Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Applied Mathematics (15)
- Non-linear Dynamics (13)
- Fluid Dynamics (12)
- Engineering (8)
- Partial Differential Equations (8)
-
- Nuclear (7)
- Optics (7)
- Electrical and Computer Engineering (6)
- Mathematics (6)
- Electromagnetics and Photonics (5)
- Quantum Physics (4)
- Numerical Analysis and Computation (3)
- Atomic, Molecular and Optical Physics (2)
- Algebra (1)
- Analysis (1)
- Computational Engineering (1)
- Condensed Matter Physics (1)
- Dynamic Systems (1)
- Dynamical Systems (1)
- Geometry and Topology (1)
- Harmonic Analysis and Representation (1)
- Oceanography (1)
- Oceanography and Atmospheric Sciences and Meteorology (1)
- Operations Research, Systems Engineering and Industrial Engineering (1)
- Other Applied Mathematics (1)
- Other Physics (1)
- Plasma and Beam Physics (1)
- Statistical, Nonlinear, and Soft Matter Physics (1)
- Institution
- Publication Year
- Publication
-
- Andrei Ludu (9)
- Electronic Theses and Dissertations (5)
- Articles (3)
- Physics Faculty Research & Creative Works (3)
- Dissertations (2)
-
- Electrical & Computer Engineering Faculty Publications (2)
- Faculty Publications (2)
- Publications (2)
- Dartmouth Scholarship (1)
- Doctoral Dissertations (1)
- Faculty Research, Scholarly, and Creative Activity (1)
- Mathematics and Statistics Department Faculty Publication Series (1)
- Peter Palffy-Muhoray (1)
- Portland Institute for Computational Science Publications (1)
- Publication Type
Articles 1 - 30 of 34
Full-Text Articles in Physics
Interactions And Dynamics Of One-Dimensional Droplets, Bubbles And Kinks, Garyfallia Katsimiga, Simeon I. Mistakidis, Boris A. Malomed, Dimitris J. Frantzeskakis, Ricardo Carretero-Gonzalez, Panayotis G. Kevrekidis
Interactions And Dynamics Of One-Dimensional Droplets, Bubbles And Kinks, Garyfallia Katsimiga, Simeon I. Mistakidis, Boris A. Malomed, Dimitris J. Frantzeskakis, Ricardo Carretero-Gonzalez, Panayotis G. Kevrekidis
Physics Faculty Research & Creative Works
We Explore The Dynamics And Interactions Of Multiple Bright Droplets And Bubbles, As Well As The Interactions Of Kinks With Droplets And With Antikinks, In The Extended One-Dimensional Gross–Pitaevskii Model Including The Lee–Huang–Yang Correction. Existence Regions Are Identified For The One-Dimensional Droplets And Bubbles In Terms Of Their Chemical Potential, Verifying The Stability Of The Droplets And Exposing The Instability Of The Bubbles. The Limiting Case Of The Droplet Family Is A Stable Kink. The Interactions Between Droplets Demonstrate In-Phase (Out-Of-Phase) Attraction (Repulsion), With The So-Called Manton's Method Explicating The Observed Dynamical Response, And Mixed Behavior For Intermediate Values Of …
Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias
Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias
Doctoral Dissertations
In recent years, there has been an explosion of interest in media bearing quartic
dispersion. After the experimental realization of so-called pure-quartic solitons, a
significant number of studies followed both for bright and for dark solitonic struc-
tures exploring the properties of not only quartic, but also setic, octic, decic etc.
dispersion, but also examining the competition between, e.g., quadratic and quartic
dispersion among others.
In the first chapter of this Thesis, we consider the interaction of solitary waves in
a model involving the well-known φ4 Klein-Gordon theory, bearing both Laplacian and biharmonic terms with different prefactors. As a …
Coherent Control Of Dispersive Waves, Jimmie Adriazola
Coherent Control Of Dispersive Waves, Jimmie Adriazola
Dissertations
This dissertation addresses some of the various issues which can arise when posing and solving optimization problems constrained by dispersive physics. Considered here are four technologically relevant experiments, each having their own unique challenges and physical settings including ultra-cold quantum fluids trapped by an external field, paraxial light propagation through a gradient index of refraction, light propagation in periodic photonic crystals, and surface gravity water waves over shallow and variable seabeds. In each of these settings, the physics can be modeled by dispersive wave equations, and the technological objective is to design the external trapping fields or propagation media such …
Soliton Based All-Optical Data Processing In Waveguides, Amaria Javed
Soliton Based All-Optical Data Processing In Waveguides, Amaria Javed
Dissertations
The growing demand for higher data processing speed and capacity motivates the replacement of the current electronic data processing by optical data processing in analogy with the successful replacement of electronic data communication by optical data communication. In a quest to achieve comprehensive optical data processing we aim at using solitons in waveguide arrays to perform all-optical data processing operations. Solitons are special nonlinear waves appreciated for their ability to conserve their shape and velocity before and after scattering. They are observed naturally in diverse fields of science, namely, nonlinear physics, mathematics, hydrodynamics, biophysics, and quantum field theory, etc. with …
Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea
Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea
Publications
Irrotational flow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrödinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for …
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F = 1 Bose-Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark-dark-bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark-bright-bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature …
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose-Einstein Condensates, Garyfallia Katsimiga, Simeon I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose-Einstein Condensates, Garyfallia Katsimiga, Simeon I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Physics Faculty Research & Creative Works
We Present The Phase Diagram, The Underlying Stability And Magnetic Properties As Well As The Dynamics Of Nonlinear Solitary Wave Excitations Arising In The Distinct Phases Of A Harmonically Confined Spinor F = 1 Bose-Einstein Condensate. Particularly, It Is Found That Nonlinear Excitations In The Form Of Dark-Dark-Bright Solitons Exist In The Antiferromagnetic And In The Easy-Axis Phase Of A Spinor Gas, Being Generally Unstable In The Former While Possessing Stability Intervals In The Latter Phase. Dark-Bright-Bright Solitons Can Be Realized In The Polar And The Easy-Plane Phases As Unstable And Stable Configurations Respectively; The Latter Phase Can Also Feature …
On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov
On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov
Articles
A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …
Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov
Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov
Articles
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Articles
We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …
Entanglement Entropy, Dualities, And Deconfinement In Gauge Theories, Mohamed M. Anber, Benjamin J. Kolligs
Entanglement Entropy, Dualities, And Deconfinement In Gauge Theories, Mohamed M. Anber, Benjamin J. Kolligs
Portland Institute for Computational Science Publications
Computing the entanglement entropy in confining gauge theories is often accompanied by puzzles and ambiguities. In this work we show that compactifying the theory on a small circle S 1/L evades these difficulties. In particular, we study Yang-Mills theory on R3×S 1/L with double-trace deformations or adjoint fermions and hold it at temperatures near the deconfinement transition. This theory is dual to a multi-component (electric-magnetic) Coulomb gas that can be mapped either to an XY-spin model with Zp symmetry-preserving perturbations or dual Sine-Gordon model. The entanglement entropy of the dual SineGordon model exhibits an extremum at the …
Neutrino Pair Cerenkov Radiation For Tachyonic Neutrinos, Ulrich D. Jentschura, Istvan Nandori
Neutrino Pair Cerenkov Radiation For Tachyonic Neutrinos, Ulrich D. Jentschura, Istvan Nandori
Physics Faculty Research & Creative Works
The emission of a charged light lepton pair by a superluminal neutrino has been identified as a major factor in the energy loss of highly energetic neutrinos. The observation of PeV neutrinos by IceCube implies their stability against lepton pair Cerenkov radiation. Under the assumption of a Lorentz-violating dispersion relation for highly energetic superluminal neutrinos, one may thus constrain the Lorentz-violating parameters. A kinematically different situation arises when one assumes a Lorentz-covariant, space-like dispersion relation for hypothetical tachyonic neutrinos, as an alternative to Lorentz-violating theories. We here discuss a hitherto neglected decay process, where a highly energetic tachyonic neutrino may …
Kinetic Theory Of Dark Solitons With Tunable Friction, Hilary M. Hurst, Dimitry K. Efimkin, I. B. Spielman, Victor Galitski
Kinetic Theory Of Dark Solitons With Tunable Friction, Hilary M. Hurst, Dimitry K. Efimkin, I. B. Spielman, Victor Galitski
Faculty Research, Scholarly, and Creative Activity
We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a non-interacting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semi-classical dynamics of the dark soliton, a particle-like object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative mass …
Nonlinear Schrodinger Equation In Nematic Liquid Crystals, Peter Palffy-Muhoray, J. A. Reyes
Nonlinear Schrodinger Equation In Nematic Liquid Crystals, Peter Palffy-Muhoray, J. A. Reyes
Peter Palffy-Muhoray
We derive the amplitude equation, in the weakly nonlinear regime, for an optical wave packet that propagates in an initially undistorted nematic liquid crystal. By using the dyad representation Q(ij), we find the retarded and nonlocal equation for the nematic configuration and solve it in Fourier space. This allows us to calculate the amplitude dependent dispersion relation for a nematic liquid crystal in a given initial undistorted stationary state. We consider a linearly polarized wave packet that travels along the principal axis of the nematic dielectric tensor. We find a nonlinear Schrodinger equation for the amplitude, which includes an additional …
Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu
Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu
Andrei Ludu
No abstract provided.
Optical Nonlinear Interactions In Dielectric Nano-Suspensions, Ramy El-Ganainy
Optical Nonlinear Interactions In Dielectric Nano-Suspensions, Ramy El-Ganainy
Electronic Theses and Dissertations
This work is divided into two main parts. In the first part (chapters 2-7) we consider the nonlinear response of nano-particle colloidal systems. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these arrangements the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. We …
Interaction Of Tollmien-Schlichting Waves In The Air With The Sea Surface, Shahrdad G. Sajjadi, Harihar Khanal
Interaction Of Tollmien-Schlichting Waves In The Air With The Sea Surface, Shahrdad G. Sajjadi, Harihar Khanal
Publications
No abstract provided.
Optical Solitons In Periodic Structures, Konstantinos Makris
Optical Solitons In Periodic Structures, Konstantinos Makris
Electronic Theses and Dissertations
By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a …
Discrete Surface Solitons, Sergiy Suntsov
Discrete Surface Solitons, Sergiy Suntsov
Electronic Theses and Dissertations
Surface waves exist along the interfaces between two different media and are known to display properties that have no analogue in continuous systems. In years past, they have been the subject of many studies in a diverse collection of scientific disciplines. In optics, one of the mechanisms through which optical surface waves can exist is material nonlinearity. Until recently, most of the activity in this area was focused on interfaces between continuous media but no successful experiments have been reported. However, the growing interest that nonlinear discrete optics has attracted in the last two decades has raised the question of …
Energy Landscape Of D -Dimensional Q -Balls, Marcelo Gleiser, Joel Thorarinson
Energy Landscape Of D -Dimensional Q -Balls, Marcelo Gleiser, Joel Thorarinson
Dartmouth Scholarship
We investigate the properties of Q-balls in d spatial dimensions. First, a generalized virial relation for these objects is obtained. We then focus on potentials V(ϕϕ†)=∑3n=1an(ϕϕ†)n, where an is a constant and n is an integer, obtaining variational estimates for their energies for arbitrary charge Q. These analytical estimates are contrasted with numerical results and their accuracy evaluated. Based on the results, we offer a simple criterion to classify large and small d-dimensional Q-balls for this class of potentials. A minimum charge is then computed and its dependence on spatial dimensionality is shown to scale as Qmin∼exp(d). We also briefly …
Lattice Quantum Algorithm For The Schrodinger Wave Equation In 2+1 Dimensions With A Demonstration By Modeling Soliton Instabilities, Jeffrey Yepez, George Vahala, Linda L. Vahala
Lattice Quantum Algorithm For The Schrodinger Wave Equation In 2+1 Dimensions With A Demonstration By Modeling Soliton Instabilities, Jeffrey Yepez, George Vahala, Linda L. Vahala
Electrical & Computer Engineering Faculty Publications
A lattice-based quantum algorithm is presented to model the non-linear Schrödinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit-qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. …
Optical Wave Propagation In Discrete Waveguide Arrays, Jared Hudock
Optical Wave Propagation In Discrete Waveguide Arrays, Jared Hudock
Electronic Theses and Dissertations
The propagation dynamics of light in optical waveguide arrays is characteristic of that encountered in discrete systems. As a result, it is possible to engineer the diffraction properties of such structures, which leads to the ability to control the flow of light in ways that are impossible in continuous media. In this work, a detailed theoretical investigation of both linear and nonlinear optical wave propagation in one- and two-dimensional waveguide lattices is presented. The ability to completely overcome the effects of discrete diffraction through the mutual trapping of two orthogonally polarized coherent beams interacting in Kerr nonlinear arrays of birefringent …
Quantum Lattice Representation Of Dark Solitons, George Vahala, Linda L. Vahala, Jeffrey Yepez
Quantum Lattice Representation Of Dark Solitons, George Vahala, Linda L. Vahala, Jeffrey Yepez
Electrical & Computer Engineering Faculty Publications
The nonlinear Schrodinger (NLS) equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate (BEC) is described by the Gross-Pitaevskii equation, which for a highly anisotropic (cigar-shaped) magnetic trap reduces to a one-dimensional (1D) cubic NLS in an external potential. A quantum lattice algorithm is developed for the dark solitons. Simulations are presented for both black (stationary) solitons as well as (moving) dark solitons. Collisions of dark solitons are compared with the exact analytic solutions and coupled dark-bright vector solitons are examined. The quantum algorithm requires 2 qubits per scalar field …
Discrete Nonlinear Wave Propagation In Kerr Nonlinear Media, Joachim Meier
Discrete Nonlinear Wave Propagation In Kerr Nonlinear Media, Joachim Meier
Electronic Theses and Dissertations
Discrete optical systems are a subgroup of periodic structures in which the evolution of a continuous electromagnetic field can be described by a discrete model. In this model, the total field is the sum of localized, discrete modes. Weakly coupled arrays of single mode channel waveguides have been known to fall into this class of systems since the late 1960's. Nonlinear discrete optics has received a considerable amount of interest in the last few years, triggered by the experimental realization of discrete solitons in a Kerr nonlinear AlGaAs waveguide array by H. Eisenberg and coworkers in 1998. In this work …
Nonlinear Equations And Wavelets, Andrei Ludu
Dynamics Of Formation Of Soliton Conductivity In A 2 D-Array Of Linear Chains Containing Commensurate Charge Density Waves Near The Contact With A Normal Metal, Yuriy V. Pershin Dr, Alexander S. Rozhavsky
Dynamics Of Formation Of Soliton Conductivity In A 2 D-Array Of Linear Chains Containing Commensurate Charge Density Waves Near The Contact With A Normal Metal, Yuriy V. Pershin Dr, Alexander S. Rozhavsky
Faculty Publications
We make a numerical study of the conversion of conduction electrons into charge density wave (CDW) topological solitons at the interface between a normal metal and a 2D-array of the CDW-carrying linear chains. The interplay of commensurability potential, interchain interaction, and electric field on the dynamics of soliton formation is studied. When the interchain interaction exceeds the commensurability energy, the dynamic mechanism of creation of fractionally charged solitons near the contact is suppressed and specific contact nonlinearity in transport current is not observed.
Nonlinear Phenomena In Nuclei: The Antisoliton Model For Fission, Andrei Ludu
Nonlinear Phenomena In Nuclei: The Antisoliton Model For Fission, Andrei Ludu
Andrei Ludu
No abstract provided.
Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu
Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu
Andrei Ludu
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated. Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discussed. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one re-obtains the well-known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear …
A New Dynamic Mechanism Of Topological Charge Creation In A Commensurate One-Dimensional Charge Density Wave Near The Contact With A Normal Metal, A. S. Rozhavsky, Yuriy V. Pershin Dr, A. S. Kovalev
A New Dynamic Mechanism Of Topological Charge Creation In A Commensurate One-Dimensional Charge Density Wave Near The Contact With A Normal Metal, A. S. Rozhavsky, Yuriy V. Pershin Dr, A. S. Kovalev
Faculty Publications
The dynamics of conversion of conduction electrons into topological solitons of a charge density wave (CDW) commensurability in an external electric field is investigated. A novel mechanism of initiation of a nonlinear CDW current in the vicinity of the interface between a CDW and a normal metal is revealed and explained. The nonlinear current is produced by the conduction solitons created by the moving profile of the order parameter, formed during the conversion of electrons into collective phase excitations of a CDW. The field dependence of the current is of threshold nature and has no analogs in the bulk mechanisms …
Nonlinear Liquid Drop Model. Cnoidal Waves, Andrei Ludu
Nonlinear Liquid Drop Model. Cnoidal Waves, Andrei Ludu
Andrei Ludu
No abstract provided.