Statistical, Nonlinear, and Soft Matter Physics Commons^™

Predicting Solar Protons: A Statistical Approach, Jonathan C. Spaulding

Theses and Dissertations

A small fraction of solar flares are accompanied by high energy (>10 MeV) protons. These events can cause degradation or failure of satellite systems and can be harmful to humans in space or in high altitude flight. For risk management purposes, the Air Force is interested in predicting these events. Several algorithms exist to do this operationally, but none predict when these events will occur with much accuracy. Here, we analyzed 3610 M1 and greater flares including 106 with proton events from the GOES sensors from 1 Jan 1986 to 31 Dec 2004 to produce new results, including a …

Gas-Kinetic Schemes For Direct Numerical Simulations Of Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Reλ =72.0 and the turbulence Mach number Ma_t between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K (t), the dissipation rate ε (t), …

Disk-Shaped Bose-Einstein Condensates In The Presence Of An Harmonic Trap And An Optical Lattice, Todd Kapitula, Panayotis G. Kevrekidis, D. J. Frantzeskakis

University Faculty Publications and Creative Works

We study the existence and stability of solutions of the two-dimensional nonlinear Schrödinger equation in the combined presence of a parabolic and a periodic potential. The motivating physical example consists of Bose-Einstein condensates confined in an harmonic (e.g., magnetic) trap and an optical lattice. By connecting the nonlinear problem with the underlying linear spectrum, we examine the bifurcation of nonlinear modes out of the linear ones for both focusing and defocusing nonlinearities. In particular, we find real-valued solutions (such as multipoles) and complex-valued ones (such as vortices). A primary motivation of the present work is to develop "rules of thumb" …

Displacement Detection With A Vibrating Rf Superconducting Interference Device: Beating The Standard Linear Limit, Eyal Buks, Stav Zaitsev, Eran Segev, Baleegh Abdo, M. P. Blencowe

Dartmouth Scholarship

We study a configuration for displacement detection consisting of a nanomechanical resonator coupled to both a radio frequency superconducting interference device and to a superconducting stripline resonator. We employ an adiabatic approximation and rotating wave approximation and calculate the displacement sensitivity. We study the performance of such a displacement detector when the stripline resonator is driven into a region of nonlinear oscillations. In this region the system exhibits noise squeezing in the output signal when homodyne detection is employed for readout. We show that displacement sensitivity of the device in this region may exceed the upper bound imposed upon the …

Entopic Lattice Boltzmann Representations Required To Recover Navier Stokes Flows, Brian Keating, George Vahala, Jeffrey Yepez, Min Soe, Linda L. Vahala

Electrical & Computer Engineering Faculty Publications

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional …

Orientation Of Optically Trapped Nonspherical Birefringent Particles, Wolfgang Singer, Timo A. Nieminen, Ursula J. Gibson, Norman R. Heckenberg

Dartmouth Scholarship

While the alignment and rotation of microparticles in optical traps have received increased attention recently, one of the earliest examples has been almost totally neglected—the alignment of particles relative to the beam axis, as opposed to about the beam axis. However, since the alignment torques determine how particles align in a trap, they are directly relevant to practical applications. Lysozyme crystals are an ideal model system to study factors determining the orientation of nonspherical birefringent particles in a trap. Both their size and their aspect ratio can be controlled by the growth parameters, and their regular shape makes computational modeling …

Low Magnetic Prandtl Number Dynamos With Helical Forcing, Pablo D. Mininni, David C. Montgomery

Dartmouth Scholarship

We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from ∼0.3 to ∼0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velocity …

Numerical Solutions Of The Three-Dimensional Magnetohydrodynamic Α Model, Pablo D. Mininni, David C. Montgomery, Annick Pouquet

Dartmouth Scholarship

We present direct numerical simulations and α-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD α model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the α model correctly reproduce the growth rate of magnetic energy during the kinematic regime, it also captures the nonlinear saturation level and the late generation of a large scale …

High-Latitude Propagation Studies Using A Meridional Chain Of Lf/Mf/Hf Receivers, J Labelle

Dartmouth Scholarship

For over a decade, Dartmouth College has oper- ated programmable radio receivers at multiple high-latitude sites covering the frequency range 100–5000 kHz with about a 1-s resolution. Besides detecting radio emissions of auro- ral origin, these receivers record characteristics of the iono- spheric propagation of natural and man-made signals, docu- menting well-known effects, such as the diurnal variation in the propagation characteristics of short and long waves, and also revealing more subtle effects. For example, at auroral zone sites in equinoctial conditions, the amplitudes of dis- tant transmissions on MF/HF frequencies are often enhanced by a few dB just before …

Anisotropy Of Exchange Stiffness And Its Effect On The Properties Of Magnets, K. D. Belashchenko

Kirill Belashchenko Publications

Using the spin-spiral formulation of the tight-binding linear muffin-tin orbital method, the principal components of the exchange stiffness tensor are calculated for typical hard magnets including tetragonal CoPt-type and hexagonal YCo₅ alloys. The exchange stiffness is strongly anisotropic in all studied alloys. This anisotropy makes the domain wall surface tension anisotropic. Competition between this anisotropic surface tension and magnetostatic energy controls the formation and dynamics of nanoscale domain structures in hard magnets. Anisotropic domain wall bending is described in detail from the general point of view and with application to cellular Sm–Co magnets. It is shown that the repulsive …

Resonant Emergence Of Global And Local Spatiotemporal Order In A Nonlinear Field Model, Marcelo Gleiser, Rafael C. Howell

Dartmouth Scholarship

We investigate the nonequilibrium evolution of a scalar field in (2+1) dimensions. The field is set in a double-well potential in contact (open) or not (closed) with a heat bath. For closed systems, we observe the synchronized emergence of coherent spatiotemporal configurations, identified with oscillons. This initial global ordering degenerates into localized order until all oscillons disappear. We show that the synchronization is driven by resonant parametric oscillations of the field’s zero mode and that local ordering is only possible outside equipartition. None of these orderings occur for open systems.

Adiabatic Invariance With First Integrals Of Motion, Artur D. Adib

Dartmouth Scholarship

The construction of a microthermodynamic formalism for isolated systems based on the concept of adiabatic invariance is an old but seldom appreciated effort in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33, 225 (1910)]. An apparently independent extension of such formalism for systems bearing additional first integrals of motion was recently proposed by Hans H. Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic invariance even in such singular cases. After some remarks in connection with the formalism pioneered by Hertz, it will be suggested that such an extension can …

Nonequilibrium Precursor Model For The Onset Of Percolation In A Two-Phase System, Marcelo Gleiser, Rafael C. Howell, Rudnei O. Ramos

Dartmouth Scholarship

Using a Boltzmann-like equation, we investigate the nonequilibrium dynamics of nonperturbative fluctuations within the context of Ginzburg-Landau models. As an illustration, we examine how a two-phase system initially prepared in a homogeneous, low-temperature phase becomes populated by precursors of the opposite phase as the temperature is increased. We compute the critical value of the order parameter for the onset of percolation, which signals the breakdown of the conventional dilute gas approximation.

Comment On `Numerical Analysis Of Bose-Einstein Condensation In Three-Dimensional Harmonic Oscillator Potential' By Martin Ligare [Am. J. Phys. 66 (3), 185-190 (1998)] - An Extension To Anisotropic Traps And Lower Dimensions, Martin K. Ligare

Faculty Journal Articles

No abstract provided.

Velocity Field Distributions Due To Ideal Line Vortices, Thomas D. Levi, David C. Montgomery

Dartmouth Scholarship

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on “nearest-neighbor” contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity “tail” on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the …

Thermal Lattice Boltzmann Simulation For Multispecies Fluid Equilibration, Linda L. Vahala, Darren Wah, George Vahala, Jonathan Carter, Pavol Pavlo

Electrical & Computer Engineering Faculty Publications

The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar-and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude …

Numerical Analysis Of Bose-Einstein Condensation In A Three-Dimensional Harmonic Oscillator Potential, Martin K. Ligare

Faculty Journal Articles

Bose–Einstein condensation is the anomalous accumulation of particles in the ground state of a system of bosons, when compared with the population in a system of particles obeying classical statistics. I use undergraduate-level statistical mechanics and a symbolic algebra computer program to study the occupation numbers of the energy levels of a finite number of noninteracting particles confined in a three-dimensional harmonic oscillator potential. I also calculate the heat capacity of the gas. The harmonic oscillator potential simplifies the calculations and approximates the conditions of the recent experiments achieving Bose–Einstein condensation in laser-cooled alkali vapors.

Applying Binomial Statistics To Weighted Monte Carlo, Sue Ellen Mccloskey, William C. Hall, Wilfred J. Braithwaite

Journal of the Arkansas Academy of Science

Weighted Monte Carlo calculations requiring a uniform sampling of the problem-space can suffer from diminished statistical significance because many, if not most, of the randomly-chosen sampling points contribute only slightly to the desired result. Their contribution is reduced in size due the variable-size of the weighting terms. In contrast, none of the randomly-chosen points which are favored by variable size weighting terms will have their statistical significance enhanced beyond that of just one random point in the Monte Carlo sampling. A Monte Carlo analysis was used in earlier work to verify both Gauss' Law and Newton's Shell Theorem. Both examples …

Nlo Waveguide "And" Switch And Method Therefor, John J. Kester, Iyad A. Dajani, Peter M. Ranon, Thomas G. Alley

AFIT Patents

Method and apparatus are provided for NLO switching by first providing a phase-matched SHG grating which outputs a reinforced SHG beam only when two input beams of frequency (ω) are present in two modes of such wg. The so encoded NLO switch is operated by directing at least two input pulsed laser beams of frequency (ω) into the two modes of the wg to generate a reinforced pulsed output SHG beam and output same from the wg in an NLO switching process. The two input beams desirably have a separate pulse train and the spatial and temporal overlap of the …

Mcplib: A Collection Of Nonlinear Mixed Complementarity Problems, Steven P. Dirkse, Michael C. Ferris

University Faculty Publications and Creative Works

The origins and some motivational details of a collection of nonlinear mixed complementarity problems are given. This collection serves two purposes. Firstly, it gives a uniform basis for testing currently available and new algorithms for mixed complementarity problems. Function and Jacobian evaluations for the resulting problems are provided via a GAMS interface, making thorough testing of algorithms on practical complementarity problems possible. Secondly, it gives examples of how to formulate many popular problem formats as mixed complementarity problems and how to describe the resulting problems in GAMS format. We demonstrate the ease and power of formulating practical models in the …

First-Order Amplitude For General State-To-State Transitions In Hydrogen By Projectile Impact, Jack C. Straton

Physics Faculty Publications and Presentations

The closed analytic form for bound-state transitions due to projectile impact is found in the intermediate representation. The coordinate integral is obtained by evaluating the remaining two integrals in the general multicenter integral derived previously [J.C. Straton, Phys. Rev. A 41, 71 (1990)]. Evaluating the remaining time integral depends upon relating a sum of modified Bessel functions of the second kind K_N+1/2(z) to a simple polynomial in 1/z. The results of Van Den Bos and De Heer [Physica 34, 333 (1967)] are shown to be missing a phase factor of (-i)^(l′+l)

An Artificial Neural Approach To The Decomposition Problem, Chandrashekar L. Masti

Electrical & Computer Engineering Theses & Dissertations

The goal of this thesis is to develop an artificial neural approach toward addressing the intractability involved with the decomposition problem. The search for the lattice of substitution property (s. p.) partitions essential to decompositions is cast into the framework of constraint satisfaction. An artificial neural network is developed to provide solutions by performing optimization of a mathematically derived objective function over the problem space. The issue of transitivity is verified to belong to a class of problems beyond the scope of solvability for conventional quadratic-order constraint satisfaction neural networks. A theorem is stated and proved establishing that third-order correlations …

A Study Of Leslie Model Under Stochastic Environments, Kamran Shaukat

Dissertations and Theses

The prediction and analysis of changes in the numbers of biological populations rest on mathematical formulations of demographic events (births and deaths) classified by the age of individuals. The development of demographic theory when birth and death rates vary statistically over time is the central theme of this work. A study of the standard Leslie model for the demographic dynamics of populations in variable environments is made. At each time interval a Leslie matrix of survival rates and fertilities of a population is chosen according to a Markov process and the population numbers in different age classes are computed. Analytical …

Some Implications Of The Second Law Of Thermodynamics, Nancy Barklage

Student Scholarship

Thermodynamics is the branch of science concerned with energy changes that accompany all natural processes. While there are three primary laws, the Second Law of Thermodynamics is the most far-reaching due to its influence on the direction of time and its philosophical implications for life and the universe. Central to this law is the concept of entropy, which serves as a measure of disorder or randomness within a system. All spontaneous processes are irreversible and naturally progress toward a state of maximum entropy and lowest energy. 

One significant implication of the Second Law involves the origin of life. While the …