scholarly journals Multilevel Laser Induced Continuum Structure

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 891
Author(s):  
Kaloyan Zlatanov ◽  
Nikolay Vitanov
Keyword(s):  
Bound States ◽  
Coherent Control ◽  
Initial Conditions ◽  
Type System ◽  
Lower Dimension ◽  
Continuum State ◽  
Control Techniques ◽  
Continuum Structure ◽  
Degenerate States

Laser-induced-continuum-structure (LICS) allows for coherent control techniques to be applied in a Raman type system with an intermediate continuum state. The standard LICS problem involves two bound states coupled to one or more continua. In this paper, we discuss the simplest non-trivial multistate generalization of LICS which couples two bound levels, each composed of two degenerate states through a common continuum state. We reduce the complexity of the system by switching to a rotated basis of the bound states, in which different sub-systems of lower dimension evolve independently. We derive the trapping condition and explore the dynamics of the sub-systems under different initial conditions.

scholarly journals A Mass- and Energy-Conserving Numerical Model for a Fractional Gross–Pitaevskii System in Multiple Dimensions

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1765
Author(s):  
Adán J. Serna-Reyes ◽  
Jorge E. Macías-Díaz
Keyword(s):  
Initial Conditions ◽  
Type System ◽  
Continuous System ◽  
Mass Conservation ◽  
Continuous Model ◽  
Manuscript Studies ◽  
Multiple Dimensions ◽  
Negative Constant ◽  
Energy Conserving ◽  
Finite Difference Discretization

This manuscript studies a double fractional extended p-dimensional coupled Gross–Pitaevskii-type system. This system consists of two parabolic partial differential equations with equal interaction constants, coupling terms, and spatial derivatives of the Riesz type. Associated with the mathematical model, there are energy and non-negative mass functions which are conserved throughout time. Motivated by this fact, we propose a finite-difference discretization of the double fractional Gross–Pitaevskii system which inherits the energy and mass conservation properties. As the continuous model, the mass is a non-negative constant and the solutions are bounded under suitable numerical parameter assumptions. We prove rigorously the existence of solutions for any set of initial conditions. As in the continuous system, the discretization has a discrete Hamiltonian associated. The method is implicit, multi-consistent, stable and quadratically convergent. Finally, we implemented the scheme computationally to confirm the validity of the mass and energy conservation properties, obtaining satisfactory results.

A Comparative Study of Mass Based Vibration Dampers

2017 ◽  
Author(s):  
Mohamed Gharib ◽  
Mansour Karkoub
Keyword(s):  
Comparative Study ◽  
Passive Control ◽  
Initial Conditions ◽  
Free Vibrations ◽  
Decay Rates ◽  
Coupled Systems ◽  
Primary System ◽  
Operating Personnel ◽  
Control Techniques ◽  
Dynamic Structures

Undesired vibrations in structures, buildings, and machines lead to reduction in the life of the system and greatly affects the safety of the occupying or operating personnel. In addition, economic and time losses could result from needed repairs or reconstruction. Many control techniques, active and passive, have been devised over the years to reduce/eliminate the vibrations in the aforementioned systems. Passive vibration control techniques are favorable over the active ones due to their simplicity, ease of implementation, cost, and power consumption. In dynamic structures, such as large buildings, passive control techniques are favored over their active counterparts. The most common types of passive control devices are tuned mass and impact dampers. The advocates of each of these devices boasts advantages of the others; however, there have been no systematic studies to compare and quantify the effectiveness of each of these types of devices as well as their suitability for specific applications. In this paper, a comparative study between the tuned mass dampers and impact dampers is conducted. A one-story structure is used to show the effectiveness of each of these devices in absorbing the vibrations of the structure. The coupled systems are modeled and simulated under free vibrations. The time responses are acquired using the same geometric parameters, excitation, and initial conditions. The comparisons are based on the settling time and amplitude decay rates of the primary system using each damper type. The numerical results show that both dampers can produce similar dampening effects if the parameters are optimized; however, correlating the dampers parameters is a challenging problem in the field of vibration and control.

scholarly journals SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

2004 ◽  
Vol 16 (08) ◽  
pp. 977-1071 ◽  
Author(s):  
A. SOFFER ◽  
M. I. WEINSTEIN
Keyword(s):  
Excited State ◽  
Ground State ◽  
Bound States ◽  
Initial Conditions ◽  
Bound State ◽  
Large Time Behavior ◽  
Multiple Time ◽  
Time Behavior ◽  
Small Initial Data ◽  
Nonlinear Schrödinger

We prove for a class of nonlinear Schrödinger systems (NLS) having two nonlinear bound states that the (generic) large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive radiation. Our analysis elucidates the mechanism through which initial conditions which are very near the excited state branch evolve into a (nonlinear) ground state, a phenomenon known as ground state selection. Key steps in the analysis are the introduction of a particular linearization and the derivation of a normal form which reflects the dynamics on all time scales and yields, in particular, nonlinear master equations. Then, a novel multiple time scale dynamic stability theory is developed. Consequently, we give a detailed description of the asymptotic behavior of the two bound state NLS for all small initial data. The methods are general and can be extended to treat NLS with more than two bound states and more general nonlinearities including those of Hartree–Fock type.

scholarly journals Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Guangwang Su ◽  
Taixiang Sun ◽  
Bin Qin
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Type System ◽  
Higher Order ◽  
System Of Difference Equations

We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually.

scholarly journals Coherent control techniques for two-state quantum systems: A comparative study

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Boyan T. Torosov ◽  
Bruce W. Shore ◽  
Nikolay V. Vitanov
Keyword(s):  
Comparative Study ◽  
Coherent Control ◽  
Quantum Systems ◽  
Control Techniques

scholarly journals Solution of the Maximum of Difference Equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn}\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}

2020 ◽  
Vol 5 (1) ◽  
pp. 275-282
Author(s):  
Dagistan Simsek ◽  
Burak Ogul ◽  
Fahreddin Abdullayev
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Type System ◽  
Global Behavior ◽  
System Of Difference Equations

AbstractIn the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations, (1)\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}} where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.

Genetic and Bacterial Programming for B-Spline Neural Networks Design

2007 ◽  
Vol 11 (2) ◽  
pp. 220-231 ◽  
Author(s):  
János Botzheim ◽  
◽  
Cristiano Cabrita ◽  
László T. Kóczy ◽  
Antonio E. Ruano ◽  
...  
Keyword(s):  
Neural Networks ◽  
Fuzzy Systems ◽  
Initial Conditions ◽  
Microbial Evolution ◽  
Programming Approach ◽  
Complex Task ◽  
Design Phase ◽  
Biologically Inspired ◽  
B Spline ◽  
Control Techniques

The design phase of B-spline neural networks is a highly computationally complex task. Existent heuristics have been found to be highly dependent on the initial conditions employed. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this paper, the Bacterial Programming approach is presented, which is based on the replication of the microbial evolution phenomenon. This technique produces an efficient topology search, obtaining additionally more consistent solutions.

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