Dynamics In Equilibrium Research Articles

Dynamic Operational Planning in Warfare: A Stochastic Game Approach to Military Campaigns

ABSTRACTWe study a two‐player discounted zero‐sum stochastic game model for dynamic operational planning in military campaigns. At each stage, the players manage multiple commanders who order military actions on objectives that have an open line of control. When a battle over the control of an objective occurs, its stochastic outcome depends on the actions and the enabling support provided by the control of other objectives. Each player aims to maximize the cumulative number of objectives they control, weighted by their criticality. To solve this large‐scale stochastic game, we derive properties of its Markov perfect equilibria by leveraging the logistics and military operational command and control structure. We show the consequential isotonicity of the optimal value function with respect to the partially ordered state space, which in turn leads to a significant reduction of the state and action spaces. We also accelerate Shapley's value iteration algorithm by eliminating dominated actions and investigating pure equilibria of the matrix game solved at each iteration. We demonstrate the computational value of our equilibrium results on a case study that reflects representative operational‐level military campaigns with geopolitical implications. Our analysis reveals a complex interplay between the game's parameters and dynamics in equilibrium, resulting in new military insights for campaign analysts.

Dynamical critical behavior of the two-dimensional three-state Potts model.

We investigate the dynamical critical behavior of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. We focus on the mean-squared deviation of the magnetization M (MSD_{M}) as a function of time, as well as on the autocorrelation function of M. Our simulations reveal the existence of two crossover behaviors at times τ_{1}∼L^{z_{1}} and τ_{2}∼L^{z_{2}}, separating three dynamical regimes. MSD_{M} appears to shift from ordinary diffusion in the first regime, to anomalous diffusion in the second, and finally to be constant in the third regime. The magnetization autocorrelation function, on the other hand, is found to fluctuate between exponential decay, stretched-exponential decay, and then again exponential decay along these three regimes. This behavior is in agreement with the one reported recently for the two-dimensional Ising ferromagnet [Phys. Rev. E 108, 034118 (2023)2470-004510.1103/PhysRevE.108.034118], indicating that the existence of two dynamic critical exponents is not a peculiarity of the Ising model itself. A comparison of both MSD_{M} and the magnetization's autocorrelation function suggests that within our numerical accuracy the exponents z_{1} and z_{2} are shared between the Ising and three-state Potts models at least for the particular case of single spin-flip dynamics studied here, even though their equilibrium universality classes are clearly distinct. Continuity of MSD_{M} requires that α(z_{2}-z_{1})=γ/ν-z_{1}, in which α is the anomalous exponent in the intermediate regime. Since the ratio γ/ν is not shared between the two models, it follows that α is not shared either, an aspect well verified in our simulations. Finally, we also discuss the relevance of our main findings using another useful observable, namely the line magnetization M_{l}.

On the analysis of two-time correlation functions: equilibrium versus non-equilibrium systems.

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of timescales and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical evolution in XPCS measurements, with subsequent extraction of one-time correlations. While the theoretical foundation for the quantitative analysis of TTCs is primarily established for equilibrium systems, where key parameters such as the diffusion coefficient remain constant, non-equilibrium systems pose a unique challenge. In such systems, different projections ('cuts') of the TTC may lead to divergent results if the underlying fundamental parameters themselves are subject to temporal variations. This article explores widely used approaches for TTC calculations and common methods for extracting relevant information from correlation functions, particularly in the light of comparing dynamics in equilibrium and non-equilibrium systems.

The INVESTIGATION OF ASYMMETRIC DYNAMICS OF BORSA ISTANBUL INDEX WITH QUANTILE UNIT ROOT TEST

In this study, we apply the quantile unit root test, which provides robust inferences for non-normal processes based on the quantile autoregression approach, to examine the asymmetric dynamic process of the BIST100 Borsa Istanbul index. The quantile autoregression approach allows the measurement of the persistency of shocks of different magnitudes and signs affecting the stock market index and can capture the adjustment of asymmetric dynamics in the long-run equilibrium of the index. Therefore, quantile unit root tests add new approaches to index dynamics compared to traditional unit root methodologies based on the least squares regression method. Our results show that the index not only returns to the mean but also exhibits asymmetric behavior in its dynamic structure. Compared to traditional unit root tests, quantile unit root tests provide more evidence to support the efficiency of the stock market index and show that the stock market index at different frequencies does not consistently have a unit root. Asymmetric inferences in shock magnitude and sign play an important role in asset pricing and forecasting in the securities market.

Critical dynamical behavior of the Ising model.

We investigate the dynamical critical behavior of the two- and three-dimensional Ising models with Glauber dynamics in equilibrium. In contrast to the usual standing, we focus on the mean-squared deviation of the magnetization M,MSD_{M}, as a function of time, as well as on the autocorrelation function of M. These two functions are distinct but closely related. We find that MSD_{M} features a first crossover at time τ_{1}∼L^{z_{1}}, from ordinary diffusion with MSD_{M}∼t, to anomalous diffusion with MSD_{M}∼t^{α}. Purely on numerical grounds, we obtain the values z_{1}=0.45(5) and α=0.752(5) for the two-dimensional Ising ferromagnet. Related to this, the magnetization autocorrelation function crosses over from an exponential decay to a stretched-exponential decay. At later times, we find a second crossover at time τ_{2}∼L^{z_{2}}. Here, MSD_{M} saturates to its late-time value ∼L^{2+γ/ν}, while the autocorrelation function crosses over from stretched-exponential decay to simple exponential one. We also confirm numerically the value z_{2}=2.1665(12), earlier reported as the single dynamic exponent. Continuity of MSD_{M} requires that α(z_{2}-z_{1})=γ/ν-z_{1}. We speculate that z_{1}=1/2 and α=3/4, values that indeed lead to the expected z_{2}=13/6 result. A complementary analysis for the three-dimensional Ising model provides the estimates z_{1}=1.35(2),α=0.90(2), and z_{2}=2.032(3). While z_{2} has attracted significant attention in the literature, we argue that for all practical purposes z_{1} is more important, as it determines the number of statistically independent measurements during a long simulation.

Monetary policy with non-Ricardian households

This paper analyzes how the presence of non-Ricardian households can alter the dynamics in a New-Keynesian Dynamic Stochastic General Equilibrium (NK-DSGE) model. The model is calibrated using data for the US economy. We focus on two key areas. The first is the link between monetary policy and consumption inequality in the presence of non-Ricardian households. We find that a contractionary monetary policy shock increases consumption inequality. Part of this increase is due to a novel government transfer channel. This channel becomes significantly stronger when steady state debt is positive. We also find that because of this link, the presence of non-Ricardian households amplifies the impact of monetary policy on output and inflation. The second area relates to the choice of monetary policy rule. We compare six monetary policy rules, including a new labor income targeting rule. We find that labor income targeting outperforms all other rules for most parameter values. Nominal GDP targeting is better than labor income targeting only when the share of non-Ricardian households is large or when the households exhibit low habit persistence.

Learning and firm dynamics in a stochastic equilibrium

New firms have unknown profitability types, but they learn in the market. With imperfect information, the learning mechanism matters at the firm level and in the aggregate. This paper studies the effect of learning on the distribution of firms, aggregate dynamics, and welfare when firm growth and the entry and exit dynamics are belief-driven. Aggregate uncertainty affects heterogeneous firm beliefs about own types. Faster learning raises firms' continuation values, lowers the selection threshold belief, and thickens the belief distribution's right tail. Aggregate uncertainty lowers firm value by reducing firms' learning speed. Transitory aggregate shocks have persistent impacts on the economy by shifting existing firms' belief updating paths, affecting firm decisions along both intensive and extensive margins. Faster learning improves social welfare.

Linear response theory in stock markets

Linear response theory relates the response of a system to a weak external force with its dynamics in equilibrium, subjected to fluctuations. Here, this framework is applied to financial markets; in particular we study the dynamics of a set of stocks from the NASDAQ during the last 20 years. Because unambiguous identification of external forces is not possible, critical events are identified in the series of stock prices as sudden changes, and the stock dynamics following an event is taken as the response to the external force. Linear response theory is applied with the log-return as the conjugate variable of the force, providing predictions for the average response of the price and return, which agree with observations, but fails to describe the volatility because this is expected to be beyond linear response. The identification of the conjugate variable allows us to define the perturbation energy for a system of stocks, and observe its relaxation after an event.

The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The r-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length r. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of mDr, where mD is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential shows little sensitivity to the lattice spacing at small mDr ≲ 1 and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.

Enhanced Disrupting Effect of Benzophenone-1 Chlorination Byproducts to the Androgen Receptor: Cell-Based Assays and Gaussian Accelerated Molecular Dynamics Simulations

Benzophenone-1 (BP-1), one of the commonly used ultraviolet filters, has caused increasing public concern due to frequently detected residues in environmental and recreational waters. Its susceptibility to residual chlorine and the potential to subsequently trigger endocrine disruption remain unknown. We herein investigated the chlorination of BP-1 in swimming pool water and evaluated the endocrine disruption toward the human androgen receptor (AR). The structures of monochlorinated (P1) and dichlorinated (P2) products were separated and characterized by mass spectrometry and 1H-1H NMR correlation spectroscopy. P1 and P2 exhibited significantly higher antiandrogenic activity in yeast two-hybrid assays (EC50, 6.13 μM and 9.30 μM) than did BP-1 (12.89 μM). Our 350 ns Gaussian accelerated molecular dynamics simulations showed the protein dynamics in a long-time scale equilibrium, and further energy calculations revealed that although increased hydrophobic interactions are primarily responsible for enhanced binding affinities between chlorinated products and the AR ligand binding domain, the second chloride in P2 still hinders the complex motion because of the solvation penalty. The mixture of BP-1-P1-P2 elicited additive antiandrogenic activity, well fitted by the concentration addition model. P1 and P2 at 1 μM consequently downregulated the mRNA expression of AR-regulated genes, NKX3.1 and KLK3, by 1.7-9.1-fold in androgen-activated LNCaP cells. Because chlorination of BP-1 occurs naturally by residual chlorine in aquatic environments, our results regarding enhanced antiandrogenic activity and disturbed AR signaling provided evidence linking the use of personal care products with potential health risks.

Predator–prey dynamics in general equilibrium and the role of trade

We examine the implications of trade in an economy with two interrelated natural resources, focusing on the case of a simple predator–prey relationship. We derive a three-sector general equilibrium model where production functions are linked via the ecological dynamics of the natural system. Under autarky, this economy exhibits a steady-state equilibrium that overexploits the prey stock, reducing the linked predator population and overall welfare in the absence of harvesting controls. When two economies engage in trade, differences in the dynamics of the two resource systems can become the basis for comparative advantage. In this case, the predator–prey relationship leads to a source of comparative advantage in harvesting prey for a country with a lower autarky steady-state proportion of predators to prey. This feature has not been noticed in the literature and leads to a counterintuitive implication: free trade can help conserve predator and prey stocks in the country with the higher autarkic steady-state proportion of predators to prey. To illustrate the relevance of our analytic findings, we present the stylized empirical example of the effect of Chinook salmon imports on killer whale populations.

Learning and Firm Dynamics in a Stochastic Equilibrium

Imperfect information and individual firm learning affect the cross-sectional firm size distribution and matters for social welfare and aggregate fluctuations. This paper finds a tractable setup to study firm entry, exit, growth, and distribution with heterogeneity in firm beliefs and aggregate uncertainty. A firm learns about its unknown profitability (type) over time. Aggregate uncertainty affects firms' beliefs about individual types. Firm learning results in a Pareto right tail in cross-sectional firm belief distribution, thereby shaping the firm size distribution. When firm value and household welfare are misaligned, slow learning brings additional welfare loss relative to the constrained efficiency under imperfect information. With aggregate uncertainty, transitory shocks have persistent impacts due to the learning mechanism's hangover effect.

A general tool for LTE thermochemistry for adiabatic non-diffusive reactive fluid dynamics: Applications to 2D planar discontinuity flows in SPH

Chemical reactions in fluid dynamics deeply modify physical flow conditions through the contribution of the energy from reactions, as well as through the variations of the mean molecular weight and of the ratio of specific heats. This occurs typically on time scales largely much smaller than the diffusive time scales of chemicals, especially for shock waves due to explosive events. In this work we show how it is possible to include a stand alone algorithm, dealing with both molecular and nuclear thermochemistry in a computational unreactive, non-diffusive, adiabatic flow dynamics in local thermal equilibrium (LTE) within an explicit scheme of integration, free of the adopted computational framework. To this purpose, we worked using the Free Lagrangian GASPHER framework, belonging to the smooth particle hydrodynamics methods (SPH). Assuming the same initial physical conditions, some comparisons are made among reactive to unreactive 2D planar discontinuity flows, assuming the same initial chemical compositions as simple as possible for a better understanding of the role not only of the thermochemical reaction energy, but also of the mean molecular weight and of the ratio of specific heats in fluid dynamics.

Intermittent many-body dynamics at equilibrium

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q-breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Nonlinear waves in bipolar complex viscous astroclouds

A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (\(f\)-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.

Nonlinear eigen-mode structures in complex astroclouds

The evolutionary dynamics of strongly nonlinear waves (of arbitrary amplitude) in an inhomogeneous complex astrophysical viscous cloud is investigated without recourse to any kind of swindle. It consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neural hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method transforms the analytic model into a conjugated pair of intermixed non-integrable energy integral laws. A natural excitation of electrostatic quasi-monotonic compressive dispersive shock-like eigen-modes is numerically demonstrated. In contrast, the self-gravitational waves grow purely as non-monotonic compressive oscillatory shock-like structures. The unique features of both the distinct classes are depicted. Their non-trivial significance in the astro-context is emphasized.

Fast Folding Dynamics of an Intermediate State in RNase H Measured by Single-Molecule FRET.

We have studied the folding kinetics of the core intermediate (I) state of RNase H by using a combination of single-molecule FRET (smFRET) and hidden Markov model analysis. To measure fast dynamics in thermal equilibrium as a function of the concentration of the denaturant GdmCl, a special FRET labeled variant, RNase H 60-113, which is sensitive to folding of the protein core, was immobilized on PEGylated surfaces. Conformational transitions between the unfolded (U) state and the I state could be described by a two-state model within our experimental time resolution, with millisecond mean residence times. The I state population was always a minority species in the entire accessible range of denaturant concentrations. By introducing the measured free energy differences between the U and I states as constraints in global fits of the GdmCl dependence of FRET histograms of a differently labeled RNase H variant (RNase H 3-135), we were able to reveal the free energy differences and, thus, population ratios of all three macroscopic state ensembles, U, I and F (folded state) as a function of denaturant concentration.

Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system.

In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes.

Translocation of Molecules with Different Architectures through a Brush-Covered Microchannel

We investigate the transport of macromolecules with different architectures through polymer brush-covered microchannels by means of molecular dynamics simulations. Linear macromolecules and star polymers with different functionalities and arm lengths are driven through the channel by a Poiseuille flow with various pressure gradients. A comparison between the diffusive dynamics in equilibrium and upon Poiseuille flows reveals dramatic changes of the transport properties. While the self-diffusion for linear chains and stars with large functionality and short arms (the latter representing the limit of hard spheres) is faster than for stars with intermediate softness, the current density of macromolecules in Poiseuille flows depends strongly on the flow strength and tends to decrease monotonically with increasing functionality. Our measurements of density and flow profiles as well as binary interactions among different species (brushes, solvent, macromolecular inclusions) shed light on complex translocation processes, which are of importance in biology and micromechanical applications.

Pervasive inattentiveness

In this paper we analyze how inattentiveness in capital investment decisions shapes business cycle dynamics in a dynamic stochastic general equilibrium (DSGE) model with inattentiveness. We find that the model with pervasive inattentiveness matches several business cycle moments much better than an otherwise identical model without informational frictions in investment. These findings reinforce the need for pervasive stickiness to mimic the inertia found in macroeconomic data.