scholarly journals Green’s Functions with Oblique Neumann Boundary Conditions in the Quadrant

2020 ◽  
Author(s):  
S. Franceschi
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

scholarly journals Analytical Green’s functions for continuum spectra

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Eugenio Megías ◽  
Mariano Quirós
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Dirichlet Boundary ◽  
Green’S Functions ◽  
Neumann Boundary ◽  
Approximate Equation ◽  
New Physics ◽  
Dirichlet Boundary Conditions ◽  
Gauge Bosons ◽  
Linear Dilaton

Abstract Green’s functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension z, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS5, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to z → ∞. This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green’s functions (with a mass gap mg ∼ TeV and a continuum for s >$$ {m}_g^2 $$ m g 2 ) which could then be easily incorporated in the experimental codes. The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. All Green’s functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at s = $$ {M}_n^2 $$ M n 2 − iMnΓn, denoting a discrete (infinite) set of broad resonances with masses (Mn) and widths (Γn). For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation s = −4$$ {m}_g^2{\mathcal{W}}_n^2 $$ m g 2 W n 2 [±(1 + i)/4], where $$ \mathcal{W} $$ W n is the n-th branch of the Lambert function.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

Boundary conditions for Green's functions of spatially inhomogeneous superconducting systems

1988 ◽  
Vol 74 (3) ◽  
pp. 306-311 ◽  
Author(s):  
B. P. Leskov ◽  
A. N. Makeev ◽  
A. V. Svidzinskii
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spatially Inhomogeneous

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

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