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Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
Modern potential energy surfaces have shifted attention to molecular simulations of chemical reactions. While various methods can estimate rate constants for conformational transitions in molecular dynamics simulations, their applicability…
In this article, we propose an efficient method for sampling the relevant state space in condensed phase reactions. In the present method, the reaction is described by solving the electronic Schr\"{o}dinger equation for the solute atoms in…
We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
Analyzing synthesis pathways for target molecules in a chemical reaction network annotated with information on the kinetics of individual reactions is an area of active study. This work presents a computational methodology for searching for…
We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…
Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial…
The discovery of transition pathways to unravel distinct reaction mechanisms and, in general, rare events that occur in molecular systems is still a challenge. Recent advances have focused on analyzing the transition path ensemble using the…
Within the framework of building energy assessment, this article proposes to use a derivative based sensitivity analysis of heat transfer models in a building envelope. Two, global and local, estimators are obtained at low computational…
We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time…
Turbulent reacting flows occur in a variety of engineering applications such as chemical reactors and power generating equipment (gas turbines and internal combustion engines). Turbulent reacting flows are characterized by two main…
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli\`evre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The…
Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…
We discuss the ``soft-ratcheting'' algorithm which generates targeted stochastic trajectories in molecular systems with scores corresponding to their probabilities. The procedure, which requires no initial pathway guess, is capable of…
We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of…
In this paper we focus on comparative diagnostic trials which are frequently employed to compare two markers with continuous or ordinal results. We derive explicit expressions for the optimal sampling ratio based on a common variance…