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Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
In this work, we present the integrated structure-control design of a 2-DOF underactuated mechanical system, aiming to achieve a periodic motion of the end-effector. The desired behavior is generated via input-output linearization, followed…
In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solutions. Dynamic renormalization and fixed point algorithms for…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We show how the dynamics of a specific subset of states can be separated from the dynamic of the total quantum state via a time-dependent projector-based formalism of adiabatic elimination. Within our formalism, we assume explicit time…
The adiabatic theorem and "shortcuts to adiabaticity" for the adiabatic dynamics of time-dependent decoherence-free subspaces are explored in this paper. Starting from the definition of the dynamical stable decoherence-free subspaces, we…
We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…
A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required.…
The authors present a new molecular dynamics algorithm for sampling the isothermal-isobaric ensemble. In this approach the velocities of all particles and volume degrees of freedom are rescaled by a properly chosen random factor. The…
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky…