Related papers: Traction Boundary Conditions for Molecular Static …
We study the spectral problem associated with the equation governing the small transverse motions of a viscoelastic tube of finite length conveying an ideal fluid. The boundary conditions considered are of general form, accounting for a…
In this paper we examine boundary effects in a fractional chemotactic equation derived from a kinetic transport model describing cell movement in response to chemical gradients (chemotaxis). Specifically, we analyze reflecting boundary…
An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
Multiscale modelling methodologies build macroscale models of materials with complicated fine microscale structure. We propose a methodology to derive boundary conditions for the macroscale model of a prototypical non-linear heat exchanger.…
We present results on the trace regularity of the stress vector on the boundary of an elastic solid satisfying the time-dependent, displacement-traction problem for the Navier equations of linear elasticity in a bounded domain of…
This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI),…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…
We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner…
We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…
We discuss the force-velocity relations obtained in a two-state crossbridge model for molecular motors. They can be calculated analytically in two limiting cases: for a large number and for one pair of motors. The effect of the…
We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
We consider the model equations for the Timoshenko beam as a first order system in the framework of evolutionary equations. The focus is on boundary damping, which is implemented as a dynamic boundary condition. A change of material laws…
In most results concerning bounds on the heat transport in the Rayleigh-B\'{e}nard convection problem no-slip boundary conditions for the velocity field are assumed. Nevertheless it is debatable, whether these boundary conditions reflect…
A sliding-mode-based adaptive boundary control law is proposed for a class of uncertain thermal reaction-diffusion processes subject to matched disturbances. The disturbances are assumed to be bounded, but the corresponding bounds are…