Statistical Physics Research Articles

Queues with resetting: a perspective

Abstract Performance modeling is a key issue in queuing theory and operation research. It is well-known that the length of a queue that awaits service or the time spent by a job in a queue depends not only on the service rate, but also crucially on the fluctuations in service time. The larger the fluctuations, the longer the delay becomes and hence, this is a major hindrance for the queue to operate efficiently. Various strategies have been adapted to prevent this drawback. In this perspective, we investigate the effects of one such novel strategy namely resetting or restart, an emerging concept in statistical physics and stochastic complex process, that was recently introduced to mitigate fluctuations-induced delays in queues. In particular, we show that a service resetting mechanism accompanied with an overhead time can remarkably shorten the average queue lengths and waiting times. We examine various resetting strategies and further shed light on the intricate role of the overhead times to the queuing performance. Our analysis opens up future avenues in operation research where resetting-based strategies can be universally promising.

From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence

We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusivity of individual vortices using ideas from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of non-trivial SV states in this system, specifically the emergence and melting of a vortex crystal.

Extremes of summer Arctic sea ice reduction investigated with a rare event algorithm

AbstractVarious studies identified possible drivers of extremes of Arctic sea ice reduction, such as observed in the summers of 2007 and 2012, including preconditioning, local feedback mechanisms, oceanic heat transport and the synoptic- and large-scale atmospheric circulations. However, a robust quantitative statistical analysis of extremes of sea ice reduction is hindered by the small number of events that can be sampled in observations and numerical simulations with computationally expensive climate models. Recent studies tackled the problem of sampling climate extremes by using rare event algorithms, i.e., computational techniques developed in statistical physics to reduce the computational cost required to sample rare events in numerical simulations. Here we apply a rare event algorithm to ensemble simulations with the intermediate complexity coupled climate model PlaSim-LSG to investigate extreme negative summer pan-Arctic sea ice area anomalies under pre-industrial greenhouse gas conditions. Owing to the algorithm, we estimate return times of extremes orders of magnitude larger than feasible with direct sampling, and we compute statistically significant composite maps of dynamical quantities conditional on the occurrence of these extremes. We find that extremely low sea ice summers in PlaSim-LSG are associated with preconditioning through the winter sea ice-ocean state, with enhanced downward longwave radiation due to an anomalously moist and warm spring Arctic atmosphere and with enhanced downward sensible heat fluxes during the spring-summer transition. As a consequence of these three processes, the sea ice-albedo feedback becomes active in spring and leads to an amplification of pre-existing sea ice area anomalies during summer.

Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements

Abstract. In the online seminar series “Perspectives on climate sciences: from historical developments to future frontiers”, which took place during 2020–2021, well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. This special issue aims to create a platform for a more detailed elaboration of the topics discussed in the seminars but also to publish new scientific findings. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue. In line with the spirit of the seminar series, this paper is structured along thematic areas of the broad field of climate science, conveying different perspectives on the climate system: geophysical fluid dynamics, dynamical systems theory, multiscale processes, statistical physics, paleoclimate and the human dimension.

Highly efficient batch adsorption of anionic dye in wastewater using nanocomposite: experimental and theoretical studies

The adsorptive properties of the Erionyl Red (ER) dye on bentonite (B) intercalated with cetyltrimethylammonium bromide (HDTMA-B) were investigated using experimental and statistical physics methods. The dye was then taken up by the intercalated bentonite from a real water sample. After intercalation, X-ray diffraction analysis indicates an increase in HDTMA-B basal spacing to 15.2 Ả. Scanning electron microscopy images show the formation of large particles and many cavities. The results revealed that the material had high properties to adsorb organic molecules (greater than 99%). The Langmuir-Freundlich model, described the isotherms, whereas the second-order model better captured the kinetic of dye adsorption. The maximum ER uptake observed was 478mgg-1 at a temperature of 328K. Reusability of nanocomposite showed stability, over five cycles. Thermodynamic analysis suggested spontaneous (negative ΔG°) and endothermic (positive ΔH°) adsorption processes. The statistical physics model was also used to estimate the orientation of ER adsorption on the material. The oxygens connected to the dye in the HDTMA-B structure played in particular an important role in the adsorption mechanisms of dye. This study combines experiment data with a theoretical approach to provide a new explanation for the mechanism. The removal of dyes from wastewater, in particular Erionyl red, is vital for the protection of the environment and public health. Nanocomposite appears to be an effective, durable, and environmentally friendly adsorbent for the removal of Erionyl red dye from synthetic solutions and real wastewater.

Experimentation on stochastic trajectories: From Brownian motion to inertial confined dynamics

Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing some of the underlying ideas of stochastic processes through direct experimentation. Students analyze stochastic trajectories of beads in a bouncing bed of smaller beads subjected to an external periodic drive. The analysis of the trajectories involves the application of a vast toolkit of statistical estimators that are useful in many fields of physics.

Experimental and numerical study of hydrogen adsorption by the Ni0.6Mg0.4Fe2O4 compound

This paper proposes an experimental and numerical study of the hydrogen storage properties of the Ni0.6Mg0.4Fe2O4 compound. Firstly, the sol-gel method was used to synthesize the compound Ni0.6Mg0.4Fe2O4. Second, the synthesized compound's morphological and structural properties were ascertained using X-ray and SEM techniques. Third, the experimental hydrogen adsorption's kinetics and isotherms were carried out. At last, the experimental hydrogen adsorption isotherms were compared to a mathematical model based on the formalism of statistical physics. With the use of this model, it was possible to ascertain the following: on the one hand, the stereographic parameters involved in the adsorption process, such as the number of receptor sites (n1 and n2), their density (Nm1 and Nm2), as well as the energy parameters (P1 and P2) and the energies of adsorption for each type of site (ΔEads1 and ΔEads2). On the other hand, the thermodynamic functions that regulate the hydrogen adsorption reaction, such as the internal and Gibbs energies, as well as the entropy versus temperature and pressure. Ni0.6Mg0.4Fe2O4 has a significant hydrogen storage capacity (0.15 wt %) at moderate temperatures. The numerical results showed that hydrogen is inserted into two types of interstitial sites via an exothermic process.

A multilayer adsorption of perfluorohexanesulfonic and perfluorobutanesulfonic acids on bio-based polyurethane/chitosan foam: Advanced interpretation of the adsorption mechanism

This work presents an application of a multilayer model derived from statistical physics to the adsorption experimental data of two industrial pollutants, namely perfluorohexanesulfonic (PFHxS) and Perfluorobutanesulfonic (PFBS) acids on a bio–based polyurethane /chitosan(PU/CH) adsorbent foam, at T = 298–328 K and pH 4. This model shows that the number of PFHxS and PFBS layers formed on adsorbent surface increases from 1.61 to 3.80, and from 1.56 to 2.26 respectively by increasing the temperature.This means that the adsorbate molecules are arranged on a variable number of layers. For instance, at 328 K, it was deduced that around 80 % of PFHxS acid was taken up by the PU/CH composite, forming a total of four layers, whereas the remaining 20 % contributed to the formation of three layers. The estimation and analysis of the number of molecules bound per active site is useful to understand the adsorption mechanism. PFHxS and PFBS adsorb on PU/CH in non-parallel configuration, through a multimolecular docking characterized by more than one molecule per active site. The PU/CH performances are investigated in terms of the maximum adsorption capacity of both the tested industrial pollutants, retrieving similar values for both PFHxS and PFBS. Two adsorption energies are calculated showing that physical forces are contributing to remove these pollutants. Interstingly, thermodynamic calculations are also introduced and interpreted to understand the adsorption mechanism at macroscopic level.These theoretical scientific evidences provide a plausible explanation of the PFHxS and PFBS adsorption mechanisms and contribute to understand this interfacial process at molecular level.

Machine learning and statistical physics modeling of tetracycline adsorption using activated carbon derived from Cynometra ramiflora fruit biomass

The current investigation reports the usage of adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN), the two recognized machine learning techniques in modelling tetracycline (TC) adsorption onto Cynometra ramiflora fruit biomass derived activated carbon (AC). Many characterization methods utilized, confirmed the porous structure of synthesized AC. ANN and ANFIS models utilized pH, dose, initial TC concentration, mixing speed, time duration, and temperature as input parameters, whereas TC removal percentage was designated as the output parameter. The optimized configuration for the ANN model was determined as 6-8-1, while the ANFIS model employed trimf input and linear output membership functions. The obtained results showed a strong correlation, indicated by high R2 values (ANNR2: 0.9939 & ANFISR2: 0.9906) and low RMSE values (ANNRMSE: 0.0393 & ANFISRMSE: 0.0503). Apart from traditional isotherms, the dataset was fitted to statistical physics models wherein, the double-layer with a single energy satisfactorily explained the physisorption mechanism of TC adsorption. The sorption energy was 21.06 kJ/mol, and the number of TC moieties bound per site (n) was found to be 0.42, conclusive of parallel binding of TC molecules to the adsorbent surface. The adsorption capacity at saturation (Qsat) was estimated to be 466.86 mg/g – appreciably more than previously reported values. These findings collectively demonstrate that the AC derived from C. ramiflora fruit holds great potential for efficient removal of TC from a given system, and machine learning approaches can effectively model the adsorption processes.

Insights into nitrobenzene adsorption mechanism on apricot stone activated carbon: A study via statistical physics models and thermodynamic analysis

Statistical physics modelling was performed to analyze the adsorption forces and the thermodynamics of the removal of nitrobenzene molecules using an activated carbon obtained from apricot stones. This adsorbent was prepared using phosphoric acid activation and exhibited a surface area of 1762 m2 g−1, total pore volume of 1.09 cm3 g−1 and an experimental maximum adsorption capacity of 295.63 mg g−1 for nitrobenzene at 298 K. The removal of this organic molecule was exothermic. A double layer adsorption model with two energies was utilized to calculate the main steric parameters for the removal of this compound. This model was employed to perform a thermodynamic analysis of this adsorption system. It was concluded that 2 and 3 adsorption sites can be involved for the removal of nitrobenzene molecules on activated carbon surface. Physical interaction forces were expected to participate in the removal of this pollutant. This activated carbon can be regenerated with NaOH thus offering the alternative of its recycling to reduce the removal costs of this organic molecule from water.

Coalescent processes emerging from large deviations

The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman’s coalescent process, which produces a binary tree, emerges universally from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offsprings distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here, we investigate the regime where the variance of the offspring distribution is finite but comparable to the population size. This is achieved by studying a model in which the log offspring sizes have stretched exponential tails. Such offspring distributions are motivated by biology, where they emerge from a toy model of growth in a heterogeneous environment, but also from mathematics and statistical physics, where limit theorems and phase transitions for sums over random exponentials have received considerable attention due to their appearance in the partition function of Derrida’s random energy model (REM). We find that the limit coalescent is a β-coalescent—a previously studied model emerging from evolutionary dynamics models with heavy-tailed offspring distributions. We also discuss the connection to previous results on the REM.

Statistical physics investigation on the simultaneous adsorption mechanism of Cd2+ and Pb2+ on amino functionalized activated carbon derived from coal gasification fine slag

In this study, a novel surface amino-functionalized activated carbon (T-AC) was synthesized from coal gasification fine slag (CGFS) and used as an adsorbent for heavy metal ions. T-AC exhibits excellent adsorption capacity for Cd2+ and Pb2+. The adsorption process of Cd2+ and Pb2+ onto T-AC was found to be spontaneous. The dominant adsorption process was chemisorption, primarily involving chelation and covalent bonding. In binary systems, as the initial concentration increases, the independent adsorption effect of Pb2+ and Cd2+ gradually becomes a competitive adsorption effect. Statistical physical models revealed that the adsorption of T-AC for Cd2+ and Pb2+ in single systems followed a multi-molecular adsorption process, whereas in binary systems, it involved a multi-anchorage process. The adsorption capacity was primarily influenced by the number of ions attached to the receptor sites and the density of the adsorbent receptor sites. Moreover, elevating temperature enhanced the thermal movement of heavy metal ions within the pore structure of the adsorbent, reducing their tendency to aggregate at the active sites. This work provides insights into the microscopic-level adsorption process of heavy metal ions by carbon-based materials and contributed to understand of the adsorption behavior.

HOW DO E-WORKSHEET USING WIZER.ME BASED GOOGLE SITE IMPROVE HIGHER ORDER THINKING SKILLS AND COMMUNICATION SKILLS?

Higher Order Thinking Skills (HOTS) and Communication Skills (CS) must be taught to pre-service physics teacher in the twenty-first century if they are to become future professional physics teacher. Based on the results of the preliminary study it is known that the HOTS and CV categories of physics education students are still lacking with an average score of 25 and 3. In addition, learning time in class is limited to solving problems so lecturers want to take advantage of technology in making teaching materials that facilitate independent practice outside the classroom, easily accessible to pre-service physics teacher (paperless), easy to provide feedback and correction results from worksheets so that learning evaluation is more effective and efficient. One treatment that can be applied to train HOTS and CS is to use teaching materials in the form of electronic-worksheets (e-worksheets) using Wizer.me based Google Site. E-worksheets will be more optimal if applied in learning, namely the Contextual Teaching and Learning (CTL) model and the Blended Problem-Based Learning (B-PBL) model. The purpose of this study was to determine the effectiveness of e-worksheets in CTL and B-PBL using Wizer.me based Google Site, changes to HOTS and CS and to determine student perceptions of using e-worksheets. The research method is quasi-experimental with a two-treatment counterbalanced design. The population of this study was all statistical physics classes for the 2022/2023 academic year, consisting of 2 classes with a total of 66 students. The sampling technique was purposive sampling, with 33 students in each class. Data collection techniques used the HOTS test, communication skills observation sheets and perception questionnaires about the use of CTL and B-PBL-based e-worksheets. The HOTS test is in the form of a description with a total of 3 questions including analyzing (C4), evaluating (C5) and creating (C4). Communication skills observation sheets include systematics/format, use of language, completeness and sequence of contents. The perception questionnaire consists of 9 questions using the Guttman scale. Based on the results of data analysis, it is known that CTL and B-PBL-based e-worksheets are effective in training HOTS and CS with large categories, namely 0.88 and 0.91. The increase in HOTS and CS was in the high category in both classes but the increase in the BPBL-CTL class was better with N-Gain, namely 0.87 and 0.92. The results of the questionnaire analysis stated that physics education students gave a good response with almost all students stating that the use of e-worksheets using Wizer.me based Google Site could increase HOTS and CS and physics education students were more independent in finding solutions to problems. Based on the results of data analysis, it can be concluded that e-worksheets in CTL and B-PBL using Wizer.me based Google Site can increase HOTS and CS.

Experimental and theoretical study for the sorption of Ni2+ and Cd2+ onto phosphoryl functionalized aluminum silicate composite

Phosphoryl functionalized Aluminum silicate (ASP) composite sorbent was synthesized using sol–gel technique and characterized with different techniques. The synthesized sorbent was tested for the sorption of Ni2+ and Cd2+ in aqueous solution at both single- and binary-solute systems under simulated conditions using batch technique. Batch experiments were executed as a function of pH, initial metal ion concentration and temperature. Structural and surface morphology of the synthesized sorbent were determined using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and Scanning electron microscopy (SEM). The studied kinetic models suggested that the sorption of Ni2+ and Cd2+ onto ASP was found to follow the pseudo-second order and the Langmuir-Freundlich model was the best model to depict the sorption isotherms. The sorption equilibria of both ions were analyzed using two diverse statistical physics models (homogeneous and heterogeneous monolayer models). A Theoretical scrutiny of statistical physics calculations indicated that Ni2+ and Cd2+ sorption was multi-ionic where two sorption sites were involved but with a diverse contribution degree. The removal nature of Ni2+ and Cd2+ was endothermic and the calculated sorption amounts at saturation implied that Ni2+> Cd2+. Calculated interaction energies indicated the participation of physical forces in the sorption of both ions onto the synthesized sorbent surface and the variation of these sorption energies confirmed that both sorption sites participated in the removal of Ni2+ and Cd2+ but through different interactions type. Ions sorption capacity was increased with the temperature owing to increase in thermal agitation. This study reveals that phosphoryl functionalized aluminum silicate is an efficient sorbent that can be used for the sorption of Ni2+ and Cd2+ from aqueous solutions in both single- and binary -solute systems.

A Theory of Best Choice Selection through Objective Arguments Grounded in Linear Response Theory Concepts

In this study, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow for the ranking of “agents”, “opinions”, etc., all defined in a very broad sense. We aim toward any process which should a priori demand or lead to some consensus in order to attain the presumably best choice among many possibilities. In order to specify the framework, we discuss previous attempts, recalling trivial means of scores—weighted or not—Condorcet paradox, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), etc. We demonstrate, through geometrical arguments on a toy example and with four criteria, that the pre-selected order of criteria in previous attempts makes a difference in the final result. However, it might be unjustified. Thus, we base our “best choice theory” on the linear response theory in statistical physics: we indicate that one should be calculating correlations functions between all possible choice evaluations, thereby avoiding an arbitrarily ordered set of criteria. We justify the point through an example with six possible criteria. Applications in many fields are suggested. Furthermore, two toy models, serving as practical examples and illustrative arguments are discussed.

Physicochemical assessment of ammonium adsorption using a palm shell-based adsorbent activated with acetic acid: experimental and theoretical studies.

The adsorption of ammonium from water was studied on an activated carbon obtained using raw oil palm shell and activated with acetic acid. The performance of this adsorbent was tested at different operating conditions including the solution pH, adsorbent dosage, and initial ammonium concentration. Kinetic and equilibrium studies were carried out, and their results were analyzed with different models. For the adsorption kinetics, the pseudo-first order equation was the best model to correlate this system. Calculated adsorption rate constants ranged from 0.071 to 0.074 g/mg min. The ammonium removal was 70-80% at pH 6-8, and it was significantly affected by electrostatic interaction forces. Ammonium removal (%) increased with the adsorbent dosage, and neutral pH condition favored the adsorption of this pollutant. The best ammonium adsorption conditions were identified with a response surface methodology model where the maximum removal was 91.49% with 2.27 g/L of adsorbent at pH 8.11 for an initial ammonium concentration of 36.90 mg/L. The application of a physical monolayer model developed by statistical physics theory indicated that the removal mechanism of ammonium was multi-ionic and involved physical interactions with adsorption energy of 29 kJ/mol. This activated carbon treated with acetic acid is promising to depollute aqueous solutions containing ammonium.

Sustainable removal of caffeine and acetaminophen from water using biomass waste-derived activated carbon: Synthesis, characterization, and modelling

The removal of caffeine (CFN) and acetaminophen (ACT) from water using low-cost activated carbons prepared from artichoke leaves (AAC) and pomegranate peels (PAC) was reported in this paper. These activated carbons were characterized using various analytical techniques. The results showed that AAC and PAC had surface areas of 1203 and 1095 m2 g−1, respectively. The prepared adsorbents were tested for the adsorption of these pharmaceuticals in single and binary solutions. These experiments were performed under different operating conditions to evaluate the adsorption properties of these adsorbents to remove CFN and ACT. AAC and PAC showed maximum adsorption capacities of 290.86 and 258.98 mg g−1 for CFN removal, 281.18 and 154.99 mg g−1 for the ACT removal over a wide pH range. The experimental equilibrium adsorption data fitted to the Langmuir model and the kinetic data were correlated with the pseudo-second order model. AAC showed the best adsorption capacities for the removal of these pharmaceuticals in single systems and, consequently, it was tested for the simultaneous removal of these pollutants in binary solutions. The simultaneous adsorption of these compounds on AAC was improved using the central composite design and response surface methodology. The results indicated an antagonistic effect of CFN on the ACT adsorption. AAC regeneration was also analyzed and discussed. A statistical physics model was applied to describe the adsorption orientation of the tested pollutants on both activated carbon samples. It was concluded that AAC is a promising adsorbent for the removal of emerging pollutants due to its low cost and reusability properties.

Statistical physics modelling of adsorption isotherms of water vapour on shale: Stereographic, energetic and thermodynamic investigations

AbstractUnderstanding the mechanisms of shale–water interaction by water vapour adsorption is crucial for predicting shale gas productivity. In this study, equilibrium adsorption data of water vapour on four different shales of the Sichuan Basin at three temperatures (298, 308, and 318 K) were measured using static gravity techniques. The water vapour adsorption isotherms were simulated by three statistical physics models. Steric parameters, including the number of water vapour molecules adsorbed per site (n), monolayer adsorption amount (q0), and adsorption energy (ΔEa), and thermodynamic parameters such as configuration entropy (Sa), internal energy (Eint), and free energy (Ga) derived from the selected model were used to explain the adsorption mechanism. The model analyses suggest that the adsorbed water vapour molecules are attached to the shale surface in a multi‐anchorage manner. The adsorption of the first layer shows a Type I characteristics, while the adsorption of the subsequent layer is of Type III. The calculated adsorption energies indicate that the physical adsorption takes place on the water vapour molecules on the shale, and the main interaction forces are hydrophilic bonding forces and van der Waals forces. Negative Eint and Ga values indicate that the spontaneous properties are for water vapour adsorption and that the system requires the release of energy to capture the water vapour molecules.

Ranking species in complex ecosystems through nestedness maximization

Identifying the rank of species in a complex ecosystem is a difficult task, since the rank of each species invariably depends on the interactions stipulated with other species through the adjacency matrix of the network. A common ranking method in economic and ecological networks is to sort the nodes such that the layout of the reordered adjacency matrix looks maximally nested with all nonzero entries packed in the upper left corner, called Nestedness Maximization Problem (NMP). Here we solve this problem by defining a suitable cost-energy function for the NMP which reveals the equivalence between the NMP and the Quadratic Assignment Problem, one of the most important combinatorial optimization problems, and use statistical physics techniques to derive a set of self-consistent equations whose fixed point represents the optimal nodes’ rankings in an arbitrary bipartite mutualistic network. Concurrently, we present an efficient algorithm to solve the NMP that outperforms state-of-the-art network-based metrics and genetic algorithms. Eventually, our theoretical framework may be easily generalized to study the relationship between ranking and network structure beyond pairwise interactions, e.g. in higher-order networks.

The sharp interface limit of an Ising game

The Ising model of statistical physics has served as a keystone example of phase transitions and many mathematical methods.  We introduce and explore an Ising game, a variant of the Ising model that features competing agents influencing the behavior of the spins. With long-range interactions, we consider a mean-field limit resulting in a nonlocal potential game at the mesoscopic scale. This game exhibits a phase transition and multiple constant Nash-equilibria in the supercritical regime.        Our analysis focuses on a sharp interface limit for which potential minimizing solutions to the Ising game concentrate on two of the constant Nash-equilibria.   We show that the mesoscopic problem can be recast as a mixed local/nonlocal space-time Allen-Cahn type minimization problem. We prove, using a Gamma-convergence argument, that the limiting interface minimizes a space-time anisotropic perimeter type energy functional. This macroscopic scale problem could also be viewed as a problem of optimal control of interface motion.      Sharp interface limits of Allen-Cahn type functionals have been well studied.  We build on that literature with new techniques to handle a mixture of local derivative terms and nonlocal interactions.  The boundary conditions imposed by the game theoretic considerations also appear as novel terms and require special treatment.