Andrew Mansour

DESPASITO: Determining Equilibrium State and Parametrization: Application for SAFT, Intended for Thermodynamic Output First open-source application for thermodynamic calculations and parameter fitting for the Statistical Associating Fluid Theory (SAFT) EOS and SAFT-𝛾-Mie coarse-grained simulations. This software has two primary facets. The first facet is a means to evaluate the SAFT-𝛾-Mie EOS for binary VLE. This framework allows easy implementation of more advanced thermodynamic calculations as well as additional forms of SAFT or other equations of state. The second facet is parameterization for the equation of state (EOS) but these can also be used for simulations. This application has the ability to fit EOS parameters for self and cross interaction parameters to the following binary experimental thermodynamic data type: Temperature variable vapor-liquid equilibria Binary flash calculation Saturation properties Liquid properties Solubility parameter Although this package is primar...

Molecular dynamics is based on solving Newton's equations for many-particle systems that evolve along complex, highly fluctuating trajectories. The orbital instability and short-time complexity of Newtonian orbits is in sharp contrast to the more coherent behavior of collective modes such as density profiles. The notion of virtual molecular dynamics is introduced here based on temporal coarse-graining via Pade approximants and the Ito formula for stochastic processes. It is demonstrated that this framework leads to significant efficiency over traditional molecular dynamics and avoids the need to introduce coarse-grained variables and phenomenological equations for their evolution. In this framework, an all-atom trajectory is represented by a Markov chain of virtual atomic states at a discrete sequence of timesteps, transitions between which are determined by an integration of conventional molecular dynamics with Pade approximants and a microstate energy annealing methodology. Th...

Simulations of virus-like particles needed for computer-aided vaccine design highlight the need for new algorithms that accelerate molecular dynamics. Such simulations via conventional molecular dynamics present a practical challenge due to the millions of atoms involved and the long timescales of the phenomena of interest. These phenomena include structural transitions, self-assembly, and interaction with a cell surface. A promising approach for addressing this challenge is multiscale factorization. The approach is distinct from coarse-graining techniques in that it (1) avoids the need for conjecturing phenomenological governing equations for coarse-grained variables, (2) provides simulations with atomic resolution, (3) captures the cross-talk between disturbances at the atomic and the whole virus-like particle scale, and (4) achieves significant speedup over molecular dynamics. A brief review of multiscale factorization methods is provided, as is a prospective on its development.

Advances in multiscale theory and computation provide a novel paradigm for simulating many-particle classical systems. The Deductive Multiscale Simulator (DMS) is built on two of these advances, i.e., multiscale Langevin (ML) and multiscale factorization (MF). Both capture the coevolution of the the coarse-grained (CG) and microscopic (atom-resolved) states. This coevolution provides these methods with greater efficiency over conventional MD and yields insights into the coupling of processes across multiple scales in space and time. The design and implementation of DMS as an open source computational platform is presented here. DMS is written in Python and can be used as a program or a library. It incorporates MDAnalysis, a library for analyzing MD trajectories, and numerical Python packages for performing computations such as construction of CG variables and microstates consistent with the CG state. DMS uses GROMACS to simulate the dynamics of the microstate, and then uses this mic...

We report a reaction-diffusion system in which two initially separated electrolytes, mercuric chloride (outer) and potassium iodide (inner), interact in a solid hydrogel media to produce a propagating front of mercuric iodide precipitate. The precipitation process is accompanied by a polymorphic transformation of the kinetically favored (unstable) orange, (metastable) yellow, and (thermodynamically stable) red polymorphs of HgI2. The sequence of crystal transformation is confirmed to agree with the Ostwald Rule of Stages. However, a region is found of initial inner iodide concentration, where a stationary pattern of alternating metastable/stable crystals is formed. A theoretical model based on reaction diffusion coupled to a special nucleation and growth mechanism is proposed. Its numerical solution is shown to reproduce the experimental results.

A computational method is suggested for the simulation of Liesegang patterns in two dimensions on structureless meshes. The method is based on a model that incorporates dynamical equations for the nucleation and growth of solid particles of different sizes into reaction-diffusion equations. We find the model cannot be numerically solved with Galerkin-based finite element methods and cell-centered finite volume methods. Instead, the vertex-based finite volume method is used to correctly reproduce the Liesegang pattern on structureless meshes. The numerical solution is then compared with specially designed experiments on Liesegang patterns in various geometries, and it is shown to be in good agreement.

In the first part of this work, we present an experimental study of the precipitation/redissolution reaction-diffusion system of initially separated components in two distinct organic gels: agar and gelatin. The system is prepared by diffusing a concentrated ammonia solution into a gel matrix that contains nickel sulfate. In agar, the system exhibits a pulse propagation due to the concomitant precipitation reaction between Ni(II) and hydroxide ions and redissolution due to ammonia. At a later stage of propagation, a transition to Liesegang banding is shown to take place. The dynamics of the distance traveled by the precipitation pulse, its width, and mass are shown to exhibit power laws. Moreover, the mass of the bands is shown to oscillate in time, indicating the emergence of a complex mass enrichment mechanism of the formed Liesegang bands. At the microscopic level, we show evidence that the system undergoes a continuous polymorphic transition concomitant with a morphological change whereby the solid in the pulse, which consists of nanospheres of α-nickel hydroxide transforms to form the bands, which consists of larger platelets of β-nickel hydroxide. This clearly indicates the existence of a dynamic Ostwald ripening mechanism that underlies the dynamics on both scales. On the other hand, in gelatin, although we can still obtain similar power laws as in the case of agar, no transition to bands was observed. It is shown that in this case, the propagating pulse is made of nanoparticles of α-nickel hydroxide with an average diameter ~50 nm.

In this paper we investigate the dynamics of front propagation in the family of reactions (nA + mB (k)→ C) with initially segregated reactants in one dimension using hyperbolic reaction-diffusion equations with the mean-field approximation for the reaction rate. This leads to different dynamics than those predicted by their parabolic counterpart. Using perturbation techniques, we focus on the initial and intermediate temporal behavior of the center and width of the front and derive the different time scaling exponents. While the solution of the parabolic system yields a short time scaling as t(1/2) for the front center, width, and global reaction rate, the hyperbolic system exhibits linear scaling for those quantities. Moreover, those scaling laws are shown to be independent of the stoichiometric coefficients n and m. The perturbation results are compared with the full numerical solutions of the hyperbolic equations. The crossover time at which the hyperbolic regime crosses over to the parabolic regime is also studied. Conditions for static and moving fronts are also derived and numerically validated.