scholarly journals Non-universal Casimir Forces at Approach to Bose–Einstein Condensation of an Ideal Gas: Effect of Dirichlet Boundary Conditions

2020 ◽  
Vol 181 (3) ◽  
pp. 944-951
Author(s):  
M. Napiórkowski ◽  
J. Piasecki ◽  
J. W. Turner
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Ideal Gas ◽  
Einstein Condensate ◽  
Dirichlet Boundary Conditions ◽  
Einstein Condensation ◽  
Casimir Forces ◽  
Leading Term ◽  
Bose Einstein

Abstract We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose–Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is $$\sim 1/D^{2}$$ ∼ 1 / D 2 with a non-universal amplitude. The next order correction is $$\sim \ln D/D^3$$ ∼ ln D / D 3 . These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is $$\sim 1/D^3$$ ∼ 1 / D 3 with a universal amplitude. We associate this discrepancy with the D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.

On the Number of Solutions to Semilinear Boundary Value Problems

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Markus Kunze ◽  
Rafael Ortega
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Upper Bound ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Number Of Solutions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

AbstractWe consider semilinear elliptic problems of the form Δu + g(u) = f(x) with Neumann boundary conditions or Δu+λ1u+g(u) = f(x) with Dirichlet boundary conditions, and we derive conditions on g and f under which an upper bound on the number of solutions can be obtained.

scholarly journals Abelian mirror symmetry of $$ \mathcal{N} $$ = (2, 2) boundary conditions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Mirror Symmetry ◽  
Dirichlet Boundary ◽  
Triangular Matrix ◽  
Neumann Boundary ◽  
Dirichlet Boundary Conditions ◽  
Verma Modules ◽  
Abelian Gauge ◽  
Mirror Theory

Abstract We evaluate half-indices of $$ \mathcal{N} $$ N = (2, 2) half-BPS boundary conditions in 3d $$ \mathcal{N} $$ N = 4 supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-indices perfectly match with each other. We find that a naive mirror symmetry between the exceptional Dirichlet boundary conditions defining the Verma modules of the quantum Coulomb and Higgs branch algebras does not always hold. The triangular matrix obtained from the elliptic stable envelope describes the precise mirror transformation of a collection of half-indices for the exceptional Dirichlet boundary conditions.

scholarly journals On the abundance of supersymmetric strings in AdS 3 x S 3 x S 3 x S 1 describing BPS line operators

2021 ◽  
Author(s):  
Diego H Correa ◽  
Victor I Giraldo-Rivera ◽  
Martín Lagares
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Open String ◽  
Neumann Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Open Strings ◽  
Straight Line ◽  
Fermionic Fields

Abstract We study supersymmetric open strings in type IIB $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed R-R and NS-NS fields. We focus on strings ending along a straight line at the boundary of $AdS_3$, which can be interpreted as line operators in a dual CFT$_2$. We study both classical configurations and quadratic fluctuations around them. We find that strings sitting at a fixed point in $S^3 \times S^3 \times S^1$, i.e. satisfying Dirichlet boundary conditions, are 1/2 BPS. We also show that strings sitting at different points of certain submanifolds of $S^3 \times S^3 \times S^1$ can still share some fraction of the supersymmetry. This allows to define supersymmetric smeared configurations by the superposition of them, which range from 1/2 BPS to 1/8 BPS. In addition to the smeared configurations, there are as well 1/4 BPS and 1/8 BPS strings satisfying Neumann boundary conditions. All these supersymmetric strings are shown to be connected by a network of interpolating BPS boundary conditions. Our study reveals the existence of a rich moduli of supersymmetric open string configurations, for which the appearance of massless fermionic fields in the spectrum of quadratic fluctuations is crucial.

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.

Effects of Pressure Boundary on Dynamic Torque Behavior of Hydroviscous Drive

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Jianzhong Cui ◽  
Jun Liu ◽  
Fangwei Xie ◽  
Cuntang Wang ◽  
Pengliang Hou
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Pressure Profile ◽  
Neumann Boundary Conditions ◽  
Torque Control ◽  
Dirichlet Boundary Conditions ◽  
Squeeze Film ◽  
Soft Start

The object of this work is to investigate the effect of the change of film pressure resulting from axial squeeze-film motion between driving and driven disks on the performance of hydroviscous drive (HVD). A simplified mathematical model of the steady and laminar flow between parallel disks is established with consideration of three kinds of pressure boundary conditions. Some analytical solutions of film thickness, rotate speed of driven disk, viscous torque, and total torque are obtained. The numerical results show that the torque response depends on the relationship between the inlet pressure and the outlet pressure when considering the Dirichlet boundary conditions. The soft-start under Dirichlet boundary conditions and Mixed boundary conditions reflects the constant-torque startup and torque control startup, respectively. Compared with the two boundary conditions above, the soft-start under pressure profile boundary from Neumann boundary conditions has advantages for speed regulation. The effects of the ratio of inner and outer radius on the torque profiles and soft-start time are mainly related to Dirichlet boundary conditions and pressure profile boundary from Neumann boundary conditions.

The Influence of Dirichlet Boundary Conditions on the Dynamics for a Diffusive Predator–Prey System

2019 ◽  
Vol 29 (09) ◽  
pp. 1950113
Author(s):  
Jun Jiang ◽  
Jinfeng Wang ◽  
Yingwei Song
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Linear Instability ◽  
Dirichlet Boundary Conditions ◽  
Homogeneous State ◽  
Predator Prey ◽  
Prey System ◽  
Homogeneous Dirichlet Boundary Conditions

A reaction–diffusion predator–prey system with homogeneous Dirichlet boundary conditions describes the lethal risk of predator and prey species on the boundary. The spatial pattern formations with the homogeneous Dirichlet boundary conditions are characterized by the Turing type linear instability of homogeneous state and bifurcation theory. Compared with homogeneous Neumann boundary conditions, we see that the homogeneous Dirichlet boundary conditions may depress the spatial patterns produced through the diffusion-induced instability. In addition, the existence of semi-trivial steady states and the global stability of the trivial steady state are characterized by the comparison technique.

scholarly journals Long-term behaviour in a chemotaxis-fluid system with logistic source

2016 ◽  
Vol 26 (11) ◽  
pp. 2071-2109 ◽  
Author(s):  
Johannes Lankeit
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Logistic Source ◽  
State Formula ◽  
Bounded Smooth ◽  
Homogeneous Dirichlet Boundary Conditions

We consider the coupled chemotaxis Navier–Stokes model with logistic source terms: [Formula: see text] [Formula: see text] [Formula: see text] in a bounded, smooth domain [Formula: see text] under homogeneous Neumann boundary conditions for [Formula: see text] and [Formula: see text] and homogeneous Dirichlet boundary conditions for [Formula: see text] and with given functions [Formula: see text] satisfying certain decay conditions and [Formula: see text] for some [Formula: see text]. We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state [Formula: see text].

Distribution of quantum states in enclosures of finite size: II

1991 ◽  
Vol 69 (11) ◽  
pp. 1342-1361
Author(s):  
J. Hugo Souto ◽  
A. N. Chaba
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Finite Size ◽  
Neumann Boundary ◽  
Summation Formula ◽  
Quantum States ◽  
Dirichlet Boundary Conditions ◽  
Actual Number ◽  
Mathematical Functions ◽  
Poisson’S Summation Formula

By making use of the modified form of Poisson's summation formula, we calculate the expression for the number of eigenstates, N(K), with eigenvalues [Formula: see text] of a particle in spherical and cylindrical enclosures of finite size, and with its wave-function subject to Dirichlet boundary conditions and Neumann boundary conditions at the walls of the container. We also obtain the oscillatory terms in addition to the important nonoscillatory terms already known and compare our results with the actual number of such states computed from the tables of the zeros of the relevant special mathematical functions. The inclusion of these oscillatory terms improves the accuracy of the expressions in all cases, especially in the case of the cylinder, where these are quite significant. Some possible applications of the results obtained here are also indicated.

scholarly journals Ensemble dependence of critical Casimir forces in films with Dirichlet boundary conditions

2019 ◽  
Vol 99 (6) ◽  
Author(s):  
Christian M. Rohwer ◽  
Alessio Squarcini ◽  
Oleg Vasilyev ◽  
S. Dietrich ◽  
Markus Gross
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Casimir Forces
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