Related papers: A note on consistency conditions on dimer models
We consider three different continuum polymer models, that all depend on a tunable parameter r that determines the strength of the excluded-volume interactions. In the first model chains are obtained by concatenating hard spherocylinders of…
We discuss how orbital degeneracy, which is usually removed by a cooperative Jahn-Teller distortion, could under appropriate circumstances lead rather to a Resonating Valence Bond spin-orbital liquid. The key points are: i) The tendency to…
Existence and spatio-temporal symmetric patterns of periodic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays are studied under the Hartman-Nagumo growth conditions. The method is based…
We develop a general theory for linear stability of traveling waves of second order in time PDE's. More precisely, we introduce an explicitly computable index $\om^*\in (0, \infty]$ (depending on the self-adjoint part of the linearized…
There exists a class of gauge models incorporating a finite density of matter in which the Higgs mechanism is provided by condensates of gauge (or gauge and scalar) fields, i.e., there are vector condensates in this case. We describe vortex…
Recently, Dreyer and Duderstadt have proposed a modification of the Becker--Doering cluster equations which now have a nonconvex Lyapunov function. We start with existence and uniqueness results for the modified equations. Next we derive an…
We establish two results concerning a class of geometric rough paths $\mathbf{X}$ which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for $\mathbf{X}$ in $\alpha$-H\"older…
Starting from a travelling wave ansatz we show successively that the shape of a nonlinear excitation generally depends also on the 1st, 2nd, ... time derivative of the position X of the excitation. From the Hamilton equations we derive a…
We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of…
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One…
We show that if a numerical method is posed as a sequence of operators acting on data and depending on a parameter, typically a measure of the size of discretization, then consistency, convergence and stability can be related by a…
We extend the action for evolution equations of KdV and MKdV type which was derived in [Capel/Nijhoff] to the case of not periodic, but only equivariant phase space variables, introduced in [Faddeev/Volkov]. The difference of these…
Using tropical convexity Dochtermann, Fink, and Sanyal proved that regular fine mixed subdivisions of Minkowski sums of simplices support minimal cellular resolutions. They asked if the regularity condition can be removed. We give an…
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. By mapping lattice Boltzmann schemes to Finite Difference schemes, we…
Last passage percolation and directed polymer models on $\mathbb Z^2$ are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK…
We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two-…
This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector…
We study generalized scalar field models coupled to impurities in Minkowski spacetime with arbitrary dimensions. The investigation concerns a class of models that depends explicitly on the spacetime coordinates and also, it reveals the…
The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the $L^2\cap L^\infty$ orbital stability of a…
We study the stability of first-order dissipative spin-hydrodynamic frameworks. We considered two different first-order dissipative spin-hydrodynamic frameworks. The first one considers the spin chemical potential ($\omega^{\alpha\beta}$)…