Equilibrium Evolution Research Articles

Platform Revenue Strategy Selection Considering Consumer Group Data Privacy Regulation

In the era of big data, consumer group privacy has become an important source of revenue for the digital platform. Considering the situation that the platform collects consumer group data privacy to generate business revenue, we explore how the service matching level and commission rate affect the platform revenue, social welfare, and seller benefits. Based on the theory of group privacy, the three-party equilibrium evolution is solved by constructing a sequential game model including platform, seller, and consumer alliance. It is found that when the service matching level of the platform is greater than the threshold value, there are two main situations: on the one hand, if using the data privacy of a consumer group is subject to market regulation, the platform will set a high commission rate and service matching level in order to maximize profit. However, social welfare and seller’s business benefit both reach a minimum in this case, and the three-party game cannot attain equilibrium. On the other hand, when the market governor relaxes the platform’s regulation on the use of consumer group privacy data and data revenue efficiency is high enough, the platform can maximize the revenue by increasing the service matching level and reducing the commission rate. The optimal commission rate depends on the data revenue efficiency of the platform. Moreover, when the platform sets the highest commission rate and the service matching level is at a medium level, a stable partial equilibrium among the three-party will be achieved. These conclusions can give some insights into platform’s business model choice decision.

Single-Laser-Pulse-Driven Thermal Limit of the Quasi-Two-Dimensional Magnetic Ordering in Sr2IrO4

Upon femtosecond-laser stimulation, generally materials are expected to recover back to their thermal-equilibrium conditions, with only a few exceptions reported. Here we demonstrate that deviation from the thermal-equilibrium pathway can be induced in canonical 3D antiferromagnetically (AFM) ordered Sr$_2$IrO$_4$ by a single 100-fs-laser pulse, appearing as losing long-range magnetic correlation along one direction into a glassy condition. We further discover a `critical-threshold ordering' behavior for fluence above approximately 12 mJ/cm$^2$ which we show corresponds to the smallest thermodynamically stable $c$-axis correlation length needed to maintain long-range quasi-two-dimensional AFM order. We suggest that this behavior arises from the crystalline anisotropy of the magnetic-exchange parameters in Sr$_2$IrO$_4$, whose strengths are associated with distinctly different timescales. As a result, they play out very differently in the ultrafast recovery processes, compared with the thermal equilibrium evolution. Thus, our observations are expected to be relevant to a wide range of problems in the nonequilibrium behavior of low-dimensional magnets and other related ordering phenomena.

Evolution of multimodal final user equilibrium considering public transport network design history

Analysing the properties of a network equilibrium can help to have a better view about network state, robustness, and the effect of any variation in the network. This study investigated the impacts of network design history on day-to-day multimodal user equilibrium. In particular, we analyze the long-term evolution of the network, including opening new multimodal options and its impacts on the final network equilibrium. First, the analysis focuses on static network loading with different successive configurations. Then, a more realistic setting is studied by simulation. A large-scale multimodal network with the flexible opening over time of three possible transport facilities shows that the final equilibrium is not unique; more importantly, significant differences can be observed in public transportation occupancy, while user equilibrium is enforced in all situations. Some solutions prove to be better from the collective viewpoint (shorter total travel time), thus giving new insight into public transport planning.

A Galerkin method for the weak formulation of current diffusion and force balance in tokamak plasmas

This paper presents a new numerical approach to the simulation of plasma equilibrium evolution in tokamaks. It is based on an unusual coupling formulation of current diffusion and axi-symmetric equilibrium equations that does not require the use of flux-surface averages and allows for fast Newton-type iterations schemes. A detailed derivation of the coupled system of non-linear equations and its discretization is provided. Numerical examples, based on an implementation in the free-boundary equilibrium code FEEQS, highlight feasibility and applicability.

Diffusive time evolution of the Grad–Shafranov equation for a toroidal plasma

We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by reproducing the essential features of a scenario for the upcoming Italian experiment Divertor Tokamak Test Facility, with a good degree of accuracy. Although we find the resistive diffusion time scale to be of the order of $10^4$ s, we observe a macroscopic change in the plasma volume on a time scale of $10^2$ s, comparable to the foreseen duration of the plasma discharge by design. In the final part of the work, we compare our self-consistent solution to the more common Solov'ev one, and to a family of nonlinear configurations.

A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429–1450, 2018), Vermolen and Gefen (BMM 12:301–323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340–348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.

Supply Chain Investment in Carbon Emission-Reducing Technology Based on Stochasticity and Low-Carbon Preferences

Due to excessive greenhouse gas emissions, carbon emission-reducing measures are urgently needed. Important emission-reduction measures mainly include carbon trading and low-carbon cost subsidies. Comprehensive consideration of these two policies is a research hotspot in the field of low-carbon technology investment. Based on this background, this paper considers the impact of consumer low-carbon preferences on market demand and the impact of uncertainty in carbon emission-reduction behaviour. We construct a stochastic differential game model with upstream and downstream enterprises based on cost-sharing coordination under a cost subsidy. From a dynamic perspective, this paper researches the optimal equilibrium strategy and evolution characteristics of the joint emission-reduction mechanism in a supply chain. This paper discusses the sensitivity of the parameters and uses numerical simulation to verify the impact of each parameter on the emission-reduction decision-making activities of stakeholders after introducing the cost subsidy. The results show that a cost subsidy policy can promote carbon emission-reduction investment and supply chain profit. Thus, it is important to strengthen technical cooperation and exchange among enterprises.

Investigating slow shock in low-impedance materials using a direct impact Hopkinson bar setup

This work implements a direct impact Hopkinson bar, suitable for investigating the evolution of dynamic force equilibrium in low-impedance materials. Polycarbonate as the bar material favours for a long pulse duration of 2.6 ms for an overall length of only 5 m, allowing to compress large specimens to high strains. This setup is applied to polyurethane foams with different densities ranging from 80 - 240 kg/m3. Dynamic compression tests are performed at strain rates of 0.0017, 0.5 and 500 /s on the foams at room temperature. Depending on density, they show a saturation in increase of yield strength at strain rates of 500 /s, or even show a negative strain rate sensitivity for the lowest density. This behaviour is explained by comparing the dynamic force equilibrium to a phenomenon similar to shock in solid materials: For low densities and high rates of strain, homogeneous compression is replaced by a localized collapse front with a jump in stress across the front. Digital image correlation is performed to analyse elastic and plastic compaction waves by means of Lagrange diagrams.

Evaluation of the impact of EMBRACE II protocol in Spanish centers, with a large cohort of patients using a ranking index.

PurposeThe aim of this paper was to assess development of high-dose-rate (HDR) cervix brachytherapy (BT) implants in three Spanish institutions before and after introduction of EMBRACE II protocol.Material and methods392 patients from three different institutions, treated between 2009 and 2019 were analyzed. D90 of high-risk clinical target volume (HR-CTV) and D2cc of organs at risk (OARs) of all patients were collected. Statistical distribution was analyzed for two different periods of time: before and after EMBRACE II publication. Index I was applied based on collected dosimetric quantities (D90 and D2cc) to enhance equilibrium between HR-CTV coverage and doses to OARs. Variation in dosimetry and index depending on CTV and technique used (IC vs. IC/IT) were also evaluated.ResultsAdaptation of institutions to EMBRACE II protocol resulted in a statistically significant increase of D90 HR-CTV (Institution 1; p < 0.00001) or decrease of D2cc OARs (Institution 2; p < 0.04). Increase in the use of interstitial component showed higher coverage of HR-CTV for Institution 3 (p = 0.03), and lower doses to OARs for the same coverage of HR-CTV at Institution 2 (p-OARs < 0.03). Even though index I was only significantly different between periods for Institution 1 (p < 0.0000001), it was able to show a reduction of dose variability related to higher expertise and higher interstitial component.ConclusionsDepending on local protocol before EMBRACE II, the adaptation through increasing interstitial component and physician and physicist training, resulted in a significant increase of HR-CTV doses or reduction of OARs doses. Index I was able to describe an evolution of equilibrium between CTV coverage and OARs’ sparing.

Microstructures and phase transformation in directionally solidified TiAl-Nb alloys

Intermetallic Ti-45Al-8Nb-(W, B, Y) (at.%) and Ti-46Al-5Nb alloys are directionally solidified at a constant growth rate of 30 µm·s−1 using a Bridgman type apparatus. The quenched microstructures and lengths of different phase regions were observed and measured after various growing times of 0–30 min. Results show that the phase transformations in different phase regions are mainly depending on the high temperature microstructure and the supercooling degree during quenching process. After isothermal holding, the primary phase grows into the liquid phase, the dendrites change from equiaxed to columnar grains, and the length of the L+β phase region, L+β+α phase region and mushy zone varies, indicating that the entire directional solidification process can be described by a static equilibrium — nonequilibrium — dynamic equilibrium evolution process. In addition, the gap between the original growth interface and front interface shows that the actual crystal growth rate is not equal to the drawing velocity during directional solidification.

Dynamics of reversed shear Alfvén eigenmode and energetic particles during current ramp-up

Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfvén eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and non-linear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizing wave-EP power transfer. In the linear stage, EPs induce evident mode structure and frequency shifts; meanwhile, RSAE saturates by radial decoupling with resonant EPs due to weak magnetic shear, and gives rise to global EP convective transport and fast frequency chirping in the non-adiabatic regime. The spatiotemporal scales of phase space wave-EP interactions are characterized by the perpendicular wavelength and wave-particle trapping time. The simulations provide insights into general as well as specific features of the RSAE spectra and EP transport in experimental observations, and illustrate the fundamental physics of wave-EP resonant interaction with the interplay of the magnetic geometry, plasma non-uniformity and non-perturbative EPs. Possible application for understanding the non-adiabatic frequency chirping as convective and relaxation branches is also discussed.

Experimental determination of the elasticity of porous ceramics under the gas saturation and temperature treatment

After the formulation of the theory of poroelasticity, which describes the elasticity of fluid saturated porous media, many experimental studies have been reported on the determination of the elasticity of porous materials under the various physical and structural conditions. However, there are limited studies on how the elasticity behave under the variation of the physical conditions of the saturated fluid. This study presents an attempt to characterize the influence of the pore-saturated gas media and their physical properties on the elasticity of porous ceramic materials. Resonant ultrasound spectroscopic measurements were performed on test specimens of alumina with ∼40% porosity, zirconia with ∼48% porosity, and sintered fully dense zirconia to determine the hydrostatic pressure-dependent macroscopic elasticity. Here, we report the variation of elasticity of porous and full dense samples over approximately five orders of magnitude (800–0.02 psi) in absolute pressure. A material softening with increased pressure was observed from the porous specimens and the rate of softening is quantified with different gas saturation by helium, nitrogen and argon. The time evolution of mechanical equilibrium of the porous materials at low pressure (0.02 psi) and moderately high-temperature (150 °C) conditions will also be discussed.

Theory of microstructure-dependent glassy shear elasticity and dynamic localization in melt polymer nanocomposites.

We present an integrated theoretical study of the structure, thermodynamic properties, dynamic localization, and glassy shear modulus of melt polymer nanocomposites (PNCs) that spans the three microstructural regimes of entropic depletion induced nanoparticle (NP) clustering, discrete adsorbed layer driven NP dispersion, and polymer-mediated bridging network. The evolution of equilibrium and dynamic properties with NP loading, total packing fraction, and strength of interfacial attraction is systematically studied based on a minimalist model. Structural predictions of polymer reference interaction site model integral equation theory are employed to establish the rich behavior of the interfacial cohesive force density, surface excess, and a measure of free volume as a function of PNC variables. The glassy dynamic shear modulus is predicted to be softened, reinforced, or hardly changed relative to the pure polymer melt depending on system parameters, as a result of the competing and qualitatively different influences of interfacial cohesion (physical bonding), free volume, and entropic depletion on dynamic localization and shear elasticity. The localization of polymer segments is the dominant factor in determining bulk PNC softening and reinforcement effects for moderate to strong interfacial attractions, respectively. While in the athermal entropy-dominated regime, the primary origin of mechanical reinforcement is the stress stored in the aggregated NP subsystem. The PNC shear modulus is often qualitatively correlated with the segment localization length but with notable exceptions. The present work provides the foundation for developing a theory of segmental relaxation, Tg changes, and collective NP dynamics in PNCs based on a self-consistent treatment of the cooperative activated motions of segments and NPs.

Estimating MFDs, trip lengths and path flow distributions in a multi-region setting using mobile phone data

The present work proposes a global framework to estimate all MFD model parameters using mobile phone data. The three major components that are estimated in the present context are MFD shapes, regional trip lengths and path flow distribution. A trip enrichment scheme based on the map matching process is proposed for the trips that have sparser records. Time dependent penetration rates are estimated by fusing the OD matrix and the Loop Detector Data (LDD). Two different types of penetration rates of vehicles are proposed based on the OD flow and the trips starting within an origin, respectively. The estimated MFDs based on two types of penetration rates are stable with very low scatter. In the following step, macro-paths and their corresponding trip lengths are estimated. This work is the first to present empirical evidences of the dynamic evolution of mean trip lengths over the day, which is very difficult to capture with other types of data sources. The last component is the time dependent path flow distributions between the different macro-paths for a given OD pair. The manuscript is concluded by presenting the time evolution of the User Equilibrium (UE) gap for different macroscopic OD pairs. It is noticed that UE principle holds true most of the time, except for OD pairs that have macro-paths transversing through congested reservoirs, especially during peak hours.

Introduction and Validation of the APEC Code for the Simulation of Plasma Equilibrium and Evolution in the Presence of 3-D Passive Structures

Recently, a novel code for the simulation of the plasma equilibrium and its evolution has been developed and fully implemented in ANSYS. We named it ANSYS Plasma Equilibrium and Evolution Code (APEC). It is based on the solution of the Grad–Shafranov equation and exploits the finite-element method using the magnetic potential vector formulation. In this article, we present a further development on the coupling of the axisymmetric plasma equilibrium equations, describing the plasma behavior, with the full 3-D eddy current equations, defining the surrounding 3-D structures. One test case, related to the International Thermonuclear Experimental Reactor (ITER) tokamak, has been fully analyzed and benchmarked with a validated code showing the validity of the proposed approach. In particular, the benchmark has concerned the comparison of the initial equilibrium and plasma evolution.

Research on the influence mechanism of resettlers participation in migrant work in the context of relationship network

Under the network environment, the simulation for the evolution of the interaction behavior between immigrants is explored from two aspects of the crowd risk appetite and neighbor behavior effectiveness. The utility will choose decision-making behavior of the immigrants combined with the randomness of complex social network, establish the stochastic equilibrium evolution model of neighbor preferred, and use MATALAB and Netlogo to simulation analysis. The results show that: 1) The different risk preference of individual groups have different behavior decision state evolution regular; 2) social network structure of the randomness and connectivity play an important role for the stability of the crowd behavior decision-making and evolution; 3) the size of the information flow in the social network relationship and neighbor preferences effect on the balance of work behavior evolution. The study to some extent analyzed the influence factors of immigrants’ behavior change, explains the inherent law of the people neighbor preferred behavior evolution, provide the supportive theoretical evidence for the immigrants’ behavior management under the network environment.

Out-of-equilibrium chiral magnetic effect and momentum relaxation in holography

The authors study the chiral magnetic effect in out of equilibrium situations in a holographic setup describing a far from equilibrium evolution. They find that the anomaly induced response shows a late equilibration and suggest that this could be a universal feature of anomalous transport, which could provide an important lesson for observations in heavy ion collisions.

Simulation of disruptions triggered by Vertical Displacement Events (VDE) in tokamak and leading edge effect in plasma energy deposition to material surfaces

The paper describes two major non-linear properties of the vertical instability of a tokamak plasma, which has a vertical elongation: (a) inductive excitation of surface (edge) currents stabilizing the instability and converting it into fast equilibrium evolution, and (b) creation of a wetting zone without the normal component of the magnetic field when the plasma has contact with material surfaces. Two major disruption effects for both mitigated and non-mitigated disruptions, important for JET and ITER, were considered: (a) excitation of vertical disruption during the current quench (i.e., abnormal plasma current ramp down) and (b) related to the wetting zone, potential leading edge effect in plasma energy deposition to the in-vessel tiles during disruptions. Our considerations together with a 2-D version of the VDE (Vertical Disruption Event) code are based on a new mathematical model, called Tokamak MHD (TMHD), as a replacement for the conventional model, a model that cannot solve numerical problems related to extreme plasma anisotropy and negligible mass. The code includes a 3-D model of surface currents on a thin conductive wall and has a well-specified algorithm for extension to vertical disruptions that excite asymmetric kink modes.

Low pressure dependent elasticity of porous ceramics.

The primary goal of this study was to characterize the influence of the pore-saturated gas media and their physical properties on the elasticity of porous ceramic materials. Resonant ultrasound spectroscopic measurements were performed on test specimens of alumina with ~40% porosity, zirconia with ~48% porosity, and sintered fully dense zirconia to determine the hydrostatic pressure-dependent macroscopic elasticity. Here, we report the variation of elasticity of porous and full dense samples over approximately five orders of magnitude (800-0.02 psi) in absolute pressure. The time evolution of mechanical equilibrium of the porous materials at low pressure and high-temperature conditions will also be discussed.

Prediction and quantification of bacterial biofilm detachment using Glazier–Graner–Hogeweg method based model simulations

Morphological changes in bacterial biofilm structures arise from the fluid-structure interactions between the biofilm and the surrounding fluid. Depending on the magnitude of the force acting on the structure, the bacteria rearrange to attain an equilibrium shape or get washed away by the moving fluid. Understanding the dynamics behind the evolution of such equilibrium or failed states can aid in development of tools for biofilm removal or eradication. We develop a Glazier–Graner–Hogeweg method-based model to explore the collective evolution of biofilm morphology arising from cell-cell and cell-fluid interactions. We show that low adherence and high motility of the cells leads to sloughing of biofilms. Also, streamers are found to form under laminar flow conditions in tightly packed biofilms. In mixed species biofilms, we found that a species with less cell-cell binding affinity gets eroded faster than its counterpart. Therefore, we hypothesize that in nature these less-adherent species should be present encapsulated within the biofilm structure to maximize their chances of survival.