Related papers: Shape Coherence and Finite-Time Curvature Evolutio…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
We construct a FLRW universe considering an anisotropic scaling between space and time at extremely high and low energies only. In this context, Friedmann equations contain an additional term arising from spatial curvature which implements…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…
Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and…
The evolution of observable quantities of finite quantum systems is analyzed when the latter are subject to nondestructive measurements. The type and number of measurements characterize the level of decoherence produced in the system. A…
We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to…
We study the evolution of non-linear spherically symmetric inhomogeneities in string cosmology. Friedmann solutions of different spatial curvature are matched to produce solutions which describe the evolution of non-linear density and…
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…
In this paper, we study a new area-preserving curvature flow for closed convex planar curves. This flow will decrease the length of the evolving curve and make the curve more and more circular during the evolution process. And finally, the…
Quantum coherence reflects the origin of quantumness and might be capable of extracting the subtle nature of a system. We investigate the ground-state coherence and steered coherence in the Lipkin-Meshkov-Glick model and show that they…
We show that in the limit of strongly interacting environment a system initially prepared in a Decoherence Free Subspace (DFS) coherently evolves in time, adiabatically following the changes of the DFS. If the reservoir cyclicly evolves in…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…
Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid…
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…