Equilibrium Profile Research Articles

On the transition to dripping of an inverted liquid film

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the LCM and FCM, respectively), and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased. For any fixed volume, the LCM reaches the horizontal state where it attains a cosine-shaped profile. For sufficiently small volume, the FCM and Stokes solutions attain a weak Young–Laplace equilibrium profile, the approach to which is described by an asymptotic analysis generalising that of Kalliadasis & Chang (J. Fluid Mech., vol. 261, 1994, pp. 135–168) for the LCM. For large volumes, the bifurcation curves for the FCM and Stokes model have a turning point so that the fully inverted state is never reached. For fixed flow rate, the LCM blows up at a critical angle that is well predicted by asymptotic analysis. The bifurcation curve for the FCM either has a turning point or else reaches a point at which the surface profile has an infinite slope singularity, indicating the onset of multi-valuedness. The latter is confirmed by the Stokes model, which can be continued to obtain overturning surface profiles. Overall, the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle.

MHD simulation on magnetic compression of field reversed configurations with NIMROD

Magnetic compression has long been proposed a promising method for plasma heating in a field reversed configuration (FRC). However, it remains a challenge to fully understand the physical mechanisms underlying the compression process, due to its highly dynamic nature beyond the one-dimensional (1D) adiabatic theory model (Spencer et al 1983 Phys. Fluids 26 1564). In this work, magnetohydrodynamics simulations on the magnetic compression of FRCs using the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355) and their comparisons with the 1D theory have been performed. The effects of the assumptions of the theory on the compression process have been explored, and the detailed profiles of the FRC during compression have been investigated. The pressure evolution agrees with the theoretical prediction under various initial conditions. The axial contraction of the FRC can be affected by the initial density profile and the ramping rate of the compression magnetic field, but the theoretical predictions on the FRC’s length in general and the relation in particular hold approximately well during the whole compression process, where r s is the major radius of FRC separatrix and r o is that of the magnetic axis. The evolutions of the density and temperature can be affected significantly by the initial equilibrium profile and the ramping rate of the compression magnetic field. During the compression, the major radius of the FRC is another parameter that is susceptible to the ramping rate of the compression field. Basically, for the same magnetic compression ratio, the peak density is higher and the FRC’s radius r s is smaller than the theoretical predictions.

Games of GANs: game-theoretical models for generative adversarial networks

Generative Adversarial Networks (GANs) have recently attracted considerable attention in the AI community due to their ability to generate high-quality data of significant statistical resemblance to real data. Fundamentally, GAN is a game between two neural networks trained in an adversarial manner to reach a zero-sum Nash equilibrium profile. Despite the improvement accomplished in GANs in the last few years, several issues remain to be solved. This paper reviews the literature on the game-theoretic aspects of GANs and addresses how game theory models can address specific challenges of generative models and improve the GAN’s performance. We first present some preliminaries, including the basic GAN model and some game theory background. We then present a taxonomy to classify state-of-the-art solutions into three main categories: modified game models, modified architectures, and modified learning methods. The classification is based on modifications made to the basic GAN model by proposed game-theoretic approaches in the literature. We then explore the objectives of each category and discuss recent works in each class. Finally, we discuss the remaining challenges in this field and present future research directions.

The role of the second prize in all-pay auctions with two heterogeneous prizes

We study complete information all-pay contests with n players and two heterogeneous prizes with distinct values. Among the players, n−1 are symmetric (i.e., they evaluate the prizes in a similar manner), whereas the remaining player has different valuations for each of the prizes. Our analysis focuses on the equilibrium profiles and expected payoffs for the case of three players. We also partially extend our analysis for cases with additional players. Our results show that in all-pay auctions with heterogeneous prizes, the ordering of the players according to their expected payoffs in equilibrium might vary significantly, depending on both prizes. Furthermore, although the values for the first (larger) prize have the greatest effect on the identity of the players with positive expected payoffs, the value of the second prize might have a non-negligible effect.

Stratigraphic evolution of a spectacularly exposed turbidite channel belt from the Tachrift System (late Tortonian, north‐East Morocco)

ABSTRACTThe sedimentary architecture of channelized turbidites can be highly complex as it reflects the response of submarine channels to several interplaying factors. Although intensively investigated through seismic imaging, turbidite channel fills are not convincingly calibrated for sedimentary facies at a sub‐seismic scale. This contribution addresses the sedimentary architecture and the controls on the evolution of a ca 20 m thick channel‐levee complex of the Tachrift turbidite subunit (Upper Miocene, the Melloulou Formation), which accumulated along the southern slope of the Neogene Taza‐Guercif Basin (Rifian Corridor of north‐east Morocco). Facies and architectural analyses indicate that the studied channel‐levee complex is the result of three‐fold evolution. From base to top, it is comprised of: (i) a ca 7 m thick lower mud‐prone interval containing relatively small and vertically stacked channel fills with poorly developed muddy levees; (ii) a ca 4 m thick and >1 km wide sandstone‐rich middle interval made of lateral accretion packages that become progressively less amalgamated and fine‐grained and is overlain by ca 5 m of thin‐bedded mud‐rich turbidites intercalated with hemiplegic marlstones; and (iii) an up to ca 9 m thick upper interval constituted by aggradational channel fills with well‐developed levees and variously directed lateral accretion packages. This organization suggests that, following a phase of inception (lower interval), the channel underwent extensive meandering with very minor vertical aggradation, prior to being blanketed by ‘retrogressive’ muddy lobes (middle interval) during a phase of reduced sediment input. In turn, the uppermost interval records a late phase of channel re‐establishment and aggradation that likely terminated as a result of up‐dip avulsion. It is suggested that the observed change of architectural style reflected the feedback of changing sediment input, slope equilibrium profile and channel morphodynamics.

Shearless bifurcations in particle transport for reversed-shear tokamaks

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-centre trajectories of plasma particles undergoing $\boldsymbol {E}\times \boldsymbol {B}$ drift motion, considering that the electric field has a stationary non-monotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a non-monotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the safety factor profile parameters, the appearance and breakup of these shearless curves are observed. The shearless curve's successive breakup and recovery are explained using concepts from bifurcation theory. We also present bifurcation sequences associated with the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

A new lipid-structured model to investigate the opposing effects of LDL and HDL on atherosclerotic plaque macrophages

Atherosclerotic plaques form in artery walls due to a chronic inflammatory response driven by lipid accumulation. A key component of the inflammatory response is the interaction between monocyte-derived macrophages and extracellular lipid. Although concentrations of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) particles in the blood are known to affect plaque progression, their impact on the lipid load of plaque macrophages remains unexplored. In this paper, we develop a lipid-structured mathematical model to investigate the impact of blood LDL/HDL levels on plaque composition, and lipid distribution in plaque macrophages. A reduced subsystem, derived by summing the equations of the full model, describes the dynamics of biophysical quantities relating to plaque composition (e.g. total number of macrophages, total amount of intracellular lipid). We also derive a continuum approximation of the model to facilitate analysis of the macrophage lipid distribution. The results, which include time-dependent numerical solutions and asymptotic analysis of the unique steady state solution, indicate that plaque lipid content is sensitive to the influx of LDL relative to HDL capacity. The macrophage lipid distribution evolves in a wave-like manner towards an equilibrium profile which may be monotone decreasing, quasi-uniform or unimodal, attaining its maximum value at a non-zero lipid level. Our model also reveals that macrophage uptake may be severely impaired by lipid accumulation. We conclude that lipid accumulation in plaque macrophages may serve as a partial explanation for the defective uptake of apoptotic cells (efferocytosis) often reported in atherosclerotic plaques.

Adverse inclusion of asymmetric advertisers in position auctions

Product listing platforms commonly use generalized second-price auctions to select competing advertisers for limited ad positions. However, when advertisers are asymmetric, position auctions may confound the post-auction competition structure and thus endogenize the bidders’ values of the ad positions. We build an analytical model to examine the impact of position auctions on an asymmetric market structure, which consists of a mass marketer and two specialized advertisers of heterogeneous quality efficiencies. The advertisers bid for two ad slots and then compete for the market in price and quality. We find that the asymmetric market structure may increase the uncertainty of the auction outcomes, which then may induce the advertisers to underbid using a conservative strategy profile in the locally-envy free equilibrium. Consequently, the auction outcome may adversely include the less-efficient specialized advertiser. This result is stronger than the position paradox in the classic auction literature, as the advertiser with a competitive advantage may be driven out and obtain zero profit.

Measured Fate of Beach Nourishment Sand

Houston, J.R., 2023. Measured fate of beach nourishment sand. Journal of Coastal Research, 39(3), 407–417. Charlotte (North Carolina), ISSN 0749-0208. The fate of sand placed over a 20-year period in one of the largest series of beach nourishment projects ever conducted in the United States is determined by using direct measurements of elevation vs. distance from dunes to closure depth. Four projects placed 11.25 million m3 of sand from 1998–2017 on a 28.8-km-long shoreline at Panama City on Florida's Gulf of Mexico coast. Profile measurements were available in 1996 following Hurricane Opal and in 2018 after Hurricane Michael, one of the largest hurricanes to strike the United States, which came ashore only 30 km from Panama City beaches. The profiles were about 300 m apart within the project template and extended down to closure depth. After about 20 years, 87 ± 3% of the nourishment sand remained on profiles. Some sand used for nourishment was dredged within closure depth along a 3.6-km section and resulted in sand loss of 4% ± 1% as sand partially refilled the dredged holes. About 9% ± 3% was lost to longshore transport out of the project area. Calculations based on the equilibrium profile concept used in U.S. beach nourishment design predicted beaches should have widened 30.9 m ± 0.9 m and profiles raised 0.69 m ± 0.10 m due to the measured volume of sand remaining on profiles from the start of beach nourishment in 1998 to November 2018 after Hurricane Michael. The measured change in beach width was 32.4 m ± 4.0 m, and the rise was 0.66 m ± 0.05 m. The rise of 0.66–0.69 m is comparable to the 0.81 m mean sea-level rise by the year 2100 projected by the Intergovernmental Panel on Climate Change for its worst-case temperature scenario.

Secure Downlink Transmission Strategies against Active Eavesdropping in燦OMA Systems: A Zero-Sum Game Approach

Non-orthogonal multiple access technology (NOMA), as a potentially promising technology in the 5G/B5G era, suffers from ubiquitous security threats due to the broadcast nature of the wireless medium. In this paper, we focus on artificial-signal-assisted and relay-assisted secure downlink transmission schemes against external eavesdropping in the context of physical layer security, respectively. To characterize the non-cooperative confrontation around the secrecy rate between the legitimate communication party and the eavesdropper, their interactions are modeled as a two-person zero-sum game. The existence of the Nash equilibrium of the proposed game models is proved, and the pure strategy Nash equilibrium and mixed-strategy Nash equilibrium profiles in the two schemes are solved and analyzed, respectively. The numerical simulations are conducted to validate the analytical results, and show that the two schemes improve the secrecy rate and further enhance the physical layer security performance of NOMA systems.

Thermodynamics Analysis of the Distributed Parameter Model of Counterflow Heat Exchanger

In this paper we are interested in the thermodynamic analysis of a counterflow heat exchanger, when the dynamics are described by two hyperbolic partial differential equations (PDEs). First from the first and second law of thermodynamics we derive the different models of the heat exchanger. Next we perform an analysis of the equilibrium profiles from a certain condition on the system parameters that guarantees the existence and uniqueness of the solution of the PDEs model. In this analysis we show the importance of the thermal pinch as an energy efficiency factor. Finally we study the passivity and the asymptotic stability of the considered heat exchanger essentially basing ourselves on the entropy as a storage function, entropy production as a dissipation function, and the thermodynamic availability function as a Lyapunov function.

Equilibrium perturbations for stochastic interacting systems

We consider the equilibrium perturbations for two stochastic systems: the d-dimensional generalized exclusion process and the one-dimensional chain of anharmonic oscillators. We add a perturbation of order N−α to the equilibrium profile and speed up the process by N1+κ for parameters 0<κ≤α. Under some additional constraints on κ and α, we show the perturbed quantities evolve according to the Burgers equation in the exclusion process, and to two decoupled Burgers equations in the anharmonic chain, both in the smooth regime.

惑星大気のためのラインバイラインおよび相関 &lt;i&gt;k&lt;/i&gt; 分布放射モデルの開発

A set of line-by-line and correlated k-distribution radiation models are developed aiming for applications in simulations and examinations of Venus and Mars-like planetary atmospheres. Our line-by-line model is validated by comparing the results with observations and those of previous studies under conditions of Venus, and present and possible early Mars. The radiation fields calculated by our line-by-line model agree well with observed profiles and are within the acceptable range from those presented in previous studies. The results obtained by our line-by-line model are then processed to generate a series of parameters for our correlated k-distribution model. It is confirmed that the radiation fields calculated with those sets of parameters by our correlated k-distribution model sufficiently agree with those by our line-by-line model for the atmospheres with a wide range of surface pressure. By the use of our correlated k-distribution model implemented with those sets of parameters, we evaluate the radiation field for Venus and calculate radiative-convective equilibrium profiles for Venus and Mars. The obtained vertical thermal structures for Venus are qualitatively consistent with observations, and the behaviors of surface pressure and surface temperature for Mars are similar to those reported by previous studies. Those results demonstrate that our models including the procedure for generating tables of radiation parameters are applicable to examine climates of CO2 dominant atmospheres in our solar and exoplanetary systems.

Localized compressional self-heating in magnetic islands

A spontaneous heating process is found to arise in a system where a magnetic island is present due to a linearly unstable tearing mode. The parity, the relative phases and the structure of the fields determined linearly by the tearing mode cause the compression of the plasma in the direction parallel to the magnetic field to heat the plasma in the vicinity of the separatrix in the nonlinear phase. Using a six-field electromagnetic fluid model, the process is found to be present in both two-dimensional single-helicity and three-dimensional multi-helicity simulations with both symmetric and asymmetric magnetic equilibrium profiles. A noteworthy feature of the model is that the higher-order compression terms responsible for the heating process are retained in the equations. The process is believed to be linked to experimental observations of localized hot-spots on externally induced magnetic islands.

Differential tectonic evolution and formation mechanism of three sub-sags in Wenchang Sag of Pearl River Mouth Basin, South China Sea

Notable differences in the structural characteristics and evolution of three adjacent sub-sags, i.e., the Wenchang sub-sags A, B, and C, on the downthrown side of the Zhu III South Fault in the Wenchang Sag, are significant as they affect the formation and distribution of the oil and gas in these three sub-sags. However, the differences in their tectonic evolutions and formation mechanisms have not yet been adequately explained. In this paper, stress analysis, equilibrium profiles, and paleogeomorphic restoration, are used to investigate the dynamic settings, formation mechanisms, and influencing factors of the structural deformation related to the formation of the Wenchang Sag based on interpretation of seismic data. The results of the stress analysis suggest clockwise deflection of the regional tensile stress direction from a WNW-ESE trend during the Early Paleocene to NW-SE and NNW-SSE trends during the Eocene, to a nearly N–S trend during the Oligocene, and finally to a NNE-SSW trend during the Miocene. This clockwise rotation of the regional tensile stress direction led to the formation of a dextral strike-slip stress component parallel to the NE-trending Zhu III South Fault. This strike-slip stress component formed a releasing bend in sub-sag A, and may be associated with the continuous subsidence of a thick sedimentary layer in sub-sag A. It also created a restraining bend in sub-sag B, which underwent multiple structural inversions during its extension and subsidence and has a relatively small sedimentary thickness. The double restraining bend in sub-sag C is considered to have been strongly uplifted and eroded in response to this strike-slip stress component. Four obvious structural inversions in sub-sag B are identified in this paper. These structural inversions correspond to the last four regional tectonic movements. This interpretation suggests that the formation of the structural inversions was likely related to the strong tensile stress and the small intersection angle between the direction of the regional tensile stress and the pre-existing boundary fault. The rotation of the tensile stress direction was responsible for the strike-slip movement on the pre-existing boundary fault and the formation of the releasing bend and restraining bend, which controlled the structural evolutions of the sub-sags. This reasonably explains the differential tectonic evolution of these three sub-sags in the Wenchang Sag, and provides a crucial idea for structural analysis of similar basins.

Asymptotic dynamics of a logistic SIS epidemic reaction-diffusion model with nonlinear incidence rate

A logistic SIS epidemic reaction-diffusion model with the nonlinear incidence rate SqIp in a spatially heterogeneous environment is concerned. The L∞-estimates of solutions are established under p,q>0 to explore the long-time behaviors of the model. In a special case, asymptotic dynamics and bifurcation behaviors under p=1 are analyzed in terms of the basic reproduction number. Asymptotic profiles of the endemic equilibrium for small and large diffusion rates of the susceptible and infected populations are investigated. It is found that the infectious disease is hard to control even under a policy of mobility regulation when 0<p<1 and q>1.

Well balanced finite volume schemes for shallow water equations on manifolds

In this paper we propose a novel second-order accurate well balanced scheme for shallow water equations in general covariant coordinates over manifolds. In our approach, once the gravitational field is defined for the specific case, one equipotential surface is detected and parametrized by a frame of general covariant coordinates. This surface is the manifold whose covariant parametrization induces a metric tensor. The model is then re-written in a hyperbolic form with a tuple of conserved variables composed both of the evolving physical quantities and the metric coefficients. This formulation allows the numerical scheme to automatically compute the curvature of the manifold as long as the physical variables are evolved. In a classical well balanced formulation, the knowledge of a given equilibrium is exploited for evolving the specific state seen as the sum of the equilibrium and the fluctuations of the state around the equilibrium itself. On the contrary, the numerical approach proposed here is automatically well balanced for the water at rest solution (defined by zero velocity and constant free surface) for general manifoldswithout having to exploit the exact equilibrium profile during the computation. In particular, this numerical strategy allows to preserve the accuracy of the water at rest equilibrium at machine precision and on large timescales, even for non-smooth bottom topographies. As a matter of fact, the proposed local polynomial reconstruction, needed at each time step by the scheme for evolving the state, is built in order to automatically cancel any numerical error committed for describing jumps in the bathymetry. As a further effect, also out of the equilibrium, the typical spurious non-physical oscillations of the recovered numerical solution in a neighborhood of the discontinuities are healed. Thus, once the information on both the bathymetry and the metric of the manifold are properly collected in the flux terms and in the nonconservative products, the resulting numerical strategy turns out to be more accurate in finding also non-equilibrium solutions. Numerical results close the work. After having proved that the scheme is second-order accurate, we test the recovery of the water at rest equilibrium at machine precision for different bottom topographies (eventually discontinuous) with various metric on very long simulation times. In particular, after having considered smooth bathymetries with compact support, we relax the assumption on the continuity of water at rest equilibrium with discontinuous bathymetries disturbed by a white noise.

Dynamics of the capillary rise in tilted Taylor-Hauksbee cells

In this work, we theoretically and experimentally study the issue of the spontaneous capillary rise of a viscous liquid in wedge-shaped tilted cells, with very short angles of aperture, α. We provide the equilibrium profiles yse and, by means of the Reynolds lubrication equations, we find the time-dependent profiles and the dynamic evolution of the meniscus close to the edge of the wedge, as a function of time, which follow power laws of the form ys ∼ t 1/3 . Experiments performed at various inclinations are consistent with our theoretical results.

Gyrokinetic analysis of inter-edge localized mode transport mechanisms in a DIII-D pedestal

In this study, gyrokinetic simulations are used to study pedestal fluctuations for DIII-D discharge 174082 using the GENE code. Nonlinear local simulations indicate that electron heat flux has contributions from electron temperature gradient-driven transport but at levels insufficient to satisfy power balance. We show that microtearing modes (MTM) and neoclassical transport are likely to account for the remaining observed energy losses in the electron and ion channels, respectively. The MTM instabilities found in the simulations are consistent with the high-frequency fluctuations identified in the magnetic fluctuation data from Mirnov coils. The fluctuation data in this discharge also exhibit a low-frequency band of fluctuations. By modifying the equilibrium profiles and plasma β, simulations produce MHD modes, which may be responsible for these observed low-frequency fluctuations. We compare several metrics involving ratios of fluctuation amplitudes and transport quantities for both MTMs and MHD modes. This analysis suggests that the available data are consistent with the simultaneous activity of both MHD modes and MTMs provided that the former is limited largely to the particle transport channel.

Comparison and evaluation of two different crystalloids - Normal saline and plasmalyte in patients of traumatic brain injury undergoing craniotomy.

Fluid therapy is one of the most important components of the management of patients with traumatic brain injury (TBI). The present study was planned to compare plasmalyte and normal saline (NS) in patients who underwent craniotomies for TBI in terms of their effects on acid-base equilibrium, renal functions, and coagulation profile. Fifty patients of age 18-45 years of either sex, who underwent emergency craniotomy for TBI, were included in the study. The patients were randomized into two groups. Group P (n = 25) received isotonic balanced crystalloid (plasmalyte) and Group N (n = 25) received NS intraoperatively and postoperatively till 24 h after surgery. The pH was lower in Group N (P < 0.05) at different time points after surgery. Similarly, more patients in Group N had pH <7.3 (P < 0.05); while the rest of the metabolic parameters were comparable in the two groups. Blood urea and serum creatinine were higher in Group N. Coagulation profile was comparable in the two groups. Acid-base, electrolyte balance, and renal profile were better in patients receiving plasmalyte as compared to NS. Hence, it can be a wiser choice for fluid management in patients of TBI undergoing craniotomy.