THE SPECTRA AND OPTICAL BISTABILITY OF CAVITY FIELD COUPLED TO A MECHANICAL MIRROR

2013 ◽  
Vol 11 (03) ◽  
pp. 1350033 ◽  
Author(s):  
J. H. TENG ◽  
J. MA ◽  
W. WANG
Keyword(s):  
Optical Bistability ◽  
Mean Field ◽  
Kerr Nonlinearity ◽  
Field Approximation ◽  
Peak Position ◽  
Mean Field Approximation ◽  
Cavity Field ◽  
Optomechanical System ◽  
Wide Range ◽  
Optomechanical Coupling

We investigate the effect of Kerr nonlinearity and optomechanical couplings on cavity field spectra in an optomechanical system driven by a pump field. In the mean-field approximation, the system exhibits optical bistability for a wide range of parameters. The spectra are numerically calculated for different initial states, which show that a single peak in the spectrum splits because of the presence of the optomechanical coupling and the increase of the number of phonon. In addition, the peak position in the cavity field spectra changes due to the Kerr nonlinearity, while the cavity detuning is modified. The strength of spectra determines the size of the photon-phonon conversion capabilities. These results provides a theoretical basis for optical communication.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

Processus de branchement en champ moyen et réaction PCR

2001 ◽  
Vol 33 (2) ◽  
pp. 391-403 ◽  
Author(s):  
Didier Piau
Keyword(s):  
Branching Process ◽  
Random Number ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Process Mean ◽  
Dna Mutations ◽  
Wide Range ◽  
The Mean ◽  
Efficiency Rate

Sun and Waterman model DNA mutations during the PCR reaction by a non-canonical branching process. Mean-field approximated values fit the simulated values surprisingly well. We prove this as a theoretical result, for a wide range of the parameters. Thus, we bound explicitly the biases, in law and in the mean, that the mean-field approximation induces in the random number of mutations of a DNA molecule, as a function of the initial number of molecules, of the number of PCR cycles, of the efficiency rate and of the mutation rate. The range where we prove that the approximation is good contains the observed mutation rates in many actual PCR reactions.

scholarly journals Optical bistability in two-dimensional nonlinear composites of coated cylinders with nonlinear core and graded shell

2020 ◽  
Vol 7 ◽  
pp. 6
Author(s):  
Ya M. Wu ◽  
Guo Q. Chen ◽  
Wen C. Wu ◽  
Yi X. Wang ◽  
Yang Huang
Keyword(s):  
Optical Bistability ◽  
Near Field ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Geometrical Parameters ◽  
Core Radius ◽  
The Core ◽  
Nonlinear Composite ◽  
Incident Frequency

The intrinsic optical bistability of the nonlinear composite consisting of coated cylinders with nonlinear core and graded Drude shell is investigated with self-consistent mean-field approximation. We derive the nonlinear equation of near field for such graded composite in the quasistatic limit. We demonstrate that the bistability threshold and the bistable width are highly dependent on the core radius, the incident frequency, and the graded coefficient of the coated cylinder inclusion. It is found that the optical bistability appears only when the core radius and the incident frequency satisfy some specific conditions. Therefore, the optical bistability for nonlinear composite materials may be optimized by the suitable adjustment of the physical and geometrical parameters. Our results may be helpful for the design of the nonlinear device with appropriate bistability.

Stationary properties of dispersive optical bistability in a dense exciton-biexciton system: copper chloride

1984 ◽  
Vol 313 (1525) ◽  
pp. 389-394
Keyword(s):  
Optical Bistability ◽  
Copper Chloride ◽  
Mean Field ◽  
Field Approximation ◽  
Stationary Solutions ◽  
Mean Field Approximation ◽  
Kerr Medium ◽  
Two Photon ◽  
The Mean ◽  
Medium Type

A semiclassical exciton-biexciton model for CuCl is used to obtain the stationary solutions for optical bistability (o.b.) by numerical integration of the second-order Maxwell equation in the limit of large Fresnel numbers. The results obtained from the calculation, which we call exact (ex.), are compared with corresponding numerical results by using the slowly varying envelope approximation (s.v.e.a.) as well as corresponding analytical results obtained by using the mean-field approximation (m.f.a.). The results obtained with the s.v.e.a. are shown to be in close quantitative (within 5%) agreement with the ex. results for each point in the parameter space considered, whereas the m.f.a. gives reasonably good qualitative results only (more than 20% quantitative discrepancy with ex.). Furthermore, o.b. is predicted from these calculations for incident laser field detunings on either side of the two-photon biexciton resonance as well as in the neighbourhood of the resonance. The nonlinearity in the dielectric function that causes o.b. is seen to be very nearly of the Kerr medium type, and consequently, the two-photon biexciton resonance contributes only weakly to the o.b. characteristics.

scholarly journals On Magnetic Inhibition of Thermal Convection

1972 ◽  
Vol 25 (6) ◽  
pp. 703 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy ◽  
EA Spiegel
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Quantitative Estimates ◽  
Wide Range ◽  
The Face ◽  
The Mean ◽  
The Magnetic Field

The effect of an imposed vertical magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. Solutions are found over a wide range of conditions, for free boundaries, by a combination of numerical and analytic techniques. Quantitative estimates are made of the significant modifications to the heat transfer which are brought about by the presence of the magnetic field. It is found that the general properties of nonlinear steady cellular convection seem to persist in the face of magnetic inhibition.

Dynamical Mean Field Model of a Neural-Glial Mass

2010 ◽  
Vol 22 (4) ◽  
pp. 969-997 ◽  
Author(s):  
Roberto C. Sotero ◽  
Ramón Martínez-Cancino
Keyword(s):  
Differential Equations ◽  
Field Model ◽  
Mean Field ◽  
Field Approximation ◽  
Presynaptic Terminal ◽  
Mean Field Approximation ◽  
Nerve Terminals ◽  
Mean Field Model ◽  
Wide Range ◽  
Activity Dependent

Our goal is to model the behavior of an ensemble of interacting neurons and astrocytes (the neural-glial mass). For this, a model describing N tripartite synapses is proposed. Each tripartite synapse consists of presynaptic and postsynaptic nerve terminals, as well as the synaptically associated astrocytic microdomain, and is described by a system of 13 stochastic differential equations. Then, by applying the dynamical mean field approximation (DMA) (Hasegawa, 2003a , 2003b ) the system of 13N equations is reduced to 13(13 + 2) = 195 deterministic differential equations for the means and the second-order moments of local and global variables. Simulations are carried out for studying the response of the neural-glial mass to external inputs applied to either the presynaptic terminals or the astrocytes. Three cases were considered: the astrocytes influence only the presynaptic terminal, only the postsynaptic terminal, or both the presynaptic and postsynaptic terminals. As a result, a wide range of responses varying from singles spikes to train of spikes was evoked on presynaptic and postsynaptic terminals. The experimentally observed phenomenon of spontaneous activity in astrocytes was replicated on the neural-glial mass. The model predicts that astrocytes can have a strong and activity-dependent influence on synaptic transmission. Finally, simulations show that the dynamics of astrocytes influences the synchronization ratio between neurons, predicting a peak in the synchronization for specific values of the astrocytes’ parameters.

Spin Models for Ferroelastics: towards a Spin Glass Description of Strain Glass

2011 ◽  
Vol 172-174 ◽  
pp. 1078-1083 ◽  
Author(s):  
Romain Vasseur ◽  
Turab Lookman
Keyword(s):  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Zero Field ◽  
High Symmetry ◽  
Spin Models ◽  
Wide Range ◽  
Long Range Interactions ◽  
Field Cooling

We review the description of ferroelastic transitions in terms of spin models. We show how one can systematically obtain a pseudo-spin Hamiltonian from the Landau energy describing the first order transition between Austenite/Martensite phases. It is shown that a Local Mean-field approximation predicts the same microstructure as the continuous Landau model in terms of strain variables. This method can be applied to a wide range of two and three dimensional transitions. We then demonstrate how quenched disorder in such pseudo-spin models yields the existence of a glass phase, characterized by the Edwards-Anderson order parameter. Our approach uses Mean-field approximation and Monte-Carlo simulations (using Zero Field Cooling/Field Cooling experiments) to study the influence of the long-range interactions. Although our model captures the salient features of a ferroelastic material in the presence of disorder, the influence of the disorder on the high symmetry austenite phase is not quite consistent with expected behavior. We examine different means of introducing disorder that can improve upon the results.

scholarly journals Ion correlations drive charge overscreening and heterogeneous nucleation at solid–aqueous electrolyte interfaces

2021 ◽  
Vol 118 (32) ◽  
pp. e2105154118
Author(s):  
Sang Soo Lee ◽  
Ayumi Koishi ◽  
Ian C. Bourg ◽  
Paul Fenter
Keyword(s):  
Mean Field ◽  
Charge Compensation ◽  
Solubility Limit ◽  
Field Approximation ◽  
Ion Concentration ◽  
Mean Field Approximation ◽  
Strongly Correlated ◽  
Wide Range ◽  
Dilute Aqueous Solutions ◽  
The Impact

Classical electrical double layer (EDL) models are foundational to the representation of atomistic structure and reactivity at charged interfaces. An important limitation to these models is their dependence on a mean-field approximation that is strictly valid for dilute aqueous solutions. Theoretical efforts to overcome this limitation are severely impeded by the lack of visualization of the structure over a wide range of ion concentration. Here, we report the salinity-dependent evolution of EDL structure at negatively charged mica–water interfaces, revealing transition from the Langmuir-type charge compensation in dilute salt solutions to nonclassical charge overscreening in highly concentrated solutions. The EDL structure in this overcharging regime is characterized by the development of both lateral positional correlation between adsorbed ions and vertical layering of alternating cations and anions reminiscent of the structures of strongly correlated ionic liquids. These EDL ions can spontaneously grow into nanocrystalline nuclei of ionic compounds at threshold ion concentrations that are significantly lower than the bulk solubility limit. These results shed light on the impact of ion cooperativity that drives heterogeneous nonclassical behaviors of the EDL in high-salinity conditions.

A MEAN FIELD APPROACH FOR ISING MODELS ON SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (07) ◽  
pp. 453-464 ◽  
Author(s):  
G. IANNONE ◽  
ORLANDO LUONGO
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Practical Applications ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
The Mean ◽  
Mean Field Approximations

Recently, the study of complex networks led to the analysis of the so-called scale-free models in statistical mechanics. This study has increased its importance, thanks to the wide range of applications in numerous physical contexts; for example, one important question is to understand the behavior of various models on such networks. We start first by investigating the Ising model in the mean field approximation and on scale-free networks, studying especially the Ising model with annealed dilution and Clock model, with particular attention devoted to focusing on similarities between the mean field approximations with or without scale-free statistics. A particular emphasis is given to the possible practical applications of these results in other disciplines such as medicine and social science.

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