Related papers: Transition fronts and their universality classes
This is a study of front dynamics in reaction diffusion systems near Nonequilibrium Ising-Bloch bifurcations. We find that the relation between front velocity and perturbative factors, such as external fields and curvature, is typically…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
We will discuss various aspects of thermalization, chaos and hydrodynamics in one dimensional classical Hamiltonian systems. We study two problems. First, we will revisit the Fermi-Pasta-Ulam-Tsingou (FPUT) problem in order to understand…
To optimize the design of STT-MRAM (spin-transfer torque magnetic random access memory), it is necessary to be able to predict switching (error) rates. For small elements, this can be done using a single-macrospin theory since the element…
We investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We study the transient dynamics of single species reaction diffusion systems whose reaction terms $f(u)$ vary nonlinearly near $u\approx 0$, specifically as $f(u)\approx u^{2}$ and $f(u)\approx u^{3}$. We consider three cases, calculate…
A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…
The steady sliding state of periodic structures such as charge density waves and flux line lattices is numerically studied based on two and three dimensional driven random field XY models. We focus on the dynamical phase transition between…
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…
The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified…
In this work we provide new insights into the transformer architecture, and in particular, its best-known variant, BERT. First, we propose a method to measure the degree of non-linearity of different elements of transformers. Next, we focus…
The Bramson logarithmic shift of the position of pulled fronts is a universal feature common to a large class of monostable traveling wave equations. As one varies the non-linearities it so happens that one can observe, at some critical non…
Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field…
Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…
A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…
Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…