assumptions for the Antoine equation to be valid. Homework Equations Clausius-Clapeyron Equation...

The equation is Uxx + Uyy = 0 And domain of solution is 0 < x < a, 0 < y < b Boundary conditions: Ux(0,y) = Ux(a,y) = 0 U(x,0) = 1 U(x,b) = 2 What I've done is that I did separation of variables: U(x,y)=X(x)Y(y) Plugging into the equation gives: X''Y + XY'' = 0 Rearranging: X''/X = -Y''/Y = k...

In various explanations of the event horizon which do not invoke the existence of a firewall (thereby upholding the dictum that an observer would not notice any difference upon passing the event horizon until she looked out the window), one uses the concept of a theoretical observer passing the...

This isn't homework but could be labeled "textbook style" so I'm posting it here. Homework Statement I'm trying to solve \frac{\partial^2 u} {\partial x^2} +\frac{\partial^2 u} {\partial y^2}=0 on the domain x \in [-\infty,\infty], y\in[0,1] with the following mixed boundary conditions...

Hello, I want to know if there exist any result in literature that answers my question: Under which conditions on the real valued matrix ## R ## (symmetric positive definite), the first argument results in and guarantees the second one: 1) for real valued matrices ##A, B, C,## and ## D ## with...

Homework Statement I want to find conditions over A,B,C,D to observe a stable limit cycle in the following system: \frac{dx}{dt} = x \; (A-B y) \hspace{1cm} \frac{dy}{dt} = -y \; (C-D x) Homework Equations Setting dx/dt=0 and dy/dt=0 you can find that (C/D , A/B) is a fixpoint. The Attempt...

Hello! (Wave) Does it suffice to show that the triple product is 0? If we show that $a \cdot (b \times c)=0$ we will have that $a$ is orthogonal to $b \times c$. $b \times c$ is orthogonal to both $b$ and $c$, so we will have that $a$ will be parallel to $b$ and $c$. Right? But why does...

Hello, I am curious as to how one appropriately matches an interior and exterior solution in GR, i.e. where the interior corresponds to the field of some finite spherical mass (perfect fluid sphere, for the Schwarzschild interior solution). Specifically, looking at both the Schwarzschild...

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...

I have the following limit to calculate under the assumption that ##\Re(x+y)>1##: Limit[Integrate[ 1/((1 + t^2)^n*(1 + I*t)^x (1 - I*t)^y), {t, -Infinity, Infinity}], n -> Infinity] I want to add the above assumption for integral, how to do it? does it even converge? Thanks.

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!