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We study a popular kinetic model introduced by Saintillan and Shelley for the dynamics of suspensions of active elongated particles where the particles are described by a distribution in space and orientation. The uniform distribution of…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
We investigate the role of inhomogeneous field configurations in systems with a spontaneously broken continuous global symmetry. Spontaneous breaking is usually defined as a specific double limit, first infinite volume at finite explicit…
We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…
Transformers owe much of their empirical success in natural language processing to the self-attention blocks. Recent perspectives interpret attention blocks as interacting particle systems, whose mean-field limits correspond to gradient…
In the Transformer model, "self-attention" combines information from attended embeddings into the representation of the focal embedding in the next layer. Thus, across layers of the Transformer, information originating from different tokens…
By combining aspects of the coherent and self intermediate scattering functions, measured by dynamical light scattering on a suspension of hard sphere-like particles, we show that the arrest of particle number density fluctuations spreads…
We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals'…
We study the symmetry classes of graphene quantum dots, both open and closed, through the conductance and energy level statistics. For abrupt termination of the lattice, these properties are well described by the standard orthogonal and…
A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating…
In this paper, we derive a series of exact analytical closed expressions to calculate the complex eigenfrequencies and the displacement for the corresponding eigenmodes of a viscoelastic (nano-)sphere in the presence of linear damping.…
A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant…
The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric…
Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens $X$ and makes them interact through…
Depending on the reflectional and rotational symmetries of annular combustors for aeroengines and gas turbines, self-sustained azimuthal thermoacoustic eigenmodes can be standing, spinning or mix of these two types of waves. These…
Mathematical settings in which heterogeneous structures affect electron transport through a tube-shaped quantum waveguide are studied, highlighting the interaction between heterogeneities and geometric parameters like curvature and torsion.…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Increasing evidence suggests that active matter exhibits instances of mixed symmetry that cannot be fully described by either polar or nematic formalism. Here, we introduce a minimal model that integrates self-propulsion into the active…
We study a simple model for a particle that is active due to self-phoresis and that has been proposed to model symmetric camphor grains. The particle generates a concentration field through the continuous emission of a chemical substance,…
It is known that the perfect absorption of two identical waves incident on a complex potential from left and right can occur at a fixed real energy and that the time-reversed setting of this system would act as a laser at threshold at the…