Related papers: Existence and Non-existence for Exchange-Driven Gr…
We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population based on the recent model proposed by Egu\'{\i}luz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)].…
In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance…
In this paper we prove the existence of global classical solutions to continuous coagulation-fragmentation equations with unbounded coefficients under the sole assumption that the coagulation rate is dominated by a power of the…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
We generalize the model of transition-metal nanocluster growth in aqueous solution, proposed recently [Phys. Rev. E \textbf{87}, 022132 (2013)]. In order to model time evolution of the system, kinetic equations describing time dependence of…
The late-time equilibrium behavior of generic interacting models is determined by the coupled hydrodynamic equations associated with the globally conserved quantities. In the presence of an external time-dependent drive, non-integrable…
Using the colour dipole picture for photon-nucleus interactions at small $x$ together with the Color Glass Condensate (CGC) effective theory, we demonstrate that the next-to-leading (NLO) order corrections to the cross-section for the…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
Employing the spherical collapse (SC) formalism, we investigate the linear evolution of the matter over-density for energy-momentum-squared gravity (EMSG), which in practical phenomenological terms, one may imagine as an extension of the…
We investigate the emergence of singular solutions in a non-local model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that the evolution depends strongly on the length scales of the…
We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear…
In this work, we analyze the Einstein-scalar-Gauss-Bonnet (EsGB) theory of gravity in a cosmological context using the formalism of dynamical systems. We obtain the equations of motion of the theory and introduce an appropriate set of…
The Glansdorff and Prigogine General Evolution Criterion (GEC) is an inequality that holds for macroscopic physical systems obeying local equilibrium and that are constrained under timeindependent boundary conditions. The latter, however,…
We study the phase space dynamics of the non-minimally coupled Metric-Scalar-Torsion model in both Jordan and Einstein frames. We specifically check for the existence of critical points which yield stable solutions representing the current…
We study global existence problems and asymptotic behavior of higher-dimensional inhomogeneous spacetimes with a compact Cauchy surface in the Einstein-Maxwell-dilaton (EMD) system. Spacelike $T^{D-2}$-symmetry is assumed, where $D\geq 4$…
We introduce and study a general framework for modeling the evolution of crack networks. The evolution steps are triggered by exponential clocks corresponding to local micro-events, and thus reflect the state of the pattern. In an…
In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the…
Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte…
This work examines the global dynamics of classical solutions of a two-stage (juvenile-adult) reaction-diffusion population model in time-periodic and spatially heterogeneous environments. It is shown that the sign of the principal…