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- Ideal free distribution (4)
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- Evolutionarily stable strategy (2)
- Habitat choice (2)
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- Control reproduction number (1)
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Canonoid And Poissonoid Transformations, Symmetries And Bihamiltonian Structures, Giovanni Rastelli, Manuele Santoprete
Canonoid And Poissonoid Transformations, Symmetries And Bihamiltonian Structures, Giovanni Rastelli, Manuele Santoprete
Mathematics Faculty Publications
We give a characterization of linear canonoid transformations on symplectic manifolds and we use it to generate biHamiltonian structures for some mechanical systems. Utilizing this characterization we also study the behavior of the harmonic oscillator under canonoid transformations. We present a description of canonoid transformations due to E.T. Whittaker, and we show that it leads, in a natural way, to the modern, coordinate-independent definition of canonoid transformations. We also generalize canonoid transformations to Poisson manifolds by introducing Poissonoid transformations. We give examples of such transformations for Euler’s equations of the rigid body (on so*(3) and so*(4)) and for an integrable …
On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete
On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete
Mathematics Faculty Publications
Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. …
An Octonian Algebra Originating In Combinatorics, Dragomir Ž. Đokovic, Kaiming Zhao
An Octonian Algebra Originating In Combinatorics, Dragomir Ž. Đokovic, Kaiming Zhao
Mathematics Faculty Publications
C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of δ-codes (now known as T-sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.
Global Stability Of An Sir Epidemic Model With Delay And General Nonlinear Incidence, C. Connell Mccluskey
Global Stability Of An Sir Epidemic Model With Delay And General Nonlinear Incidence, C. Connell Mccluskey
Mathematics Faculty Publications
An SIR model with distributed delay and a general incidence function is studied. Conditions are given under which the system exhibits threshold behaviour: the disease-free equilibrium is globally asymptotically stable if R0 < 1 and globally attracting if R0 = 1; if R0 > 1, then the unique endemic equilibrium is globally asymptotically stable. The global stability proofs use a Lyapunov functional and do not require uniform persistence to be shown a priori. It is shown that the given conditions are satisfied by several common forms of the incidence function.
Cooperation And Stability Through Periodic Impulse, Bo-Yu Zhang, Ross Cressman, Yi Tao
Cooperation And Stability Through Periodic Impulse, Bo-Yu Zhang, Ross Cressman, Yi Tao
Mathematics Faculty Publications
Basic games, where each individual chooses between two strategies, illustrate several issues that immediately emerge from the standard approach that applies strategic reasoning, based on rational decisions, to predict population behavior where no rationality is assumed. These include how mutual cooperation (which corresponds to the best outcome from the population perspective) can evolve when the only individually rational choice is to defect, illustrated by the Prisoner’s Dilemma (PD) game, and how individuals can randomize between two strategies when neither is individually rational, illustrated by the Battle of the Sexes (BS) game that models male-female conflict over parental investment in offspring. …
A Relative Seidel Morphism And The Albers Map, Shengda Hu, François Lalonde
A Relative Seidel Morphism And The Albers Map, Shengda Hu, François Lalonde
Mathematics Faculty Publications
In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in Ham(M), starting at the identity and ending on the subgroup that preserves a given Lagrangian submanifold L, an element in the Floer homology of L. We show that these elements are related to the absolute Seidel elements by the Albers map. We also study, for later use, the effect of reversing the signs of the symplectic structure as well as the orientations of the generators and of the operations on the Floer homologies.
Manipulation Of Single Electron Spin In A Gaas Quantum Dot Through The Application Of Geometric Phases: The Feynman Disentangling Technique, Sanjay Prabhakar, James Reynolds, Akira Inomata, Roderick V.N. Melnik
Manipulation Of Single Electron Spin In A Gaas Quantum Dot Through The Application Of Geometric Phases: The Feynman Disentangling Technique, Sanjay Prabhakar, James Reynolds, Akira Inomata, Roderick V.N. Melnik
Mathematics Faculty Publications
The spin of a single electron in an electrically defined quantum dot in a two-dimensional electron gas can be manipulated by moving the quantum dot adiabatically in a closed loop in the two-dimensional plane under the influence of applied gate potentials. In this paper we present analytical expressions and numerical simulations for the spin-flip probabilities during the adiabatic evolution in the presence of the Rashba and Dresselhaus linear spin-orbit interactions. We use the Feynman disentanglement technique to determine the non-Abelian Berry phase and we find exact analytical expressions for three special cases: (i) the pure Rashba spin-orbit coupling, (ii) the …
Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik
Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik
Mathematics Faculty Publications
A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have …
Influence Of Electromechanical Effects And Wetting Layers On Band Structures Of Ain/Gan Quantum Dots And Spin Control, Sanjay Prabhakar, Roderick V.N. Melnik
Influence Of Electromechanical Effects And Wetting Layers On Band Structures Of Ain/Gan Quantum Dots And Spin Control, Sanjay Prabhakar, Roderick V.N. Melnik
Mathematics Faculty Publications
In a series of recent papers we demonstrated that coupled electromechanical effects can lead to pronounced contributions in band structure calculations of low dimensional semiconductor nanostructures LDSNs such as quantum dots QDs , wires, and even wells. Some such effects are essentially nonlinear. Both strain and piezoelectric effects have been used as tuning parameters for the optical response of LDSNs in photonics, band gap engineering, and other applications. However, the influence of spin orbit effects in presence of external magnetic field on single and vertically coupled QD has been largely neglected in the literature. The electron spin splitting terms which …
Harish-Chandra Modules Over The Q Heisenberg-Virasoro Algebra, Xiangqian Guo, Xuewen Liu, Kaiming Zhao
Harish-Chandra Modules Over The Q Heisenberg-Virasoro Algebra, Xiangqian Guo, Xuewen Liu, Kaiming Zhao
Mathematics Faculty Publications
In this paper, it is proved that all irreducible Harish-Chandra modules over the Q Heisenberg–Virasoro algebra are of the intermediate series (all weight spaces are at most one-dimensional).
Global Stability For An Seir Epidemiological Model With Varying Infectivity And Infinite Delay, C. Connell Mccluskey
Global Stability For An Seir Epidemiological Model With Varying Infectivity And Infinite Delay, C. Connell Mccluskey
Mathematics Faculty Publications
A recent paper (Math. Biosci. and Eng. (2008) 5:389-402) presented an SEIR model using an infinite delay to account for varying infectivity. The analysis in that paper did not resolve the global dynamics for R0 > 1. Here, we show that the endemic equilibrium is globally stable for R0 > 1. The proof uses a Lyapunov functional that includes an integral over all previous states.
On Evolutionary Stability In Predator-Prey Models With Fast Behavioral Dynamics, Vlastimil Křivan, Ross Cressman
On Evolutionary Stability In Predator-Prey Models With Fast Behavioral Dynamics, Vlastimil Křivan, Ross Cressman
Mathematics Faculty Publications
No abstract provided.
Geometry Dependent Current-Voltage Characteristics Of Zno Nanostructures: A Combined Nonequilibrium Green’S Function And Density Functional Theory Study, Zhiwen Yang, Bin Wen, Roderick V.N. Melnik, Tingju Li
Geometry Dependent Current-Voltage Characteristics Of Zno Nanostructures: A Combined Nonequilibrium Green’S Function And Density Functional Theory Study, Zhiwen Yang, Bin Wen, Roderick V.N. Melnik, Tingju Li
Mathematics Faculty Publications
Current-voltage I-V characteristics of different ZnO nanostructures were studied using a combined nonequilibrium Green’s function and density functional theory techniques with the two-probe model. It was found that I-V characteristics of ZnO nanostructures depend strongly on their geometry. For wurtzite ZnO nanowires, currents decrease with increasing lengths under the same applied voltage conditions. The I-V characteristics are similar for single-walled ZnO nanotubes and triangular cross section ZnO nanowires but they are different from I-V characteristics of hexagonal cross section ZnO nanowires. Finally, our results are discussed in the context of calculated transmission spectra and densities of states.
Hamiltonian Symmetries And Reduction In Generalized Geometry, Shengda Hu
Hamiltonian Symmetries And Reduction In Generalized Geometry, Shengda Hu
Mathematics Faculty Publications
No abstract provided.
Saari’S Homographic Conjecture Of The Three-Body Problem, Florin Diacu, Toshiaki Fujiwara, Ernesto Pérez-Chavela, Manuele Santoprete
Saari’S Homographic Conjecture Of The Three-Body Problem, Florin Diacu, Toshiaki Fujiwara, Ernesto Pérez-Chavela, Manuele Santoprete
Mathematics Faculty Publications
Saari’s homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian n-body problem with constant configurational measure are homographic. In other words, if the mutual distances satisfy a certain relationship, the configuration of the particle system may change size and position but not shape. We prove this conjecture for large sets of initial conditions in three-body problems given by homogeneous potentials, including the Newtonian one. Some of our results are true for n ≥ 3.
On Using Curvature To Demonstrate Stability, C. Connell Mccluskey
On Using Curvature To Demonstrate Stability, C. Connell Mccluskey
Mathematics Faculty Publications
A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This is used to establish a negative-criterion for periodic orbits. This is extended to give a method of proving an equilibrium to be globally stable. The approach can also be used to rule out the sudden appearance of large-amplitude periodic orbits.
First Principles Molecular Dynamics Study Of Cds Nanostructure Temperature-Dependent Phase Stability, Bin Wen, Roderick V.N. Melnik
First Principles Molecular Dynamics Study Of Cds Nanostructure Temperature-Dependent Phase Stability, Bin Wen, Roderick V.N. Melnik
Mathematics Faculty Publications
First principles molecular dynamics simulations are used to determine the relative stability of wurtzite, graphitic, and rocksalt phases of the CdS nanostructure at various temperatures. Our results indicate that in the temperature range from 300 to 450 K, the phase stability sequence for the CdS nanostructure is rocksalt, wurtzite, and graphitic phases. The same situation holds for bulk CdS crystals under high pressure and 0 K. Our work also demonstrates that although the temperature can affect the total energy of the CdS nanostructure, it cannot change its phase stability sequence in the temperature range studied in this letter.
Gravitational And Harmonic Oscillator Potentials On Surfaces Of Revolution, Manuele Santoprete
Gravitational And Harmonic Oscillator Potentials On Surfaces Of Revolution, Manuele Santoprete
Mathematics Faculty Publications
In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian curvature. The two potentials leading to closed orbits are suitable generalizations of the gravitational and harmonic oscillator potential. We also show that there could be surfaces admitting only one potential that leads to closed orbits. In this case, the potential is a generalized harmonic oscillator. …
Saari’S Conjecture Is True For Generic Vector Fields, Tanya Schmah, Cristina Stoica
Saari’S Conjecture Is True For Generic Vector Fields, Tanya Schmah, Cristina Stoica
Mathematics Faculty Publications
The simplest non-collision solutions of the N-body problem are the “relative equilibria”, in which each body follows a circular orbit around the centre of mass and the shape formed by the N bodies is constant. It is easy to see that the moment of inertia of such a solution is constant. In 1970, D. Saari conjectured that the converse is also true for the planar Newtonian N-body problem: relative equilibria are the only constant-inertia solutions. A computer-assisted proof for the 3-body case was recently given by R. Moeckel, Trans. Amer. Math. Soc. (2005). We present a different kind …
The Role Of Behavioral Dynamics In Determining The Patch Distributions Of Interacting Species, Peter A. Abrams, Ross Cressman, Vlastimil Křivan
The Role Of Behavioral Dynamics In Determining The Patch Distributions Of Interacting Species, Peter A. Abrams, Ross Cressman, Vlastimil Křivan
Mathematics Faculty Publications
The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single-species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two-species–two-patch …
Reduction And Duality In Generalized Geometry, Shengda Hu
Reduction And Duality In Generalized Geometry, Shengda Hu
Mathematics Faculty Publications
Extending our reduction construction in (S. Hu, Hamiltonian symmetries and reduction in generalized geometry, Houston J. Math., to appear, math.DG/0509060, 2005.) to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) T-duality with H-fluxes for principle bundles naturally arise as reductions of factorizable Poisson Lie group actions. In particular, the groups involved may be non-abelian.
Accounting For The Effect Of Internal Viscosity In Dumbbell Models For Polymeric Fluids And Relaxation Of Dna, Xiao-Dong Yang, Roderick V.N. Melnik
Accounting For The Effect Of Internal Viscosity In Dumbbell Models For Polymeric Fluids And Relaxation Of Dna, Xiao-Dong Yang, Roderick V.N. Melnik
Mathematics Faculty Publications
The coarse-graining approach is one of the most important mod- eling methods in research of long-chain polymers such as DNA molecules. The dumbbell model is a simple but e±cient way to describe the behavior of polymers in solutions. In this paper, the dumbbell model with internal viscosity (IV) for concentrated polymeric liquids is analyzed for the steady-state and time-dependent elongational flow and steady-state shear °ow. In the elongational flow case, by analyzing the governing ordinary di®erential equations the contribution of the IV to the stress tensor is discussed for fluids subjected to a sudden elongational jerk. In the shear °ow …
Lyapunov Functions For Tuberculosis Models With Fast And Slow Progression, C. Connell Mccluskey
Lyapunov Functions For Tuberculosis Models With Fast And Slow Progression, C. Connell Mccluskey
Mathematics Faculty Publications
The spread of tuberculosis is studied through two models which include fast and slow progression to the infected class. For each model, Lyapunov functions are used to show that when the basic reproduction number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is globally asymptotically stable.
An Sveir Model For Assessing Potential Impact Of An Imperfect Anti-Sars Vaccine, Abba B. Gumel, C. Connell Mccluskey, James Watmough
An Sveir Model For Assessing Potential Impact Of An Imperfect Anti-Sars Vaccine, Abba B. Gumel, C. Connell Mccluskey, James Watmough
Mathematics Faculty Publications
The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of …
Migration Dynamics For The Ideal Free Distribution, Ross Cressman, Vlastimil Křivan
Migration Dynamics For The Ideal Free Distribution, Ross Cressman, Vlastimil Křivan
Mathematics Faculty Publications
This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency-dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that the population distribution converges to the IFD even when animals are nonideal (i.e., they do not know the quality of all patches). In particular, the IFD emerges when animals never migrate from patches with a higher payoff to patches with a …
Semi-Stable Degeneration Of Toric Varieties And Their Hypersurfaces, Shengda Hu
Semi-Stable Degeneration Of Toric Varieties And Their Hypersurfaces, Shengda Hu
Mathematics Faculty Publications
We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of K3 surface into 4 rational components, an algebraic geometric version of decomposing K3 as the fiber sum of two E(1)’s as well as it’s higher dimensional generalizations, and many other new examples.
Dynamic Coupling Of Piezoelectric Effects, Spontaneous Polarization, And Strain In Lattice-Mismatched Semiconductor Quantum-Well Heterostructures, Morten Willatzen, Benny Lassen, L.C. Lew Yan Voon, Roderick V.N. Melnik
Dynamic Coupling Of Piezoelectric Effects, Spontaneous Polarization, And Strain In Lattice-Mismatched Semiconductor Quantum-Well Heterostructures, Morten Willatzen, Benny Lassen, L.C. Lew Yan Voon, Roderick V.N. Melnik
Mathematics Faculty Publications
A static and dynamic analysis of the combined and self-consistent influence of spontaneous polarization, piezoelectric effects, lattice mismatch, and strain effects is presented for a three-layer one-dimensional AlN/GaN wurtzite quantum-well structure with GaN as the central quantum-well layer . It is shown that, contrary to the assumption of Fonoberov and Balandin [J. Appl. Phys. 94, 7178 (2003); J. Vac. Sci. Technol. B 22, 2190 (2004)], even in cases with no current transport through the structure, the strain distributions are not well captured by minimization of the strain energy only and not, as is in principle required, the total free energy …
Verma Modules Over Virasoro-Like Algebras, Xian-Dong Wang, Kaiming Zhao
Verma Modules Over Virasoro-Like Algebras, Xian-Dong Wang, Kaiming Zhao
Mathematics Faculty Publications
No abstract provided.
Dynamics Of Shape Memory Alloys Patches With Mechanically Induced Transformations, Linxiang Wang, Roderick V.N. Melnik
Dynamics Of Shape Memory Alloys Patches With Mechanically Induced Transformations, Linxiang Wang, Roderick V.N. Melnik
Mathematics Faculty Publications
A mathematical model is constructed for the modelling of two di- mensional thermo-mechanical behavior of shape memory alloy patches. The model is constructed on the basis of a modified Landau-Ginzburg theory and includes the coupling effect between thermal and mechanical fields. The free energy functional for the model is exemplified for the square to rectangular transformations. The model, based on nonlinear coupled partial differential equations, is reduced to a system of differential-algebraic equations and the backward differentiation methodology is used for its numerical analysis. Computational experiments with representative distributed mechanical loadings are carried out for patches of different sizes to …
Global Attractivity Of A Circadian Pacemaker Model In A Periodic Environment, Yuming Chen, Lin Wang
Global Attractivity Of A Circadian Pacemaker Model In A Periodic Environment, Yuming Chen, Lin Wang
Mathematics Faculty Publications
In this paper, we propose a delay differential equation with continuous periodic parameters to model the circadian pacemaker in a periodic environment. First, we show the existence of a positive periodic solution by using the theory of coincidence degree. Then we establish the global attractivity of the periodic solution under two su±cient conditions. These conditions are easily verifiable and are independent of each other. Some numerical simulations are also performed to demonstrate the main results.