Related papers: Affine processes with compact state space
The characteristic functions of multivariate Feller processes with generator of affine type, and with smooth symbol functions have an explicit representation in terms of power series with rational number coefficients and with monmoms…
An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
The role of particle shape in evaporation-induced auto-stratification in dispersed colloidal suspensions is explored with molecular dynamics simulations of mixtures of solid spheres, aspherical particles, and hollow spheres. A unified…
In this paper, we put the issue of dynamic equivalence of control systems in the context of pullbacks of coframings on infinite jet bundles over the state manifolds. While much attention has been given to differentially flat systems, i.e.…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
This review article examines the complex dynamics of thin-film flows of granular suspensions spreading over rigid solid substrates with free air interfaces. Such systems feature an involved coupling of the free-surface dynamics with the…
Even simple active systems can show a plethora of intriguing phenomena and often we find complexity were we would have expected simplicity. One striking example is the occurrence of a quiescent or absorbing state with frozen fluctuations…
I comment on the relation between two sampling methods for absorbing state models. It is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external…
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…
Let A^2 denote the affine plane over an algebraically closed field of arbitrary characteristic. Besides contributing several new results in the general theory of birational endomorphisms of A^2, this article describes certain classes of…
We give a characterization of flat affine connections on manifolds by means of a natural affine representation of the universal covering of the Lie group of diffeomorphisms preserving the connection. From the infinitesimal point of view,…
We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us…
Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. In Synthetic Differential Geometry this can be made precise by showing that a smooth manifold carries a natural structure…
We investigate the relationship between affine and Stein varieties in the context of rigid geometry. We show that the two concepts are much more closely related than in complex geometry, e.g. they are equivalent for surfaces. This rests on…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that ``being an affine building'' is…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…