Dielectric Response of a Chain of Disordered Polarizable Spheres: Numerical Simulation and Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
Pedro VillaseiÑor-Gonzalez ◽  
Cecilia Noguez ◽  
Ruben G. Barrera
Keyword(s):  
Numerical Simulation ◽  
Dielectric Response ◽  
Linear Equations ◽  
Periodic Boundary Conditions ◽  
Dimensional System ◽  
Effective Response ◽  
Static Approximation ◽  
One Dimensional ◽  
Induced Dipole ◽  
A Chain

ABSTRACTWe applied to a one-dimensional system (1D) a recently developed diagrammatic formalism, in order to calculate the effective dielectric response of a chain of polarizable spheres embeded in an homogeneous host. The effective response is calculated within the dipolar, quasi-static approximation, through the summation of selected classes of diagrams. We compared our results with a numerical simulation, where the position of each sphere was generated at random and the induced dipole moment of each sphere was calculated by solving a set of linear equations through matrix inversion and using periodic boundary conditions.

Regimes in Simple Systems

2006 ◽  
Vol 63 (8) ◽  
pp. 2056-2073 ◽  
Author(s):  
Edward N. Lorenz
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Piecewise Linear ◽  
Linear Difference Equation ◽  
The State ◽  
Explicit Calculation ◽  
Dimensional System ◽  
One Dimensional ◽  
A Chain ◽  
Barotropic Vorticity

Abstract Dynamical systems possessing regimes are identified with those where the state space possesses two or more regions such that transitions of the state from either region to the other are rare. Systems with regimes are compared to those where transitions are impossible. A simple one-dimensional system where a variable is defined at N equally spaced points about a latitude circle, once thought not to possess regimes, is found to exhibit them when the external forcing F slightly exceeds its critical value F* for the appearance of chaos. Regimes are detected by examining extended time series of quantities such as total energy. A chain of k* fairly regular waves develops if F < F*, and F* is found to depend mainly upon the wavelength L* = N/k*, being greatest when L* is closest to a preferred length L0. A display of time series demonstrates how the existence and general properties of the regimes depend upon L*. The barotropic vorticity equation, when applied to an elongated rectangular region, exhibits regimes much like those occurring with the one-dimensional system. A first-order piecewise-linear difference equation produces time series closely resembling some produced by the differential equations, and it permits explicit calculation of the expected duration time in either regime. Speculations as to the prevalence of regimes in dynamical systems in general, and to the applicability of the findings to atmospheric problems, are offered.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Milad Jangjan ◽  
Mir Vahid Hosseini
Keyword(s):  
Phase Transition ◽  
Dimensional System ◽  
Inversion Symmetry ◽  
Topological Phase ◽  
Edge States ◽  
Zero Energy ◽  
One Dimensional ◽  
Topological Phase Transition ◽  
Metal State ◽  
Topological Metal

AbstractWe theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

scholarly journals Quantifying photoinduced carriers transport in exciton–polariton coupling of MoS2 monolayers

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Min-Wen Yu ◽  
Satoshi Ishii ◽  
Shisheng Li ◽  
Ji-Ren Ku ◽  
Jhen-Hong Yang ◽  
...  
Keyword(s):  
Electronic Energy ◽  
Plasmonic Nanostructures ◽  
Transition Metal Dichalcogenide ◽  
Metallic Nanoparticle ◽  
Rabi Splitting ◽  
One Dimensional ◽  
Induced Dipole ◽  
Mos2 Monolayers ◽  
Plasmon Polaritons ◽  
Significant Attention

AbstractExciton–polariton coupling between transition metal dichalcogenide (TMD) monolayer and plasmonic nanostructures generates additional states that are rich in physics, gaining significant attention in recent years. In exciton–polariton coupling, the understanding of electronic-energy exchange in Rabi splitting is critical. The typical structures that have been adopted to study the coupling are “TMD monolayers embedded in a metallic-nanoparticle-on-mirror (NPoM) system.” However, the exciton orientations are not parallel to the induced dipole direction of the NPoM system, which leads to inefficient coupling. Our proposed one-dimensional plasmonic nanogrooves (NGs) can align the MoS2 monolayers’ exciton orientation and plasmon polaritons in parallel, which addresses the aforementioned issue. In addition, we clearly reveal the maximum surface potential (SP) change on intermediate coupled sample by the photo-excitation caused by the carrier rearrangement. As a result, a significant Rabi splitting (65 meV) at room temperature is demonstrated. Furthermore, we attribute the photoluminescence enhancement to the parallel exciton–polariton interactions.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

scholarly journals Study on the regional characteristics during foam flooding by population balance model

2020 ◽  
pp. 014459872098361
Author(s):  
Zhongbao Wu ◽  
Qingjun Du ◽  
Bei Wei ◽  
Jian Hou
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Oil Recovery ◽  
Population Balance ◽  
Growth Zone ◽  
Balance Model ◽  
Population Balance Model ◽  
Liquid Ratio ◽  
One Dimensional ◽  
Foam Flooding

Foam flooding is an effective method for enhancing oil recovery in high water-cut reservoirs and unconventional reservoirs. It is a dynamic process that includes foam generation and coalescence when foam flows through porous media. In this study, a foam flooding simulation model was established based on the population balance model. The stabilizing effect of the polymer and the coalescence characteristics when foam encounters oil were considered. The numerical simulation model was fitted and verified through a one-dimensional displacement experiment. The pressure difference across the sand pack in single foam flooding and polymer-enhanced foam flooding both agree well with the simulation results. Based on the numerical simulation, the foam distribution characteristics in different cases were studied. The results show that there are three zones during foam flooding: the foam growth zone, stable zone, and decay zone. These characteristics are mainly influenced by the adsorption of surfactant, the gas–liquid ratio, the injection rate, and the injection scheme. The oil recovery of polymer-enhanced foam flooding is estimated to be 5.85% more than that of single foam flooding. Moreover, the growth zone and decay zone in three dimensions are considerably wider than in the one-dimensional model. In addition, the slug volume influences the oil recovery the most in the foam enhanced foam flooding, followed by the oil viscosity and gas-liquid ratio. The established model can describe the dynamic change process of foam, and can thus track the foam distribution underground and aid in optimization of the injection strategies during foam flooding.

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