Critical Parameter Values Research Articles

The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality

In this work, we modify the affine wealth model of wealth distributions to examine the effects of nonconstant redistribution on the very wealthy. Previous studies of this model, restricted to flat redistribution schemes, have demonstrated the presence of a phase transition to a partially wealth-condensed state, or "partial oligarchy," at the critical value of an order parameter. These studies have also indicated the presence of an exponential tail in wealth distribution precisely at criticality. Away from criticality, the tail was observed to be Gaussian. In this work, we generalize the flat redistribution within the affine wealth model to allow for an essentially arbitrary redistribution policy. We show that the exponential tail observed near criticality in prior work is, in fact, a special case of a much broader class of critical, slower-than-Gaussian decays that depend sensitively on the corresponding asymptotic behavior of the progressive redistribution model used. We thereby demonstrate that the functional form of the tail of the wealth distribution in a near-critical society is not universal in nature but rather entirely determined by the specifics of public policy decisions. This is significant because most major economies today are observed to be near-critical.

Transition Problem and Localized Turbulent Structures in Pipes

In the classical experiments of O. Reynolds made in 1883 the critical value of a dimensionless parameter, named now the Reynolds number, $${\text{R}}{{{\text{e}}}_{c}} \approx 2000$$ , was determined. As this value is exceeded in a pipe of circular cross-section, a turbulent flow regime can occur. The attempts to define this value more exactly undertaken during the twentieth century have not met with success. In this study, we present a review of theoretical, experimental, and numerical investigations of flows in a round pipe at the stage of transition to turbulence performed in recent years, which make it possible to formulate a new view on the nature of laminar-turbulent transition in these flows.

Optimization of Basecutter Structural Parameters for Under-the-Ground Sugarcane Basecutting

HighlightsAn under-the-ground basecutting mode was employed, which is different from the typical above-the-ground basecutting mode.A series of field experiments were carried out using the response surface methodology (RSM).The complicated effect of critical parameters on three indicators (stubble breaking index, stubble uprooting index, and power consumption) was explored.The optimal values of critical parameters were determined using a multi-objective optimization method.Abstract. Basecutting is an important process in mechanical sugarcane harvesting, thus, it’s necessary to develop a high-efficient basecutter. The previous research about basecutting has mainly focused on the above-the-ground basecutting instead of under-the-ground basecutting. Therefore, the objective of this study was to analyze how the critical structural parameters, such as blade number (BN), oblique angle and bevel angle of blades (OA, BA), affect the cutting performance of a sugarcane harvester with an under-the-ground basecutting mode. A series of field tests were carried out using Liugong sugarcane harvester. The experimental indexes were determined as stubble breaking index (BI), stubble uprooting index (UI), and power consumption (PC). The ANOVA results indicated that three regression models of indicators were significant, and were in agreement with the test data. Additionally, it was concluded that OA and BN were the two most important factors when optimizing BI, UI, and PC. BA was the last factor to be considered although it had significant effect on BI and UI. The multi-objective optimization results showed that the optimal parameter combination was 3 of BN, 10° of OA, and 20° of BA, and the corresponding BI, UI, and PC reached the minimum. For sugarcane growers, reduced stubble damage and power consumption could increase the sugarcane germination and decrease the harvesting cost, respectively. For sugarcane mills, this cutting mode might cause potential decrease in sugar quality, specifically sediment levels. However, this disadvantage could be overcome by optimizing basecutter parameters. Keywords: Basecutter, Cutting mode, Power consumption, Stubble breaking, Stubble uprooting, Under-the-ground basecutting.

ЕКОНОМІКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВУ COVID-19 НА ФУНКЦІОНУВАННЯ АВТОТРАНСПОРТНОГО ПІДПРИЄМСТВА

The article covers the trends of COVID-19 influence on the economic situation of the motor transport enterprise in Ukraine. As a result of the pandemic, Ukraine has seen a reduction in production, reduction of corporate incomes, an increase of unemployment, and impoverishment. The paper investigates the consequences of the pandemic the motor transport. In the example of a small trucking company, profits and profitability decrease of the company during a pandemic is considered. An economic-mathematical model based on net present value and internal profitability is created. By changing the key parameters of the model, the sensitivity analysis is performed, which consists of substituting various hypothetical values of critical parameters into the financial model of the project with their subsequent calculation. Calculated indicators of variation. The coefficient of variation used to estimate the risk per unit of return is calculated. Recommendations on the work of the enterprise after the pandemic are given. Possibilities of basic expenses optimization are analyzed. As a result of the spread of the coronavirus, the expected reduction in employment in passenger traffic is 21%. During a pandemic, bank loans and deposits are important. However, given the economic and political instability in the country, banks face significant difficulties in formulating and implementing effective interest rate policies. Interest rates on active and passive operations of the NBU have currently risen to 7.5%. Because any loans need to be given, the internal rate of return, or internal rate of return (IRR), is analyzed. The internal rate of return is calculated using the IRR function MS Excel. For the case considered in the work, it will be impossible to give loans. Substantial assistance during a pandemic should be state support. The situation in which enterprises found themselves during the pandemic proved the need to develop new methods for the management and planning of medium and large transport enterprises. Currently, all models are based on outdated and inaccurate methods, which leads to significant differences between the desired and achieved results.

Сравнительный анализ эффективности оптического и калориметрического методов изучения околокритического состояния углеводородных смесей

By the example of a binary hydrocarbon methane–pentane mixture simulating the simplest gas-condensate system, it is shown that the optical method for studying the near-critical state of hydrocarbon fluid, using the measurement of the intensity of critical opalescence in the vicinity of the liquid–gas critical point, gives more accurate and reliable results for the dew–bubble curve and values of critical parameters of the fluid than classical adiabatic calorimetry, which uses the thermogram method to record the change in the phase state of the fluid in the near-critical region.

P,ρ,T–Relations of Equimolar Ternary Water–1-Propanol–n-Hexane in Supercritical State

New values of critical state parameters and p,ρ,T-relations of equimolar ternary homogeneous water–1-propanol–n-hexane (x=0.333… molar fraction or 0.1097, 0.3658, 0.5246 mass fraction of water, 1-propanol and n-hexane respectively) system in supercritical state are given. These values were carried out by using high-temperature, high-pressure, constant-volume piezometer along the isochores. The dependence of pressure from temperature and density at supercritical region (510.85–673.15 K, 255.7–615.62 kg/m3, 6.09–60 MPa) is described polynomial equation of state represented by expansion of the compressibility factor Z=pVm/RT=p/RTρm into a power series of density ω=ρ/ρc and temperature τ=T/Tc, ; , where ρm-molar density mole/m3, R=8.314–gas constant (J/mol·K).The average relative deviation of calculated values of pressure from experimental ones is not more than 0.6%.

Influence of XY anisotropy on a magnetoelectric effect in spin-1/2 XY chain in a transverse magnetic field

A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in transverse magnetic field is considered. A spatial orientation of the electric field is chosen to provide an exact solution of the model in terms of free spinless fermions. The simplest model of quantum spin chain demonstrating a magnetoelectric effect, a zero temperature case of the spin-1/2 XX chain in a transverse magnetic field with Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest possible form of the magnetization, polarization and susceptibility functions, depending on electric and magnetic fields in a most simple form. For the case of arbitrary XY anisotropy, a non-monotonous dependence of magnetization on the XY anisotropy parameter is figured out. This non-uniform behaviour is governed by the critical point which is connected with the possibility to drive the system gapless or gapped by the electric field. Singularities of the magnetoelectric susceptibility at the critical value of system parameters are shown.

A singular value homotopy for finding critical parameter values

Various applications in science and engineering depend upon computing real solutions to systems of analytic equations which depend upon real parameters. Locally in the parameter space, the qualitative behavior of the solutions remains the same except at critical parameter values. This article develops a singular value homotopy that aims to compute critical parameter values. Several examples are presented including computing critical parameter values for nonlinear boundary value problems, turning points for a steady-state system connected to learning and memory, and computing the maximum Gaussian curvature of a surface.

Phase transition in quantum tunneling and exact statistical mechanics for a model of parameterized double‐well potential

A model for one‐dimensional bistable systems characterized by a deformable double‐well energy landscape is introduced in order to investigate the effect of shape deformability on the order of phase transition in quantum tunneling and on the quasi‐exact integrability of the classical statistical mechanics of these systems. The deformable double‐well energy landscape is modeled by a parameterized double‐well potential possessing two fixed degenerate minima and a constant barrier height, but a tunable shape of its walls which affects the confinement of the two wells. It is found that unlike bistable models involving the standard ϕ4‐field model for which the transition in quantum tunneling is predicted to be strictly of second order, a parameterization of the double‐well potential also favors a first‐order transition occurring above a universal critical value of the shape deformability parameter. The partition function of the model is constructed within the framework of the transfer integral formalism, with emphasis on low‐lying eigenstates of the transfer integral operator. Criteria for quasi‐exact integrability of the partition function were formulated, in terms of the condition for possible existence of exact eigenstates of the transfer integral operator. The quasi‐exact solvability condition is obtained analytically, and from this, some exact eigenstates are derived at several temperatures. The exact probability densities obtained from the analytical expressions of the ground state wavefunctions at different temperatures are found to be in excellent agreement with the probability density obtained from numerical simulations of the Fokker–Planck equation.

Thermocapillary instabilities in a liquid layer subjected to an oblique temperature gradient

Abstract

Formation of spectral triplets induced by parity deformation in a quantum dot–cavity system

In this work, we conduct an investigation on the optical emission properties of a pumped-dissipative QD–cavity system within the Lindblad master equation approach, where the cavity mode is modeled through the R-deformed realization of the Heisenberg algebra (RDHA). We found that the parity deformation parameter associated with the RDHA gives rise to a collective effect in the photonic emission of the system by reordering of the one-photon optical transitions, and it is demonstrated that there are two critical values for this parameter where a new type of spectral triplet arises in the emission spectrum. Our results reveal that depending on the critical value of the deformation parameter, the spectral triplets observed in the emission spectrum exhibit signatures of the weak- and strong-coupling regimes simultaneously.

Absolute Measurement of Thoron in Surface Waters

Thoron (radon-220, 220Rn, half-life 55.6 s) is a useful aqueous tracer suitable for applications such as locating and measuring groundwater discharge in surface waters (including the coastal ocean) and detecting radium-224 (224Ra) bearing scale inside water pipes. Generally, such applications require only relative thoron measurements in the water. However, if a thoron-in-water quantification in absolute numbers is desired the knowledge of the thoron sensitivity of the measurement system is obligatory. Absolute readings would, e.g., give a measure of the 224Ra activity in the sediment, supporting the thoron, or of the quantity of 224Ra in the pipe scale. Since there is no standardised source of thoron-in-water (such as a NIST standard), there is no way to calibrate a thoron-in-water measurement system, in the usual sense. Up until now, therefore, it has not been possible to make absolute measurements of thoron in water. This paper presents a novel method of assessing the sensitivity of a mobile thoron-in-water measurement system. The paper analyses such systems and describes a straightforward experimental approach to obtain all setup-specific values of critical parameters that will allow a reasonably precise determination of the system thoron sensitivity. The method is simple enough that a thoron sensitivity calibration can be performed on site with no additional equipment.

Self-diffusion-driven pattern formation in prey–predator system with complex habitat under fear effect

In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self-diffusion. First, we modify the Rosenzweig–MacArthur predator–prey model by incorporating the effects of habitat complexity on the carrying capacity and fear effect of prey and predator functional response. We establish conditions for the existence and stability of all feasible equilibrium points of the non-spatial model, and later we prove the existence of Hopf and transcritical bifurcations in different parametric phase-planes analytically and numerically. The stability of the spatial system is studied, and we discuss the conditions for Turing instability. Selecting suitable control parameter from the Turing space, the existence conditions for stable patterns are derived using the amplitude equations. Results obtained from theoretical analysis of the amplitude equations are justified by numerical simulation results near the critical parameter value. Further, from numerical simulation, we illustrate the effect of diffusion of the dynamical system in the spatial domain by different pattern formations. Thus, our model clearly shows that the fear effect of prey and predator’s functional response makes an anti-predator behaviour including habitat complexity which helps the prey to survive in the spatio-temporal domain through diffusive process.

Spatiotemporal Dynamics Induced by Michaelis–Menten Type Prey Harvesting in a Diffusive Leslie–Gower Predator–Prey Model

This paper is devoted to study the spatiotemporal dynamics of a diffusive Leslie–Gower predator–prey model with Michaelis-Menten type harvesting in the prey population. The existence and stability of possible non-negative constant equilibria are investigated. By regarding [Formula: see text] as a bifurcation parameter, the Hopf bifurcation from the positive constant equilibrium solution is investigated. The necessary and sufficient conditions of Turing instability are explicitly obtained. We show that at the critical value of the bifurcation parameter [Formula: see text] a Turing bifurcation occurs (i.e. a pattern arises). The conditions for the stability of the pattern are also derived in detail. Moreover, the global steady state bifurcation from the positive constant equilibrium solution is investigated. In particular, the local steady state bifurcation from double zero eigenvalues is also obtained by the techniques of space decomposition and the implicit function theorem. Our results show that Michaelis–Menten type harvesting in our model plays a crucial role in the formation of spatiotemporal dynamics, which is a strong contrast to the case without harvesting.

Effects of nonthermal electrons and ion beams on ion-acoustic double layers in warm ion plasma

The effects of nonthermal electrons and ion beams on the ion acoustic double layers in warm ion plasma have been studied using the pseudopotential technique. Sagdeev potential of ion-acoustic wave in the plasma has been derived and the solution of ion acoustic double layers has been obtained. The critical value of nonthermal parameter of electrons for existence of double layers is obtained and discussed. The profiles of double layers in the plasma are drawn taking different values of density and temperature of ion beams, and the nonthermal parameter of electrons obeying the critical condition. It has been shown that both compressive and rarefactive double layers are excited in the plasma depending on the values of nonthermal electrons and ion beam parameters. The width of double layers is also graphically discussed. The results are new and may be useful in understanding the acceleration processes of charged particles in space plasma.

Mathematical and simulation methods for deriving extinction thresholds in spatial and stochastic models of interacting agents

Abstract In ecology, one of the most fundamental questions relates to the persistence of populations, or conversely to the probability of their extinction. Deriving extinction thresholds and characterizing other critical phenomena in spatial and stochastic models is highly challenging, with few mathematically rigorous results being available for discrete‐space models such as the contact process. For continuous‐space models of interacting agents, to our knowledge no analytical results are available concerning critical phenomena, even if continuous‐space models can arguably be considered to be more natural descriptions of many ecological systems than lattice‐based models. Here we present both mathematical and simulation‐based methods for deriving extinction thresholds and other critical phenomena in a broad class of agent‐based models called spatiotemporal point processes. The mathematical methods are based on a perturbation expansion around the so‐called mean‐field model, which is obtained at the limit of large‐scale interactions. The simulation methods are based on examining how the mean time to extinction scales with the domain size used in the simulation. By utilizing a constrained Gaussian process fitted to the simulated data, the critical parameter value can be identified by asking when the scaling between logarithms of the time to extinction and the domain size switches from sublinear to superlinear. As a case study, we derive the extinction threshold for the spatial and stochastic logistic model. The mathematical technique yields rigorous approximation of the extinction threshold at the limit of long‐ranged interactions. The asymptotic validity of the approximation is illustrated by comparing it to simulation experiments. In particular, we show that species persistence is facilitated by either short or long spatial scale of the competition kernel, whereas an intermediate scale makes the species vulnerable to extinction. Both the mathematical and simulation methods developed here are of very general nature, and thus we expect them to be valuable for predicting many kinds of critical phenomena in continuous‐space stochastic models of interacting agents, and thus to be of broad interest for research in theoretical ecology and evolutionary biology.

How much space of the spinal canal should be restored by hoisting the vertebrae–OPLL complex for sufficient decompression in anterior controllable antedisplacement and fusion? A multicenter clinical radiological study

Anterior controllable antedisplacement and fusion (ACAF) is a novel surgical technique for the treatment of ossification of the posterior longitudinal ligament (OPLL). Its prognostic factors for decompression have not been well studied. Additionally, no detailed radiological standard has been set for hoisting the vertebrae-OPLL complex (VOC) in ACAF. To identify the possible prognostic factors for decompression outcomes after ACAF for cervical OPLL, to determine the critical value of radiological parameters for predicting good outcomes, and to establish a radiological standard for hoisting the VOC in ACAF. This was a retrospective multicenter study. A total of 121 consecutive patients with OPLL who underwent ACAF at a point between January 2017 and June 2018 at any one of seven facilities and were monitored for at least 1 year afterward were enrolled in a multicenter study. Japanese Orthopedic Association (JOA) scores, recovery rate (RR) of neurologic function, and surgical complications were used to determine the effectiveness of ACAF. Patients were divided into two groups according to their RR for neurologic function. Patients with an RR of ≥50% and an RR of <50% were designated as having good and poor decompression outcomes, respectively. The relationship between various possible prognostic factors and decompression outcomes was assessed by univariate and multivariate analysis. The receiver operating characteristic curve was used to determine the optimal cutoff value of the radiological parameters for prediction of good decompression outcomes. Next, the patients were redivided into three groups according to the cutoff value of the selected radiological parameter (postoperative anteroposterior canal diameter [APD] ratio). Patients with postoperative APD ratios of ≤80.7%, 80.7%-100%, and ≥100% were defined as members of the incomplete, optimal, and excessive antedisplacement groups, respectively. Differences in decompression outcomes among the three groups were compared to verify the reliability of the postoperative APD ratio and assess the necessity of excessive antedisplacement. Multivariate logistic regression analysis showed that patients' age at surgery (odds ratio [OR]=1.18; 95% confidence interval [CI]=1.08-1.29; p<.01) and postoperative APD ratio (OR=0.83; 95% CI=0.77-0.90; p<.01) were independently associated with decompression outcomes. The optimal cutoff point of the postoperative APD ratio was calculated at 80.7%, with 86.2% sensitivity and 73.5% specificity. There were no significant differences in the postoperative JOA scores and RRs between the excessive antedisplacement group and optimal antedisplacement group (p>.05). However, a lower incidence of cerebrospinal fluid leakage and screw slippage was observed in the optimal antedisplacement group (p<.05). Patients' age at surgery and their postoperative APD ratio are the two prognostic factors of decompression outcomes after ACAF. The postoperative APD ratio is also the most accurate radiological parameter for predicting good outcomes. Our findings suggest that it is essential for neurologic recovery to restore the spinal canal to more than 80.7% of its original size (postoperative APD ratio >80.7%), and restoration to less than its original size (postoperative APD ratio <100%) will help reduce the incidence of surgical complications. This may serve as a valuable reference for establishment of a radiological standard for hoisting the VOC in ACAF.

Nonlinear transient analysis of rigid rotor mounted on externally pressurized double-layered porous gas journal bearings accounting velocity slip

The present work aims at estimating the journal center trajectories of a rigid rotor mounted on a hybrid, finite gas lubricated journal bearings with double-layered porous bushing using nonlinear transient analysis. To consider velocity slip in the film at the interface between film and porous region, Reynolds equation is modified using the Beavers–Joseph boundary condition. The governing equations of flow at clearance, porous regions are discretized using finite volume method. The variable values at cell-face centers are obtained using interpolation scheme of third order. Those discretized equations coupled with equations of rigid rotor motion are solved by third-order total variation diminishing Runge–Kutta scheme. Influence of velocity slip and design parameters on critical mass parameter values were explored. The observations are presented in the form of graphs that serves as a reference during the design of such bearings.

Test particle motion around a black hole in Einstein-Maxwell-scalar theory

In this paper, we explore the test particle motion around a black hole in Einstein-Maxwell-scalar (EMS) theory using three different black hole solutions within this theory. We have first analyzed the spacetime curvature structure of these solutions and shown the existence of two singularities and the first one is at the center $r=0$. In black hole spacetime, there are two regions divided by the critical value of the cosmological parameter $\lambda_0$. The photon sphere around the black hole in EMS theory has also been studied and found that it does not depend on cosmological parameter $\lambda$. We have analyzed the innermost stable circular orbits (ISCO) around the black hole and shown that for all solutions ISCO radius for neutral particle decreases with the increase of black hole charge. We have also studied the charged particle motion around the black hole where charged particle motion is considered in the presence of the gravitational field and the Coulomb potential. It is shown that ISCO radius for charged particles increases depending on the selected value of the coupling parameter which is in contradiction with observations of the inner edge of the accretion disks of the astrophysical black holes and can be used as a powerful tool to rule out the EMS theory from consideration for the gravitational field theory. It is also studied the fundamental frequencies governed by test particle orbiting around the black hole in EMS theory. Finally, as a test of black hole solution in EMS theory ISCO radii is compared with that in Kerr black hole and found that the spin parameter of Kerr can be mimic up to $a/M\simeq 0.936$.

On a mathematical model for a damped and driven double-well Bose–Einstein condensate

In this paper we consider a two-mode dynamical system as a model for a driven one-dimensional damped Bose–Einstein condensate in a double-well trapping potential. In the case of a constant external driving force the existence and stability of stationary solutions are discussed in relation to the values of the physical parameters. In the case of a time-dependent periodic external driving force the existence of limit cycles is proved, and the amplitude of these limit cycles exhibits a jump phenomenon for critical values of the physical parameters.