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 ...

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 ...

Integrability, Recursion Operators And Soliton Interactions, 2014 Bulgarian Academy of Sciences

#### Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov

*Book chapter/book*

This volume contains selected papers based on the talks,presentedat the Conference *Integrability, Recursion Operators and Soliton Interactions*, held in Sofia, Bulgaria (29-31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating ...

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 ...

Fundamental Domain Of Invariant Sets And Applications, 2013 UMass Amherst

#### Fundamental Domain Of Invariant Sets And Applications, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Viscosity Dependence Of Faraday Wave Formation Thresholds, 2013 California Polytechnic State University - San Luis Obispo

#### Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa Michelle Slaughter

*Physics*

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 ...

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, 2013 Western Kentucky University

#### Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

*Mathematics Faculty Publications*

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed ...

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, 2013 Western Kentucky University

#### Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

*Mikhail Khenner*

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed ...

Systems Of Navier-Stokes Equations On Cantor Sets, 2013 D. Baleanu

#### Systems Of Navier-Stokes Equations On Cantor Sets

*Xiao-Jun Yang*

We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Dynamics Of The Fitzhugh-Nagumo Neuron Model, 2013 California Polytechnic State University - San Luis Obispo

#### Dynamics Of The Fitzhugh-Nagumo Neuron Model, Zechariah Thurman

*Physics*

In this paper, the dynamical behavior of the Fitzhugh-Nagumo model is examined. The relationship between neuron input current and the firing frequency of the neuron is characterized. Various coupling schemes are also examined, and their effects on the dynamics of the system is discussed. The phenomenon of stochastic resonance is studied for a single uncoupled Fitzhugh-Nagumo neuron.

Boundary Value Problems For Discrete Fractional Equations, 2013 University of Nebraska-Lincoln

#### Boundary Value Problems For Discrete Fractional Equations, Pushp R. Awasthi

*Dissertations, Theses, and Student Research Papers in Mathematics*

In this dissertation we develop certain aspects of the theory of discrete fractional calculus. The author begins with an introduction to the discrete delta calculus together with the fractional delta calculus which is used throughout this dissertation. The Cauchy function, the Green's function and some of their important properties for a fractional boundary value problem for are developed. This dissertation is comprised of four chapters. In the first chapter we introduce the delta fractional calculus. In the second chapter we give some preliminary definitions, properties and theorems for the fractional delta calculus and derive the appropriate Green's function ...

Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator, 2013 W. H. Su

#### Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator, Xiao-Jun Yang

*Xiao-Jun Yang*

This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.

The Effect Of The R1648h Sodium Channel Mutation On Neuronal Excitability: A Model Study, 2013 Georgia State University

#### The Effect Of The R1648h Sodium Channel Mutation On Neuronal Excitability: A Model Study, Christopher Locandro, Robert Clewley

*Georgia State Undergraduate Research Conference*

No abstract provided.

Tourbillion In The Phase Space Of The Bray-Liebhafsky Nonlinear Oscillatory Reaction And Related Multiple-Time-Scale Model, 2013 Institute of Chemistry, Technology and Metallurgy

#### Tourbillion In The Phase Space Of The Bray-Liebhafsky Nonlinear Oscillatory Reaction And Related Multiple-Time-Scale Model, Zeljko D. Cupic

*Zeljko D Cupic*

The mixed-mode dynamical states found experimentally in the concentration phase space of the iodate catalyzed hydrogen peroxide decomposition (The Bray-Liebhafsky oscillatory reaction) are discussed theoretically in a related multiple-time-scale model, from the viewpoint of tourbillion. With aim to explain the mixed-mode oscillations obtained by numerical simulations of the various dynamical states of a model for the Bray-Liebhafsky reaction under CSTR conditions, the folded singularity points on the critical manifold of the full system and Andronov-Hopf bifurcation of the fast subsystem are calculated. The interaction between those singularities causes occurrence of tourbillion structure.

Mechaniczny Rozdział Faz Proj., 2013 Wroclaw University of Technology

#### Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, 2013 Wroclaw University of Technology

#### Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski

*Wojciech Budzianowski*

This article provides an analysis of processes for separation CO2 by using carbonic anhydrase enzyme with particular emphasis on reactive-membrane solutions. Three available processes are characterised. Main challenges and prospects are given. It is found that in view of numerous challenges practical applications of these processes will be difficult in near future. Further research is therefore needed for improving existing processes through finding methods for eliminating their main drawbacks such as short lifetime of carbonic anhydrase or low resistance of reactive membrane systems to impurities contained in flue gases from power plants.