Related papers: Reduction of periodic one-dimensional hopping mode…
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence,…
We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…
We consider stochastic rules of mass transport which lead to steady states that factorize over the links of a one-dimensional ring. Based on the knowledge of the steady states, we derive the onset of a phase transition from a liquid to a…
We provide a complete thermodynamic solution of a 1D hopping model in the presence of a random potential by obtaining the density of states. Since the partition function is related to the density of states by a Laplace transform, the…
A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coefficients of certain bivariate dual-Hahn polynomials. For a…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…
A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic…
We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interactions. The model is defined in terms of an energy…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
There is a lot of research on probabilistic transition systems. There are not many studies in probabilistic process models. The lack of investigation into the interactive aspect of probabilistic processes is mainly due to the difficulty…
Periodic one dimensional hopping model is useful to study the motion of microscopic particles, which lie in thermal noise environment. The mean velocity $V_N$ and diffusion constant $D_N$ of this model have been obtained by Bernard Derrida…
We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…
Biological systems are typically very complex and need to be reduced before they are amenable to a thorough analysis. Also, they often possess functionally important dynamic features like bistability. In model reduction, it is sometimes…
In this paper, to cope with the shortage of sufficient theoretical support resulted from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their…