Mean Field Methodology Research Articles

Risk‐sensitive large‐population linear‐quadratic‐Gaussian Games with major and minor agents

AbstractThis paper studies large‐population dynamic games involving a linear‐quadratic‐Gaussian (LQG) system with an exponential cost functional. The parameter in the cost functional can describe an investor's risk attitude. In the game, there are a major agent and a population of minor agents where is very large. The agents in the games are coupled via both their individual stochastic dynamics and their individual cost functions. The mean field methodology yields a set of decentralized controls, which are shown to be an ‐Nash equilibrium for a finite population system where . Numerical results are established to illustrate the impact of the population's collective behaviors and the consistency of the mean field estimation.

Design of laser pulse to enhance the photo-dissociation of a tri-atomic molecular system using optimal control theory based adaptive simulated annealing technique

In this communication, we design and optimize laser pulses to enhance the dissociation of a tri-atomic molecule using optimal control theory based adaptive simulated annealing technique. ClCN is chosen as tri-atomic molecular system as molecules containing fluorine and chlorine atoms are involved in the depletion of ozone layer and also dissociative electron attachment is possible. Fourier Grid Hamiltonian based 2D mean field methodology has been used for numerical calculations. We find an effective laser pulse by combining polychromatic Gaussian pulses and polychromatic linear pulses with different frequencies and different field intensities.

Efficient fitting of single-crystal diffuse scattering in interaction space: a mean-field approach.

The diffraction patterns of crystalline materials with strongly correlated disorder are characterized by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here it is demonstrated how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. As the basis of this proof-of-concept study, a toy model is used based on strongly correlated disorder in diammine mercury(II) halides.

Variational Bayesian analysis for Wiener degradation model with random effects

Random-effects Wiener degradation models have been widely used in the literature, to characterize unit-to-unit variability in a population. Bayesian inference for such models mainly relay on stochastic simulation techniques, such as Markov chain Monte Carlo (MCMC) method. However, MCMC approach will converge slowly or fail to converge for large volume data. In this paper, the variational Bayesian (VB) approach is proposed as an alternative tool for MCMC, which makes inference of Wiener degradation models with random effects more suitable for large inspection data sets. Despite of utilizing mean field methodology for VB approach, there are also certain limitations in model inference. Therefore, a three-step method is developed and embed into the VB approach, and statistical inference based on our VB approach is established. Numerical examples are provided to compare with MCMC method in terms of cost in time and accuracy in estimation for large inspection data problem. The proposed VB approach provides almost the same accuracy as MCMC, while its computational burden is much lower.

Influence of Charge Regulation and Charge Heterogeneity on Complexation between Polyelectrolytes and Proteins.

We employed a combination of single chain in mean field methodology and constant pH Monte Carlo framework to compare the influence of charge regulation and charge heterogeneity on the adsorption and bridging characteristics of polyelectrolytes in solution on proteins. By adopting a coarse-grained representation of the proteins as spherical particles and embedding a simple framework for probing charge heterogeneities, we probe the influence of charge patches, net charge of the particle, the ratio of positive to negative charges on the proteins on the net adsorption, and bridging probabilities of polyelectrolytes. Our results demonstrate that charge regulation increases the probability of bridging between two particles when compared to proteins with the same fixed charge. The influence of charge regulation first increases and then decreases with an increase in the number of charge patches of proteins. An increase in the ratio of positive to negative charges and the net charge of the protein are also seen to increase the propensity for polyelectrolyte adsorption and bridging.

Spatial Mean-Field Limits for Ultra-Dense Random-Access Networks

Random-access algorithms such as the CSMA protocol provide a popular mechanism for distributed medium access control in wireless networks. In saturated-buffer scenarios the joint activity process in such random-access networks has a product-form stationary distribution which provides useful throughput estimates for persistent traffic flows. However, these results do not capture the relevant performance metrics in unsaturated-buffer scenarios, which in particular arise in an IoT context with highly intermittent traffic sources. Mean-field analysis has emerged as a powerful approach to obtain tractable performance estimates in such situations, and is not only mathematically convenient, but also relevant as wireless networks grow larger and denser with the emergence of IoT applications. A crucial requirement for the classical mean-field framework to apply however is that the node population can be partitioned into a finite number of classes of statistically indistinguishable nodes. The latter condition is a severe restriction since nodes typically have different locations and hence experience different interference constraints. Motivated by the above observations, we develop in the present paper a novel mean-field methodology which does not rely on any exchangeability property. Since the spatiotemporal evolution of the network can no longer be described through a finite-dimensional population process, we adopt a measure-valued state description, and prove that the latter converges to a deterministic limit as the network grows large and dense. The limit process is characterized in terms of a system of partial-differential equations, which exhibit a striking local-global-interaction and time scale separation property. Specifically, the queueing dynamics at any given node are only affected by the global network state through a single parsimonious quantity. The latter quantity corresponds to the fraction of time that no activity occurs within the interference range of that particular node in case of a certain static spatial activation measure. Extensive simulation experiments demonstrate that the solution of the partial-differential equations yields remarkably accurate approximations for the queue length distributions and delay metrics, even when the number of nodes is fairly moderate.

Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach.

This study is motivated by a microfluidic device that imparts a magnetic torque on an array of bacterial flagella. Bacterial flagella can transform their helical geometry autonomously in response to properties of the background fluid, which provides an intriguing mechanism allowing their use as an engineered element for the regulation or transport of chemicals in microscale applications. The synchronization of flagellar phase has been widely studied in biological contexts, but here we examine the synchronization of flagellar tilt, which is necessary for effective pumping. We first examine the effects of helical geometry and tilt on the pumping flows generated by a single rotating flagellum. Next, we explore a mean-field model for an array of helical flagella to understand how collective tilt arises and influences pumping. The mean-field methodology allows us to take into account possible phase differences through a time-averaging procedure and to model an infinite array of flagella. We find array separation distances, magnetic field strengths, and rotation frequencies that produce nontrivial self-consistent pumping solutions. For individual flagella, pumping is reversed when helicity or rotation is reversed; in contrast, when collective effects are included, self-consistent tilted pumping solutions become untilted nonpumping solutions when helicity or rotation is reversed.

Role of polar medium on laser induced dissociation dynamics of ClCN: A theoretical study

Photo dissociation dynamics of linear triatomic molecule, cyanogen chloride (ClCN) in polar medium have been explored using Fourier grid Hamiltonian (FGH) method based two-dimensional mean field methodology. Ground electronic state potential of the molecule is calibrated with coupled cluster singles and doubles (CCSD) level ab initio theory using Gaussian 03 package taking 6-311++G(3df,2pd) as the basis set and fitted with two-dimensional coupled Morse potential and this potential is used for numerical calculation. Time-integrated probability current density is used as the measure of dissociation probability. Monochromatic and bichromatic laser fields are used as the external field and dissociation probability is calculated as the function of field frequency, dipolar position and pulse shape.

The NCE (Mean Field) Principle With Locality Dependent Cost Interactions

We study large population stochastic dynamic games where each agent assigns individually determined coupling strengths (with possible spatial interpretation) to the states of other agents in its performance function. The mean field methodology yields a set of decentralized controls which generates an -Nash equilibrium for the population of size . A key feature of the mean field approximation (here with localized interactions) is that the resulting th individual agent's control law depends on that agent's state and the precomputable weighted average trajectory of the collection of all agents each applying a decentralized control law.

Langevin dynamics studies of unsaturated phospholipids in a membrane environment

Computer simulations of three unsaturated phospholipids in a membrane environment have been carried out using Langevin dynamics and a mean-field based on the Marcelja model. The applicability of the mean-field to model unsaturated lipids was judged by comparison to available experimental NMR data. The results show that the mean-field methodology and the parameters developed for saturated lipids are applicable in simulations of unsaturated molecules, indicating that these simulations have good predictive capabilities. Single molecule simulations, each 100 ns in length, of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-elaidoyl-sn-glycero-3-phosphocholine (PEPC), and 1-palmitoyl-2-isolinoleoyl-sn-glycero-3-phosphocholine (PiLPC) reveal similarities between PEPC and DPPC. The presence of the trans double bond in PEPC has a minimum impact on the structural and dynamic properties of the molecule, which is probably the reason that isolated trans double bonds are rare in biological lipids. POPC exhibits different behavior, especially in the calculated average interchain distances, because of the cis double bond. The position of the two double bonds in PiLPC imparts special properties to the molecule.

From argon to polystyrene: Strategies in model refinement and data‐fitting for phase equilibria

AbstractLong‐range density or concentration fluctuations in the critical region of phase changes are directly tractable in modern “universal” models (Ising, Potts, percolation). Real polymers are apt to display “non‐universal” phase transitions depending on their detailed individual structures. Here mean field model can be refined in steps to portray critical fluctuations of individual systems through an approach via pseudo‐phase equilibria. Comparison between the “bridging theory” for semi‐dilute polymer solutions, originated by Koningsveld et al. (1974), and the model for the condensation of argon vapour by Gibbs, Pavlin and Yang (1983) reveals some common ingredients for a general but adaptable meanfield methodology. The mathematical mechanisms behind quasi‐linear “cross‐over” behaviour of phase loci and of plots for critical exponents are discussed.