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The theory of full counting statistics allows complete characterization of charge transport processes through nanoscale systems. The majority of existing theoretical treatments used to obtain the current cumulants rely on perturbative…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
Controlling polymorphism in molecular crystals is crucial in the pharmaceutical, dye, and pesticide industries. However, its theoretical description is extremely challenging, due to the associated long timescales ($ > 1 \, \mu s$). We…
We present a direct numerical simulation method for investigating the dynamics of dispersed particles in a compressible solvent fluid. The validity of the simulation is examined by calculating the velocity relaxation of an impulsively…
Biomolecular condensates are small droplets forming spontaneously in biological cells via phase separation. They play a role in many cellular processes, but it is unclear how cells control them. Cellular regulation often relies on…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…
This thesis is concerned with the rejection of time-varying disturbances in linear model predictive control of discrete-time systems. In the literature, disturbances are widely rejected by using velocity models, disturbance model with…
Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
Research on active control for the delay of laminar-turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review…
Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…