Related papers: Spontaneous pattern formation in an acoustical res…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
While Transformer has become the de-facto standard for speech, modeling upon the fine-grained frame-level features remains an open challenge of capturing long-distance dependencies and distributing the attention weights. We propose…
This report provides an interpretation on the periodically varying damping ratio of a dynamical system with direct control of oscillation or vibration damping. The principal parametric resonance of the system and a new type of parametric…
Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far from equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we…
When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number…
The dynamical backaction from a periodically driven optical or microwave cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Fundamentally, the driving…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
Recent advances in analysis of subband amplitude envelopes of natural sounds have resulted in convincing synthesis, showing subband amplitudes to be a crucial component of perception. Probabilistic latent variable analysis is particularly…
Radiation from acoustic sources located inside randomly-layered structures is studied using the transfer matrix method. It is shown that in contrast to the periodically layered cases where the radiation can be either enhanced or inhibited…
In this note we review several situations in which stochastic PDEs exhibit ergodic properties. We begin with the basic dissipative conditions, as stated by Da Prato and Zabczyk in their classical monograph. Then we describe the singular…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
Large Language Models (LLMs), such as the Generative Pretrained Transformer (GPT), have achieved tremendous success in various language tasks, but their emergent abilities have also raised many questions, concerns, and challenges that need…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…
Directly sending audio signals from a transmitter to a receiver across a noisy channel may absorb consistent bandwidth and be prone to errors when trying to recover the transmitted bits. On the contrary, the recent semantic communication…
The transduction process that occurs in the inner ear of the auditory system is a complex mechanism which requires a non-linear dynamical description. In addition to this, the stochastic phenomena that naturally arise in the inner ear…
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…
We report the experimental studies of a parametric excitation of a second sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity. The results on several topics in this system are presented: (i) The linear properties…