Statistical, Nonlinear, and Soft Matter Physics Commons^™

Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa M. Slaughter

Symposium

This experiment uses an electromagnetic shaker to produce standing wave patterns on the surface of a vertically oscillating sample of silicon liquid. These surface waves, known as Faraday waves, form shapes such as squares, lines, and hexagons. They are known to be dependent upon the frequency and amplitude of the forcing as well as on the viscosity and depth of the liquid in the dish. At a depth of 4mm and for various silicon liquids having kinematic viscosities of 10, 20, and 38 cSt, we determined the acceleration at which patterns form for frequencies between 10 and 60 Hz. For …

Modeling The Field Control Of The Surface Electroclinic Effect And Its Impact On Smectic Layer Strain, Kara M. Zappitelli

Physics

Chiral, smectic liquid crystal molecules align in layers and can be controlled by the application of an electric field, yielding a variety of implications for the quality of liquid crystal (LC) displays. Both the bulk electroclinic effect (BECE) and surface electroclinic effect (SECE) impact the angle at which the molecules tilt with respect to the layer normal in different areas of a LC cell due to dipole interactions. Certain LC’s exhibit a continuous Sm-A* to Sm-C* transition, where the angles of the surface and bulk molecules change continuously with electric field strength. Other LC’s exhibit first order transitions where we …

Statistical Theory Of Correlations In Random Packings Of Hard Particles, Yuliang Jin, James G. Puckett, Hernán A. Makse

Physics and Astronomy Faculty Publications

A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the n-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply the formalism to hard disks and predict the density of two-dimensional random …

Searching For Effective Forces In Laboratory Insect Swarms, James G. Puckett, Douglas H. Kelley, Nicholas T. Ouellette

Physics and Astronomy Faculty Publications

Collective animal behaviour is often modeled by systems of agents that interact via effective social forces, including short-range repulsion and long-range attraction. We search for evidence of such effective forces by studying laboratory swarms of the flying midge Chironomus riparius. Using multi-camera stereoimaging and particle-tracking techniques, we record three-dimensional trajectories for all the individuals in the swarm. Acceleration measurements show a clear short-range repulsion, which we confirm by considering the spatial statistics of the midges, but no conclusive long-range interactions. Measurements of the mean free path of the insects also suggest that individuals are on average very weakly coupled, but …

Impact Testing Of Youth-Level Helmets Versus College-Level Helmets, Nicole Hermann

Industrial Technology and Packaging

With so many studies being conducted on professional football players regarding concussions and other related brain injuries, it’s amazing that such an important demographic has been missed. While NFL players are just as subjected to serious injuries as anyone else or even more so, it is important to remember that these players are outfitted, in most cases, with top-of-the-line equipment -- especially their helmets. If the focus is shifted to a younger demographic, youth football players in middle school and high school, the equipment is far less advanced and in a vast majority of cases, has been previously used by …

Energy-Driven Pattern Formation In Planar Dipole-Dipole Systems, Jaron P. Kent-Dobias

HMC Senior Theses

A variety of two-dimensional fluid systems, known as dipole-mediated systems, exhibit a dipole-dipole interaction between their fluid constituents. The com- petition of this repulsive dipolar force with the cohesive fluid forces cause these systems to form intricate and patterned structures in their boundaries. In this thesis, we show that the microscopic details of any such system are irrelevant in the macroscopic limit and contribute only to a constant offset in the system’s energy. A numeric model is developed, and some important stable domain morphologies are characterized. Previously unresolved bifurcating branches are explored. Finally, by applying a random energy background to …

Length Effects Of A Built-In Flapping Flat Plate On The Flow Over A Traveling Wavy Foil, Nansheng Liu, Yan Peng, Xiyun Lu

Mathematics & Statistics Faculty Publications

Flow over the traveling wavy foil with a built-in rigid flapping plate at its trailing edge has been numerically studied using the multi-relaxation-time Lattice Boltzmann method and immersed boundary method. The effect of the plate length on the propulsive performance such as the thrust force, energy consumption, and propeller efficiency has been investigated. Three modes (body force dominated, body and tail force competing and tail force dominated modes) have been identified that are associated with different hydrodynamics and flow structures. It is revealed that there exists a better performance plate length region and, within this region, a high propeller efficiency …

Dynamics Underlying The Gaussian Distribution Of The Classical Harmonic Oscillator In Zero-Point Radiation, Wayne Cheng-Wei Huang, Herman Batelaan

Department of Physics and Astronomy: Faculty Publications

Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to …

Directed Percolation And The Abstract Tile Assembly Model, Tyler Garrett Moore

Graduate Theses and Dissertations

Self-assembly is a process by which simple components build complex structures through local interactions. Directed percolation is a statistical physical model for describing competitive spreading processes on lattices. The author describes an algorithm which can transform a tile assembly system in the abstract Tile Assembly Model into a directed percolation problem, and then shows simulations of the aTAM which support this algorithm. The author also investigates two new constructs designed for Erik Winfree's abstract Tile Assembly Model called the NULL tile and temperature 1.5. These constructs aid the translation between self-assembly and directed percolation and may assist self-assembly researchers in …

Equilibrating Temperaturelike Variables In Jammed Granular Subsystems, James G. Puckett, Karen E. Daniels

Physics and Astronomy Faculty Publications

Although jammed granular systems are athermal, several thermodynamiclike descriptions have been proposed which make quantitative predictions about the distribution of volume and stress within a system and provide a corresponding temperaturelike variable. We perform experiments with an apparatus designed to generate a large number of independent, jammed, two-dimensional configurations. Each configuration consists of a single layer of photoelastic disks supported by a gentle layer of air. New configurations are generated by cyclically dilating, mixing, and then recompacting the system through a series of boundary displacements. Within each configuration, a bath of particles surrounds a smaller subsystem of particles with a …

Measures Of Centrality Based On The Spectrum Of The Laplacian, Scott D. Pauls, Daniel Remondini

Dartmouth Scholarship

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information.

We explore this centrality in the context of several examples. While for sparse unweighted net- works 1-spectral centrality behaves similarly to other standard centralities, for dense weighted net- works they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) …

Comparative Statistical Analysis Of Auroral Models, Cory T. Lane

Theses and Dissertations

The location of the equatorward boundary of the auroral oval provides an appropriate means to measure the accuracy of auroral models. In this study, the equatorward boundary is represented by the location at which the energy flux data measured by DMSP satellites exceeds 0.4 erg/cm²/s. The MLAT coordinates obtained from more than 4,000 orbits through the polar region of the Northern Hemisphere comprise the data set used to compare to the outputs of five auroral models. These models are: the original Hardy auroral model of 1985 (OH), the OVATION Prime model (OP), the 2008 adaptation to the Hardy …

Flow Over A Traveling Wavy Foil With A Passively Flapping Flat Plate, Nansheng Liu, Yan Peng, Youwen Liang, Xiyun Lu

Mathematics & Statistics Faculty Publications

Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The …

Viscoelastic Transition And Yield Strain Of The Folded Protein, Yong Wang, Giovanni Zocchi

Physics Faculty Publications and Presentations

For proteins, the mechanical properties of the folded state are directly related to function, which generally entails conformational motion. Through sub-Angstrom resolution measurements of the AC mechanical susceptibility of a globular protein we describe a new fundamental materials property of the folded state. For increasing amplitude of the forcing, there is a reversible transition from elastic to viscoelastic response. At fixed frequency, the amplitude of the deformation is piecewise linear in the force, with different slopes in the elastic and viscoelastic regimes. Effectively, the protein softens beyond a yield point defined by this transition. We propose that ligand induced conformational …

Critical Torque For Kink Formation In Double-Stranded Dna, Hao Qu, Yong Wang, Chiao-Yu Tseng, Giovanni Zocchi

Physics Faculty Publications and Presentations

We measure the bending energy of double-stranded DNA in the nonlinear (sharply bent) regime. The measurements are obtained from the melting curves of stressed DNA ring molecules. The nonlinear elastic behavior is captured by a single parameter: the critical torque τc at which the molecule develops a kink. In this regime, the elastic energy is linear in the kink angle. This phenomenology is the same as for the previously reported case of nicked DNA. For the sequences examined, we find τc=31 pN×nm. This critical torque corresponds to a characteristic energy scale (π/2)τc=12 kT room relevant for molecular biology processes associated …

Approach To Accurately Measuring The Speed Of Optical Precursors, Chuan-Feng Li, Zong-Quan Zhou, Heejeong Jeong, Guang-Can Guo

Dartmouth Scholarship

Precursors can serve as a bound on the speed of information with dispersive medium. We propose a method to identify the speed of optical wavefronts using polarization-based interference in a solid-state device, which can bound the accuracy of the speed of wavefronts to less than 10−4 with conventional experimental conditions. Our proposal may have important implications for optical communications and fast information processing.

Exact Solutions For Social And Biological Contagion Models On Mixed Directed And Undirected, Degree-Correlated Random Networks, Joshua L. Payne, Kameron Decker Harris, Peter Sheridan Dodds

Dartmouth Scholarship

We derive analytic expressions for the possibility, probability, and expected size of global spread- ing events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree-degree correla- tions. Our work extends previous theoretical developments for the undirected case, and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed-form expressions.

Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid

Applications and Applied Mathematics: An International Journal (AAM)

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is …

Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed

Applications and Applied Mathematics: An International Journal (AAM)

The nonlinear propagation of small but finite amplitude dust-acoustic solitary waves (DAWs) in magnetized collision less dusty plasma has been investigated. The fluid model is a four component magnetized dusty plasma, consisting of positive and negative dust species, isothermal electrons and ions in the presence of an external magnetic field. A reductive perturbation method was employed to obtain the Zakharov Kuznetsov (ZK) equation for the first-order potential. The effects of the presence of positively charged dust fluid, the external magnetic field, and the obliqueness are obtained. The results of the present investigation may be applicable to some plasma environments, such …

Turbulence And Bias-Induced Flows In Simple Magnetized Toroidal Plasmas, B. Li, B. N. Rogers, P. Ricci, K. W. Gentle

Dartmouth Scholarship

Turbulence and bias-induced flows in simple magnetized toroidal plasmas are explored with global three- dimensional fluid simulations, focusing on the parameters of the Helimak experiment. The simulations show that plasma turbulence and transport in the regime of interest are dominated by the ideal interchange instability. The application of a bias voltage alters the structure of the plasma potential, resulting in the equilibrium sheared flows. These bias-induced vertical flows located in the gradient region appear to reduce the radial extent of turbulent structures, and thereby lower the radial plasma transport on the low field side.