Search results for "boundary"
showing 10 items of 1626 documents
Interface Localization-Delocalization in a Double Wedge: A New Universality Class with Strong Fluctuations and Anisotropic Scaling
2002
Using Monte Carlo simulations and finite-size scaling methods we study ``wetting'' in Ising systems in a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ pore with quadratic cross section. Antisymmetric surface fields ${H}_{s}$ act on the free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces of the opposing wedges, and periodic boundary conditions are applied along the $y$ direction. In the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$, ${L}_{y}/{L}^{3}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$, the system exhibits a new type of phase transition, which is the analog of the ``filling transition'' that occurs in a single wedge. It is charac…
The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers
1989
Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the …
Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution
1993
We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest…
Fluids in extreme confinement.
2012
For extremely confined fluids with two-dimensional density $n$ in slit geometry of accessible width $L$, we prove that in the limit $L\to 0$ the lateral and transversal degrees of freedom decouple, and the latter become ideal-gas-like. For small wall separation the transverse degrees of freedom can be integrated out and renormalize the interaction potential. We identify $n L^2 $ as hidden smallness parameter of the confinement problem and evaluate the effective two-body potential analytically, which allows calculating the leading correction to the free energy exactly. Explicitly, we map a fluid of hard spheres in extreme confinement onto a 2d-fluid of disks with an effective hard-core diame…
Critical Wetting and Interface Localization—Delocalization Transition in a Double Wedge
2004
Using Monte Carlo simulations and finite-size scaling methods we study “wetting” in Ising systems in a L x L x L y pore with quadratic cross section. Antisymmetric surface fields H s act on the free L x L y surfaces of the opposing wedges, and periodic boundary conditions are applied along the y-direction. Our results represent the first simulational observation of fluctuation effects in three dimensional wetting phenomena and corroborate recent predictions on wedge filling. In the limit L → ∞ L y /L 3 = const the system exhibits a new type of phase transition, which is the analog of the “filling transition” that occurs in a single wedge. It is characterized by critical exponents α = 3/4, β…
First-order phase transitions investigated by use of a Monte Carlo interface method
1992
We investigate first-order phase transitions on unfrustrated antiferromagnetic Potts models in two and three dimensions by estimating the interface free energy by use of a Monte Carlo method. Even for strong first-order transitions the occurrence of hysteresis is circumvented and our method allows for an accurate determination of ${\mathit{T}}_{\mathit{c}}$ by locating a \ensuremath{\delta}-function-shaped peak in the energy difference between configurations with and without an interface.
The parameter identification in the Stokes system with threshold slip boundary conditions
2020
The paper is devoted to an identification of the slip bound function g in the Stokes system with threshold slip boundary conditions assuming that g depends on the tangential velocity 𝑢𝜏 . To this end the optimal control approach is used. To remove its nonsmoothness we use a regularized form of the slip conditions in the state problem. The mutual relation between solutions to the original optimization problem and the problems with regularized states is analyzed. The paper is completed by numerical experiments. peerReviewed
Unusual Optical Properties of the Dense Nonequilibrium Plasma
2006
A concise overview of new optical properties of dense nonequilibrium plasma formed on the solid state target boundary is given. In this chapter, we describe phenomena such as the third harmonic generation in the skin layer, collisionless electron heating in the high frequency skin-effect regime, absorption, and reflection and transmission of radiation by a plasma with anisotropic electron distribution.
High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex array
2008
Numerical solutions of Prandtl’s equation and Navier Stokes equations are considered for the two dimensional flow induced by an array of periodic rec- tilinear vortices interacting with an infinite plane. We show how this initial datum develops a separation singularity for Prandtl equation. We investigate the asymptotic validity of boundary layer theory considering numerical solu- tions for the full Navier Stokes equations at high Reynolds numbers.
Oscillatory Solutions of Boundary Value Problems
2016
We consider boundary value problems of the form $$\displaystyle\begin{array}{rcl} & x'' = f(t,x,x'), & {}\\ & x(a) = A,\quad x(b) = B,& {}\\ \end{array}$$ assuming that f is continuous together with f x and fx′. We study also equations in a quasi-linear form $$\displaystyle{x'' + p(t)x' + q(t)x = F(t,x,x').}$$ Introducing types of solutions of boundary value problems as an oscillatory type of the respective equation of variations, we show that for a solution of definite type, the problem can be reformulated in a quasi-linear form. Resonant problems are considered separately. Any resonant problem that has no solutions of indefinite type is in fact nonresonant. The ways of how to detect solut…