Related papers: On the principles of B-smooth discontinuous flows
A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence result among thermomechanical theories in the smooth regime…
A consistent description of a shear flow, the accompanied viscous heating, and the associated entropy balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
Continuum hydrodynamic models of active liquid crystals have been used to describe dynamic self-organising systems such as bacterial swarms and cytoskeletal gels. A key prediction of such models is the existence of self-stabilising kink…
In this paper we analyze some applications of the category of exterior spaces to the study of dynamical systems (flows). We study the notion of an absorbing open subset of a dynamical system; i.e., an open subset that contains the "future…
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period {\tau} . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a…
Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
This paper is a brief update on developments in the BioDynaMo project, a new platform for computer simulations for biological research. We will discuss the new capabilities of the simulator, important new concepts simulation methodology as…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
A new concept called biased derivative is proposed. It has a potential to better understand and model some aspects of dynamical systems associated with creating bubbles.
We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…
Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular…
Two-phase flow systems in porous media have complex dynamics. It is well established that a wide range of system parameters like viscosities and porosity as well as flow parameters such as pressure gradient and fluid saturation have strong…
Fluid turbulence is commonly associated with stronger drag, greater heat transfer, and more efficient mixing than in laminar flows. In many natural and industrial settings, turbulent liquid flows contain suspensions of dispersed bubbles and…
We study models kinetic models of polymeric fluids. We introduce a notion of solutions which is based on moments of polymeric distributions. We prove global existence and uniqueness of a large class of initial data for diffusive systems of…
We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal, heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely…
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…