Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., 2012 Wroclaw University of Technology

#### Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Materiały Odstresowujące, 2012 Wroclaw University of Technology

#### Materiały Odstresowujące, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, 2012 Bard College

#### Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, Stergios Mentesidis

*Senior Projects Spring 2012*

The paper focuses on Minsky's financial fragility hypothesis incorporated in a growth model and investigates whether an inherently unstable economy can be stabilized by a big and proactive government. Using dynamical systems theory and expanding a supply-driven growth model developed by Lin, Day and Tse (1992), the paper explores how different government spending programs and financing paths can affect the growth, as well as the stability of a capitalist economy. The results and implications of the new frameworks are analyzed, using analytical and numerical methods of bifurcation, to examine the dependence of optimal government intervention on the economic environment ...

Dimension Of Stablesets And Scrambled Sets In Positive Finite Entropy Systems, 2011 UMass Amherst

#### Dimension Of Stablesets And Scrambled Sets In Positive Finite Entropy Systems, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Partially Hyperbolic Sets With Positive Measure And Acip For Partially Hyperbolic Systems, 2011 UMass Amherst

#### Partially Hyperbolic Sets With Positive Measure And Acip For Partially Hyperbolic Systems, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Escape Dynamics In The Discrete Repulsive Model, 2011 UMass, Amherst

#### Escape Dynamics In The Discrete Repulsive Model, V. Achilleos, A. Alvarez, J. Cuevas, D. J. Frantzeskakis, N. I. Karachalios, Panos Kevrekidis, B. Sanchez-Rey

*Panos Kevrekidis*

We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the Hamiltonian and the linearly damped versions of the system and showcase different potential fates of the single-site excitation, such as the possibility to be “pulled back” from outside the well or to “drive over” the barrier some of its neighbors. Next, we study the evolution of a uniform (small) segment of the chain ...

Pointwise Dimension, Entropy And Lyapunov Exponents For C1 Maps, 2011 UMass Amherst

#### Pointwise Dimension, Entropy And Lyapunov Exponents For C1 Maps, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Symmetry-Breaking Effects For Polariton Condensates In Double-Well Potentials, 2011 University of Massachusetts - Amherst

#### Symmetry-Breaking Effects For Polariton Condensates In Double-Well Potentials, A. S. Rodrigues, Panos Kevrekidis, J. Cuevas, R. Carretero-Gonzalez, D. J. Frantzeskakis

*Panos Kevrekidis*

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in ...

Characteristics Of Two-Dimensional Quantum Turbulence In A Compressible Superfluid, 2011 UMass, Amherst

#### Characteristics Of Two-Dimensional Quantum Turbulence In A Compressible Superfluid, T. W. Neely, A. S. Bradley, E. C. Samson, S. J. Rooney, E. M. Wright, K. J. H. Law, R. Carretero-Gonz´Alez, Panos Kevrekidis, M. J. Davis, B. P. Anderson

*Panos Kevrekidis*

Under suitable forcing a fluid exhibits turbulence, with characteristics strongly a#11;ected by the fluid’s confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap. As a compressible quantum fluid, this system a#11;ords a rich phenomenology, allowing coupling between vortex and acoustic energy. Small-scale stirring generates an experimentally observed disordered vortex distribution that evolves into large-scale flow in the form of a persistent current. Numerical simulation of the experiment reveals additional characteristics of two-dimensional quantum turbulence: spontaneous clustering of same-circulation vortices, and an incompressible energy spectrum with k ...

Diffeomorphisms With Global Dominated Splittings Can Not Be Minimal, 2011 UMass Amherst

#### Diffeomorphisms With Global Dominated Splittings Can Not Be Minimal, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Breathers For The Discrete Nonlinear Schrödinger Equation With Nonlinear Hopping, 2011 UMass, Amherst

#### Breathers For The Discrete Nonlinear Schrödinger Equation With Nonlinear Hopping, N. I. Karachalios, B. Sánchez-Rey, Panos Kevrekidis, J. Cuevas

*Panos Kevrekidis*

We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below the prescribed lower bounds of the power which depend on the dimension, the parameters of the lattice as well as of the frequency of breathers. In the case of supercritical power nonlinearities we investigate the interplay of these estimates with the ...

Nonlinear Waves And Solitons On Contours And Closed Surfaces, 2011 Embry-Riddle Aeronautical University

#### Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu

*Andrei Ludu*

No abstract provided.

Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, 2011 Wroclaw University of Technology

#### Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski

*Wojciech Budzianowski*

Oxy-reforming is emerging as an interesting alternative to conventional methods of hydrogen generation. The current article characterises this process through analysis of individual reactions: SMR (steam methane reforming), WGS (water gas shift) and CPO (catalytic partial oxidation). Analyses relate to optimisation of thermal conditions thus enabling cost-effectivenes of the process.

Symmetry-Breaking Bifurcation In The Nonlinear Schrödinger Equation With Symmetric Potentials, 2011 UMass, Amherst

#### Symmetry-Breaking Bifurcation In The Nonlinear Schrödinger Equation With Symmetric Potentials, E. Kirr, Panos Kevrekidis, D. Pelinovsky

*Panos Kevrekidis*

We consider the focusing (attractive) nonlinear Schr\"odinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of ...

Multiple Dark-Bright Solitons In Atomic Bose-Einstein Condensates, 2011 UMass, Amherst

#### Multiple Dark-Bright Solitons In Atomic Bose-Einstein Condensates, D. Yan, J. J. Chang, C. Hamner, Panos Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher

*Panos Kevrekidis*

Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton “molecules,” composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons ...

Breathers In Oscillator Chains With Hertzian Interactions, 2011 UMass, Amherst

#### Breathers In Oscillator Chains With Hertzian Interactions, Guillaume James, Panos Kevrekidis, Jesus Cuevas

*Panos Kevrekidis*

We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a class of Fermi-Pasta-Ulam lattices representing an uncompressed chain of beads interacting via Hertz's contact forces. We then consider the setting in which an additional on-site potential is present, motivated by the Newton's cradle under the effect of gravity. Using both direct numerical computations and a simplified asymptotic model of the oscillator chain, the so-called discrete p-Schr\"odinger (DpS) equation, we show the existence of discrete breathers and study their spectral properties and mobility. Due to the fully nonlinear character of Hertzian interactions, breathers are found to ...

Rabi Flopping Induces Spatial Demixing Dynamics, 2011 UMass, Amherst

#### Rabi Flopping Induces Spatial Demixing Dynamics, E. Nicklas, H. Strobel, T. Zibold, C. Gross, B. A. Malomed, Panos Kevrekidis, M. K. Oberthaler

*Panos Kevrekidis*

We experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.

Fluctuating And Dissipative Dynamics Of Dark Solitons In Quasicondensates S., 2011 UMass, Amherst

#### Fluctuating And Dissipative Dynamics Of Dark Solitons In Quasicondensates S., S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, Panos Kevrekidis, N. P. Proukakis, D. J. Frantzeskakis

*Panos Kevrekidis*

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [ S. P. Cockburn et al. Phys. Rev. Lett. 104 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon ...

Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, 2011 Institute for Applied Mathematics, University of Hanover, D-30167 Hanover, Germany

#### Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev

*Articles*

The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.

Dark–Bright Ring Solitons In Bose–Einstein Condensates, 2011 UMASS, Amherst

#### Dark–Bright Ring Solitons In Bose–Einstein Condensates, J. Stockhofe, Panos Kevrekidis, D. J. Frantzeskakis, P. Schmelcher

*Panos Kevrekidis*

We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of ...