Physical Sciences and Mathematics Commons^™

Advances In Modeling Gas Adsorption In Porous Materials For The Characterization Applications, Max A. Maximov

Dissertations

The dissertation studies methods for mesoporous materials characterization using adsorption at various levels of scale and complexity. It starts with the topic introduction, necessary notations and definitions, recognized standards, and a literature review.

Synthesis of novel materials requires tailoring of the characterization methods and their thorough testing. The second chapter presents a nitrogen adsorption characterization study for silica colloidal crystals (synthetic opals). These materials have cage-like pores in the range of tens of nanometers. The adsorption model can be described within a macroscopic approach, based on the Derjaguin-Broekhoff-de Boer (DBdB) theory of capillary condensation. A kernel of theoretical isotherms is …

Examining The Accumulation Statistics Of Index1 Saddle Points On The Potential Energy Surface And Imposing Early Termination On A Rejection Scheme For Off Lattice Kinetic Monte Carlo, Jonathan W. Hicks

Doctoral Dissertations

In the calculation of time evolution of an atomic system where a chemical reaction and/or diffusion occurs, off-lattice kinetic Monte Carlo methods can be used to overcome timescale and lattice based limitations from other methods such as Molecular Dynamics and kinetic Monte Carlo procedures. Off-lattice kinetic Monte Carlo methods rely on a harmonic approximation to Transition State Theory, in which the rate of the rare transitions from one energy minimum to a neighboring minimum require surmounting a minimum energy barrier on the Potential Energy Surface, which is found at an index-1 saddle point commonly referred to as a transition state. …

An Examination Of Kinetic Monte Carlo Methods With Application To A Model Of Epitaxial Growth, Dylana Ashton Wilhelm

Theses and Dissertations

Through the assembly of procedural information about physical processes, the kinetic Monte Carlo method offers a simple and efficient stochastic approach to model the temporal evolution of a system. While suitable for a variety of systems, the approach has found widespread use in the simulation of epitaxial growth. Motivated by chem- ically reacting systems, we discuss the developments and elaborations of the kinetic Monte Carlo method, highlighting the computational cost associated with realizing a given algorithm. We then formulate a solid-on-solid bond counting model of epitax- ial growth which permits surface atoms to advance the state of the system through …

Generalizable Modeling Of Charge Transport In Single Electron Transistor Devices: Application To Thermal Sensitivity In Semiconducting Island Systems, Paniz Khanmohammadi Hazaveh

Dissertations, Master's Theses and Master's Reports

Electronic devices, especially MOSFETs, have been dimensionally scaled down to enhance operation of integrated circuits, addressing challenges such as current leakage, fluctuation of intrinsic semiconductor properties, and power dissipation. Reaching dimensions below 20 nm, there are fundamental limitations that are difficult to overcome, driving alternative device paradigms to be sought utilizing the quantum mechanical behavior of electrons. Single electron transistor (SET) devices are examples of a new generation of low-power transistors designed to transport information via single electron tunneling through one or more islands separated by tunnel junctions. Experimentally explored SET devices have shown that there are advantages to using …

Physical Mechanisms Leading To The Coulomb Blockade And Coulomb Staircase Structures In Strongly Coupled Multi-Island Single-Electron Devices, Madhusudan A. Savaikar, Paul L. Bergstrom, John A. Jaszczak

Paul Bergstrom

Controlled transport of electrons through tunnel junctions and their confinement by mesoscopic structures have opened up immense possibilities of single-electron device (SED) applications. The realization of a practical working SED has remained challenging largely owing to the poor understanding of the physics of operation of singe-electron tunneling devices, especially of those with multiple nanometer-sized islands. In this simulation study of one-dimensional (1D) multi-island chains, we propose physical mechanisms that lead to the coulomb blockade (CB) and coulomb staircase (CS) characteristics that are enhanced by the geometrical disorder in the chain. With increasing source-drain (VDS = VD − VS) bias, a …

Surface Energy In Bond-Counting Models On Bravais And Non-Bravais Lattices, Tim Ryan Krumwiede

Doctoral Dissertations

Continuum models in computational material science require the choice of a surface energy function, based on properties of the material of interest. This work shows how to use atomistic bond-counting models and crystal geometry to inform this choice. We will examine some of the difficulties that arise in the comparison between these models due to differing types of truncation. New crystal geometry methods are required when considering materials with non-Bravais lattice structure, resulting in a multi-valued surface energy. These methods will then be presented in the context of the two-dimensional material graphene in a way that correctly predicts its equilibrium …

A Survey Of The Kinetic Monte Carlo Algorithm As Applied To A Multicellular System, Michael Richard Laughlin

Theses and Dissertations

We explore the origins and implementation of the Kinetic Monte Carlo method on a system of cells suspended in a liquid media. The situation presented herein has applications in the emerging field of biofabrication, which may have lasting impacts in medical science. The theory behind the method is explained in detail, starting with its emergence in the 1960s, and two major improvements to the scaling of the method are presented, along with a restriction to a special case. Finally, we give the results of several simulations.

Spatial Multi-Level Interacting Particle Simulations And Information Theory-Based Error Quantification, Evangelia Kalligiannaki, Markos Katsoulakis, Petr Plechac

Markos Katsoulakis

We propose a hierarchy of two-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking advantage of the low sampling cost in a coarse space and developing local reconstruction strategies from coarse-grained dynamics. Furthermore, a natural extension to a multilevel kinetic coarse-grained Monte Carlo is presented. Microscopic reconstruction corrects possibly significant errors introduced through coarse-graining, leading to the controlled-error approximation of the sampled stochastic process. In this manner, the proposed algorithm overcomes known shortcomings of coarse-graining of particle systems with complex …

Information-Theoretic Tools For Parametrized Coarse-Graining Of Non-Equilibrium Extended Systems, Markos Katsoulakis, Petr Plechac

Markos Katsoulakis

In this paper, we focus on the development of new methods suitable for efficient and reliable coarse-graining of non-equilibrium molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction methods based on Path-Space Information Theory, combined with statistical parametric estimation of rates for non-equilibrium stationary processes. The approach we propose extends the applicability of existing information-based methods for deriving parametrized coarse-grained models to Non-Equilibrium systems with Stationary States. In the context of coarse-graining it allows for constructing optimal parametrized Markovian coarse-grained dynamics within a parametric family, by minimizing information loss (due to coarse-graining) on the path space. …

A Relative Entropy Rate Method For Path Space Sensitivity Analysis Of Stationary Complex Stochastic Dynamics, Yannis Pantazis, Markos Katsoulakis

Markos Katsoulakis

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the relative entropy rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the relative entropy rate and the corresponding Fisher information matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-Gaussian stationary probability …