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Analysis Of Adiabatic Trapping For Quasi-Integrable Area-Preserving Maps, Armando Bazzani, Christopher Frye, Massimo Giovannozzi, Cédric Hernalsteens
Analysis Of Adiabatic Trapping For Quasi-Integrable Area-Preserving Maps, Armando Bazzani, Christopher Frye, Massimo Giovannozzi, Cédric Hernalsteens
Faculty Bibliography 2010s
Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinear resonances and slow time variation of some system parameters is considered. The focus of this paper is on discrete-time dynamical systems generated by two-dimensional symplectic maps. The possibility of extending the results of neo-adiabatic theory to quasi-integrable area-preserving maps is discussed. Scaling laws are derived, which describe the adiabatic transport as a function of the system parameters using a probabilistic point of view. These …
The Heisenberg Relation - Mathematical Formulations, Richard V. Kadison, Zhe Liu
The Heisenberg Relation - Mathematical Formulations, Richard V. Kadison, Zhe Liu
Faculty Bibliography 2010s
We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Attractive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Attractive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Faculty Bibliography 2010s
Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation (NLS) modeling attractive Bose-Einstein condensates (BECs) in a small potential are obtained via a form of nonlinear perturbation. The focus here is on perturbations to the bright soliton solutions due to small potentials which either confine or repel the BECs: under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of the bright solitons. Importantly, we do not need to assume that the nonlinearity is small, as we perform a sort of nonlinear perturbation by allowing the zeroth-order perturbation term to be governed by a …
Stationary Solutions For The 2+1 Nonlinear Schrodinger Equation Modeling Bose-Einstein Condensates In Radial Potentials, Kristina Mallory, Robert A. Van Gorder
Stationary Solutions For The 2+1 Nonlinear Schrodinger Equation Modeling Bose-Einstein Condensates In Radial Potentials, Kristina Mallory, Robert A. Van Gorder
Faculty Bibliography 2010s
Stationary solutions for the 2 + 1 cubic nonlinear Schrodinger equation modeling Bose-Einstein condensates (BEC) in a small potential are obtained via a form of perturbation. In particular, perturbations due to small potentials which either confine or repel the BECs are studied, and under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of radial BEC solutions. Numerical results are also provided for regimes where perturbative results break down (i.e., the large-potential regime). Both repulsive and attractive BECs are considered under this framework. Solutions for many specific confining potentials of physical relevance to experiments on BECs …
A Squeeze-Like Operator Approach To Position-Dependent Mass In Quantum Mechanics, Héctor M. Moya-Cessa, Francisco Soto-Eguibar, Demetrios N. Christodoulides
A Squeeze-Like Operator Approach To Position-Dependent Mass In Quantum Mechanics, Héctor M. Moya-Cessa, Francisco Soto-Eguibar, Demetrios N. Christodoulides
Faculty Bibliography 2010s
We provide a squeeze-like transformation that allows one to remove a position dependent mass from the Hamiltonian. Methods to solve the Schrodinger equation may then be applied to find the respective eigenvalues and eigenfunctions. As an example, we consider a position-dependent-mass that leads to the integrable Morse potential and therefore to well-known solutions.
Continuous And Discrete Schrodinger Systems With Parity-Time-Symmetric Nonlinearities, Amarendra K. Sarma, Mohammad-Ali Miri, Ziad H. Musslimani, Demetrios N. Christodoulides
Continuous And Discrete Schrodinger Systems With Parity-Time-Symmetric Nonlinearities, Amarendra K. Sarma, Mohammad-Ali Miri, Ziad H. Musslimani, Demetrios N. Christodoulides
Faculty Bibliography 2010s
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a discretized version of this PT-nonlinear Schrodinger equation on a lattice. When only two elements are involved, by obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry-breaking conditions. This arrangement is unique in the sense that the exceptional points are …
An Advanced Mathematical Model And Its Experimental Verification For Trilayer Conjugated Polymer Actuators, Chuc Nguyen, Gursel Alici, Gordon G. Wallace
An Advanced Mathematical Model And Its Experimental Verification For Trilayer Conjugated Polymer Actuators, Chuc Nguyen, Gursel Alici, Gordon G. Wallace
Faculty of Engineering and Information Sciences - Papers: Part A
This paper describes the establishment of an enhanced mathematical model and an inversion-based controller based on the proposed model for a trilayer conjugated polymer actuator that will steer a cochlear implant through a 3-D structure. The multilayer electroactive polymer actuator that operates in air will suit many biomedical applications. We propose to use viscoelastic models for the conducting polymer and membrane layers of the actuator so that its mechanical properties can be incorporated into the actuator more accurately. The proposed model accurately predicts the frequency response of the electrical admittance and curvature of the conjugated polymer actuators, and its efficacy …
Modelling The Rejection Of N-Nitrosamines By A Spiral-Wound Reverse Osmosis System: Mathematical Model Development And Validation, Takahiro Fujioka, Stuart J. Khan, James A. Mcdonald, Annalie Roux, Yvan Poussade, Jorg E. Drewes, Long D. Nghiem
Modelling The Rejection Of N-Nitrosamines By A Spiral-Wound Reverse Osmosis System: Mathematical Model Development And Validation, Takahiro Fujioka, Stuart J. Khan, James A. Mcdonald, Annalie Roux, Yvan Poussade, Jorg E. Drewes, Long D. Nghiem
SMART Infrastructure Facility - Papers
A mathematical model was developed based on the irreversible thermodynamic principle and hydro- dynamic calculation to predict the rejection of N-nitrosamines by spiral-wound reverse osmosis (RO) membrane systems. The developed model is able to accurately describe the rejection of N-nitrosamines under a range of permeate flux and system recovery conditions. The modelled N-nitrosamine rejections were in good agreement with values obtained experimentally using a pilot-scale RO filtration system. Simulation from the model revealed that an increase in permeate flux from10 to 30L/m2h led to an increase in the rejection of low molecular weight N-nitrosamines such as N-nitrosodimethylamine (NDMA) (from31% to …
A Mathematical Analysis Of A Membrane Bioreactor Containing A Sludge Disintegration System, Mark Nelson, Thomas Yue
A Mathematical Analysis Of A Membrane Bioreactor Containing A Sludge Disintegration System, Mark Nelson, Thomas Yue
Faculty of Engineering and Information Sciences - Papers: Part A
The activated sludge process is widely used to treat domestic and industrial wastewater. A significant drawback of this process is the production of "sludge", the disposal of which can comprise a significant proportion of the total operating costs of a wastewater treatment plant. We analyze the steady-state operation of a membrane bioreactor system (MBR) incorporating a sludge disintegration unit (SDU) to reduce sludge production. We provide a qualitative understanding of the model by finding analytically the steady-state solutions of the model and determining its stability as a function of the residence time. In practice a target value of the mixed …