Related papers: The nonlinear fragmentation equation
We introduce a model where an isotropic, dynamically-imposed stress induces fracture in a thin film. Using molecular dynamics simulations, we study how the integrated fragment distribution function depends on the rate of change and…
We solve the CCFM equation numerically in the presence of a boundary condition which effectively incorporates the non-linear dynamics. We retain the full dependence of the unintegrated gluon distribution on the coherence scale, and extract…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…
Different forms of non-linear equations which mimic parton saturation in the non-perturbative regime are examined. These equations lead to corresponding unitarization schemes in the impact parameter representation of the hadron scattering…
The dynamics of an impurity (or tracer particle) immersed in a dilute granular gas under uniform shear flow is investigated. A non-equilibrium phase transition is identified from an exact solution of the inelastic Boltzmann equation for a…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the…
Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase…
Utilizing a partitioning method based on equal (or unequal) probabilities -- without incorporating the alpha-cluster ($\alpha$-cluster) model -- allows for the derivation of diverse topological configurations of nuclear fragments resulting…
We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking…
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states.…
We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize…
We investigate the thermodynamical content of a cellular model which describes nuclear fragmentation as a process taking place in an excited disordered system. The model which reproduces very well the size distribution of fragments does not…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…