相关论文: Area constrained SOS models of interfaces
We consider a family of linearly viscoelastic shells with thickness $2\varepsilon$, clamped along a portion of their lateral face, all having the same middle surface $S=\mathbf{\theta}(\bar{\omega})\subset \mathbb{R}^3$, where…
We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group…
We present an asymptotic analysis of a mesoscale energy for bilayer membranes that has been introduced and analyzed in two space dimensions by the second and third author (Arch. Ration. Mech. Anal. 193, 2009). The energy is both non-local…
The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and…
We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
We calculate the temperature dependent condensate density $\rho^0 (T)$ of interacting bosons in three dimensions using the functional renormalization group (FRG). From the numerical solution of suitably truncated FRG flow equations for the…
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…
We present a rigorous proof of the Spacetime Penrose Inequality relating the ADM mass to the area of trapped surfaces in asymptotically flat initial data sets satisfying the dominant energy condition. The main theorem establishes that the…
The interfacial instability in a two-phase mixing layers between parallel gas and liquid streams is important to two-phase atomization. Depending on the inflow conditions and fluid properties, interfacial instability can be convective or…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We have obtained an exact expression for the phase-space volume corresponding to a microcanonical ensemble of systems under center of mass, total linear and angular momenta conservation constraints, and arbitrary constraints on the…
We report a numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of Helfrich. Two kinds of phantom tethered membrane models are studied via the…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L,…
We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the…
A general scheme has been proposed to study the critical behaviour of integrable interaction-round-a-face models with fixed boundary conditions. It has been shown that the boundary crossing symmetry plays an important role in determining…
We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the…
We present a large $q$ expansion of the 2d $q$-states Potts model free energies up to order 9 in $1/\sqrt{q}$. Its analysis leads us to an ansatz which, in the first-order region, incorporates properties inferred from the known critical…
A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS…