With 1–2% of the population affected, rheumatoid arthritis (RA) is the most frequent inflammatory arthropathy. In most cases, RA initially affects the small joints, only, especially the finger joints. The inflammations of the joints caused by this disease usually start with a synovitis. At the same time, there is a change in the filtration properties of the synovialis, which increases the enzyme rate within the synovia thus accelerating the progress of inflammation. In a later stage, granulation and neovascularisation occur in the synovia (Figs. 1 and 2), which may finally lead to the destruction of cartilage and bone structures [1]. So, it is rather unsurprising that the optical parameters [2, 3] (Table 1) change in these early stages of the disease.

Equilibrium distributions of multicomponent systems minimize the free energy functional under the constraint of mass conservation of the components. However, since the free energy is not convex in general, usually one tries to characterize and to construct equilibrium distributions as steady states of an adequate evolution equation, for example, the nonlocal Cahn-Hilliard equation for binary alloys. In this work a direct descent method for nonconvex functionals is established and applied to phase separation problems in multicomponent systems and image segmentation.

We are interested in finite volume discretization schemes and numerical solutions for a nonlocal phase segregation model, suitable for large times and interacting forces. Our main result is a scheme with definite discrete dissipation rate proportional to the square of the driving force for the evolution, i. e., the discrete antigradient of the chemical potential v. Steady states are characterized by constant v and satisfy a nonlocal stationary equation. A numerical bifurcation analysis of that stationary equation explains the observed global behavior of numerically computed trajectories of the evolution equation. For strong interaction forces the model shows steady states distinguished by small deformations of the 'mushy region' or 'interface states'. One essential open question in the discrete case is the global boundedness of v. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

We study initial-boundary value problems for elliptic-parabolic systems of nonlinear partial differential equations describing drift-diffusion- reaction processes of electrically charged species in N-dimensional bounded Lipschitzian domains. We include Fermi-Dirac statistics and admit nonsmooth material coefficients. We prove existence and uniqueness of bounded global solutions.

. We understand an image as binary grey ‘alloy’ of a black and a white component and use a nonlocal phase separation model to describe image segmentation. The model consists in a degenerate nonlinear parabolic equation with a nonlocal drift term additionally to the familiar Perona-Malik model. We formulate conditions for the model parameters to guarantee global existence of a unique solution that tends exponentially in time to a unique steady state. This steady state is solution of a nonlocal nonlinear elliptic boundary value problem and allows a variational characterization. Numerical examples demonstrate the properties of the model.

We prove a priori estimates in L 2 (0,T;W 1,2 (Ω)) and L∞(QT), existence and uniqueness of solutions to Cauchy–Neumann problems for parabolic equations (0.1) ∂σ(u) ∂t − ∑ i=1 n ∂ ∂x i ρ(u) b i t,x, ∂(u−v) ∂x +a(t,x,v,u)=0, (t,x)∈Q T =(0,T)×Ω⊂R n+1 , where ρ(u)=∂σ(u)/∂u>0 and the function v is defined by the nonlocal expression (0.2) v(t,x)=− ∫ Ω K(x,y)[σ(u(t,y))−f(t,y)] d y, instead of solving an elliptic boundary problem as in the corresponding local case. Such problems arise as mathematical models of various diffusion–drift processes driven by gradients of local particle concentrations and nonlocal interaction potentials. An example is the transport of electrons in semiconductors, where u has to be interpreted as chemical and v as electro-statical potential.

A thermodynamic designed energy model for semiconductor devices is discussed. A system of evolution equations based on an expression for the density of the free energy is derived. First principles such as entropy maximum principle and the principle of partial local equilibrium are applied. The free energy is assumed as the sum of the internal free energy and the electrostatic field energy. A 1.55 /spl mu/m RW MQW laser is used in the simulations.

An alternative to the Cahn–Hilliard model of phase separation for two-phase systems in a simplified isothermal case is given. The model is derived from a free energy with a nonlocal interacting term and allows reasonable bounds for the concentrations. Using the free energy as Lyapunov functional the asymptotic state of the system is investigated and characterized by a variational principle.

We prove existence and uniqueness of solutions u∈W1,2(Ω)∩L∞(Ω) to equations of the form−∑i=1n∂∂xiρ(u)bix,∂u∂x+ax,u,∂u∂x=0,x∈Ω.Our nonstandard assumptions on the coefficients are such that logρ(u) is concave and a(x,u,ξ)/ρ(u) is increasing in u. Such assumptions are natural in view of drift diffusion processes for example in semiconductors and chemotaxis.

We are interested in algorithms for constructing surfaces $\Gamma $ of possibly small measure that separate a given domain $\Omega $ into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the $p$-Laplacians, $p \rightarrow 1$, under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients.

We are interested in algorithms for constructing surfaces Γ of possibly small measure that separate a given domain ω into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians,p→1 under humogeneous Neumann houndary conditions. These eigenfunctions are proven to be limtes of a steepest descent method applied to suitable norm quotients. Finally we use these ideas for the construction of separators on simplex grids.

Our simulations on InP-based edge-emitting RW-lasers have been essentially based on the drift-diffusion approach. The model comprises a self-consistent description of the electronic properties and the optical field under modifications caused by heating processes. Calculations on the device performance have been done by means of the semiconductor device simulation package TESCA with energy transport equation. The quantum confined carriers are described by a (8X8) kp-Hamiltonian, self-consistently coupled to the Poisson equation and exchange-correlation potentials to give a guess for Coulomb effects. Using the package KPLIB for band structure calculations, modifications of the optical gain, caused by the presence of the strained multi quantum wells, have been simulated and will be discussed.

Using Lyapunov functionals the global behaviour of the solutions of a reaction-diffusion system modelling chemotaxis is studied for bounded piecewise smooth domains in the plane. Geometric criteria can be given so that this dynamical system tends to a (not necessarily trivial) stationary state.

An extensive series of digital simulations of the decay dynamics of photoexcited charge carriers at a semiconductor/liquid interface has been performed using the two-dimensional simulation code ToSCA, ToSCA treats majority and minority carrier capture processes separately and incorporates field-dependent carrier mobility terms. These features produce dramatic differences in the output parameters obtained when fitting experimental data with ToSCA relative to those obtained by fitting such data with prior, less complete, simulations. The simulations revealed that for a typical (n-type in our example) InP electrode in contact with outer-sphere redox reagents dissolved in the liquid phase the photoluminescence decays were generally insensitive to the value of the minority carrier charge-transfer rate constant, k(ht). Instead, diffusion and drift-induced separation of photogenerated carriers in the space-charge layer of the semiconductor dominated the time decay of the observed luminescence signal under most experimentally accessible conditions. Values of k(ht) and of the minority carrier low-level surface recombination velocity, S-p, could be obtained from an analysis of the photoluminescence decays only when the following restricted sets of conditions were satisfied simultaneously: 10(1) cm s(-1) less than or equal to S-p less than or equal to 10(5) cm s(-1), 10(-18) cm(4) s(-1) less than or equal to k(ht) less than or equal to 10(-15) cm(4) s(-1), and the electrode potential, E, was in the region 0 < E < +0.15 V relative to the flat-band potential of the n-type semiconductor/liquid interface. The simulations demonstrated that it was not possible to extract a "field dependence" of the charge-transfer rate constant when the semiconductor/liquid contact was maintained in reverse bias (E greater than or equal to +0.15 V vs the flat-band potential) and was subjected to light pulses that produced low or moderate carrier injection levels. Under such conditions, the photoluminescence decay dynamics were dominated by drift-induced charge separation in the space-charge layer of the semiconductor. Under high-level injection conditions, no "field dependence" could be observed because the majority of the photoluminescence decay dynamics occurred near the flat-band condition, so the value of the band bending in the semiconductor under dark, equilibrium conditions had negligible influence on the luminescence transients produced by a high-intensity laser pulse. Additionally, comparison between one-dimensional and two-dimensional simulations showed that use of one-dimensional simulation routines to extract S-p and k(ht) values from experimental data obtained using focused laser beam excitation can lead to severe overestimates of interfacial charge-transfer rates.