Statistics Of The Island-Around-Island Hierarchy In Hamiltonian Phase Space, 2014 Technion-Israel Institute of Technology

#### Statistics Of The Island-Around-Island Hierarchy In Hamiltonian Phase Space, Or Alus, Shmuel Fishman, James Meiss

*Applied Mathematics Faculty Contributions*

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution ...

Transients In The Synchronization Of Oscillator Arrays, 2014 Portland State University

#### Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities ...

Exact Tests For Singular Network Data, 2014 Portland State University

#### Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya

*Mathematics and Statistics Faculty Publications and Presentations*

We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds, 2014 Western Michigan University

#### Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds, Robert J. Kipka

*Dissertations*

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds Driven by applications in fields such as robotics and satellite attitude control, as well as by a need for the theoretical development of appropriate tools for the analysis of geometric systems, problems of control of dynamical systems on manifolds have been studied intensively during the past three decades. In this dissertation we suggest new mathematical techniques for the study of control and dynamic optimization problems on manifolds. This work has several components including: an extension of the classical Chronological Calculus to control and dynamical systems which are merely ...

Vanishing Configurations In Network Dynamics With Asynchronous Updates, 2014 Portland State University

#### Vanishing Configurations In Network Dynamics With Asynchronous Updates, Ian H. Dinwoodie

*Mathematics and Statistics Faculty Publications and Presentations*

We consider Boolean dynamics for biological networks where stochasticity is introduced through asynchronous updates. An exact method is given for finding states which can reach a steady state with positive probability, and a method is given for finding states which cannot reach other steady states. These methods are based on computational commutative algebra. The algorithms are applied to dynamics of a cell survival network to determine node assignments that exclude termination in a cancerous state

High Precision Rapid Convergence Of Asian Options, 2014 Utah State University

#### High Precision Rapid Convergence Of Asian Options, Mario Y. Harper

*Mario Yuuji Harper*

We show various methods that increase the precision and convergence speed of simulated stochastic processes. We demonstrate our precision and speed by using an example from the finance world, namely that of an Asian Option. An Asian Option is a path dependent pricing mechanism that is normally priced using Monte Carlo methods, it can be thought of as a path dependent diffusion equation. We show that the precision of the simulations is increased by 70% using Control Variates (derived by approximating the true mean from an analytic closed form solution). Using sequential Monte Carlo and parallel computing across a GPU ...

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, 2014 Marshall University

#### Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

*Mathematics Faculty Research*

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diﬀusion coeﬃcient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, suﬃcient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure ...

Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, 2014 University of Tennessee - Knoxville

#### Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, Matthew Singh

*EURēCA: Exhibition of Undergraduate Research and Creative Achievement*

No abstract provided.

High Precision Rapid Convergence Of Asian Options, 2014 Utah State University

#### High Precision Rapid Convergence Of Asian Options, Mario Y. Harper

*Physics Capstone Project*

We show various methods that increase the precision and convergence speed of simulated stochastic processes. We demonstrate our precision and speed by using an example from the finance world, namely that of an Asian Option. An Asian Option is a path dependent pricing mechanism that is normally priced using Monte Carlo methods, it can be thought of as a path dependent diffusion equation. We show that the precision of the simulations is increased by 70% using Control Variates (derived by approximating the true mean from an analytic closed form solution). Using sequential Monte Carlo and parallel computing across a GPU ...

Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, 2014 Georgia State University

#### Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, Rosahn Bhattarai

*Georgia State Undergraduate Research Conference*

No abstract provided.

Basins Of Attraction For Pulse-Coupled Oscillators, 2014 College of William and Mary

#### Basins Of Attraction For Pulse-Coupled Oscillators, Ryan Gryder

*Undergraduate Honors Theses*

Basins of attraction for forward invariant sets can carve out portions of phase space where one can make predictions for asymptotic dynamics. We present com- putational algorithms for computing inner approximations of basins of attraction for discrete-time dynamical systems. The algorithms, based on subdivision tech- niques for grid construction and outer approximation of images, are adaptive and eciently allow one to identify full dimensional portions of phase space where the asymptotic dynamics may be described quantitatively. As illustration, we apply the techniques to a system of three pulse-coupled oscillators, computing an inner approximation for the basin of attraction for the ...

Euler-Poincar´E Equations For G-Strands, 2014 Imperial College London

#### Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

*Conference papers*

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g^{∗} with respect to the pairing provided by the variational derivatives of the Lagrangian ...

Fractal Powers In Serrin's Swirling Vortex Solutions, 2014 Augsburg University

#### Fractal Powers In Serrin's Swirling Vortex Solutions, Pavel Bělík, Douglas P. Dokken, Kurt Scholz, Mikhail M. Shvartsman

*Faculty Authored Articles*

We consider a modification of the fluid flow model for a tornado-like swirling vortex developed by Serrin [Phil. Trans. Roy. Soc. London, Series A, Math & Phys. Sci. 271(1214) (1972), 325–360], where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based on radar data of selected severe weather events [Mon. Wea. Rev. 133(9) (2005), 2535–2551; Mon. Wea. Rev. 128(7) (2000), 2135–2164; Mon. Wea. Rev. 133(1) (2005), 97–119], indicate that the angular momentum in a tornado may not be constant with the radius, and thus suggest a different scaling of the velocity/radial distance dependence. Motivated by this suggestion, we consider Serrin's approach with the assumption that the velocity decreases as the reciprocal of the distance from the vortex axis to the power b with a ...

Can A Falling Bullet Kill You?, 2014 California Polytechnic State University - San Luis Obispo

#### Can A Falling Bullet Kill You?, Zechariah Thurman

*Zechariah Thurman*

A terminal velocity examination of the problem of the falling bullet is investigated.

Termodynamika Procesowa I Techniczna Lab., 2014 Wroclaw University of Technology

#### Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., 2014 Wroclaw University of Technology

#### Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., 2014 Wroclaw University of Technology

#### Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Mechanika Płynów Lab., 2014 Wroclaw University of Technology

#### Mechanika Płynów Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, 2014 Marshall University

#### Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson

*Theses, Dissertations and Capstones*

In this work, we give an introduction to Time Scales Calculus, the properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equation of second order. Time Scales Calculus was introduced by Stefan Hilger in 1988. It brings together the theories of difference and differential equations into one uniﬁed theory. By using the properties of the delta derivative and the delta anti-derivative, we analyze the behavior of a second order linear homogeneous dynamic equation on various time scales. After the analytical discussion, we will graphically evaluate the second order dynamic equation in Marshall ...

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, 2014 Wilfrid Laurier University

#### Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

*Theses and Dissertations (Comprehensive)*

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses ...