Time-dependent Parameters Research Articles

Tuning the separability in noncommutative space

With the help of the generalized Peres–Horodecki separability criterion (Simon’s condition) for a bipartite Gaussian state, we have studied the separability of the noncommutative (NC) space coordinate degrees of freedom. Non-symplectic nature of the transformation between the usual commutative space and NC space restricts the straightforward use of Simon’s condition in NCS. We have transformed the NCS system to an equivalent Hamiltonian in commutative space through the Bopp shift, which enables the utilization of the separability criterion. To make our study fairly general and to analyze the effect of parameters on the separability of bipartite state in NC-space, we have considered a bilinear Hamiltonian with time-dependent (TD) parameters, along with a TD external interaction, which is linear in field modes. The system is transformed (Sp(4,R)) into canonical form keeping the intrinsic symplectic structure intact. The solution of the TD-Schrödinger equation is obtained with the help of the Lewis–Riesenfeld invariant method (LRIM). Expectation values of the observables (thus the covariance matrix) are constructed from the states obtained from LRIM. It turns out that the existence of the NC parameters in the oscillator determines the separability of the states. In particular, for isotropic oscillators, the separability condition for the bipartite Gaussian states depends on specific values of NC parameters. Moreover, particular anisotropic parameter values for the oscillator may cease the separability. In other words, both the deformation parameters (θ, η) and parameter values of the oscillator (mass, frequency) are important characteristics for the separability of bipartite Gaussian states. Thus tuning the parameter values, one can destroy or recreate the separability of states. With the help of a toy model, we have demonstrated how the tuning of a TD-NC space parameter affects the separability.

Scattering from time-modulated subwavelength resonators

We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We consider the one-dimensional setting. In order to understand the energy of the system, we prove a novel higher-order discrete, capacitance matrix approximation of the subwavelength resonant quasi-frequencies. Further, we perform numerical experiments to support and illustrate our analytical results and show how periodically time-dependent material parameters affect the scattered wave field.

Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters

In this paper, we consider the time-fractional Black–Scholes model with deterministic, time-varying coefficients. These time parametric constituents produce a model with greater flexibility that may capture empirical results from financial markets and their time-series datasets. We make use of transformations to reduce the underlying model to the classical heat transfer equation. We show that this transformation procedure is possible for a specific risk-free interest rate and volatility of stock function. Furthermore, we reverse these transformations and apply one-dimensional optimal subalgebras of the infinitesimal symmetry generators to establish invariant solutions.

Experimental investigation of a Y-shaped engine inlet at subsonic flow conditions

Abstract In this paper, the results of an experimental investigation for a Y-shaped engine inlet are presented. The experiment is performed at subsonic flow conditions. The main focus is given to time-dependent total pressures measured at the aerodynamic interface plane. Distinctive frequencies carrying high energy contents of the fluctuating total pressures are given and the relation between time-dependent and time-average performance parameters is presented. The cross-correlation coefficients of the high frequency probe readings distributed through the aerodynamic interface plane are also investigated.

Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations

This paper aims to develop a direct approach, namely, the Cauchy matrix approach, to non-isospectral integrable systems. In the Cauchy matrix approach, the Sylvester equation plays a central role, which defines a dressed Cauchy matrix to provide τ functions for the investigated equations. In this paper, using the Cauchy matrix approach, we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions. These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem. Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction. These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.

The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity

In this article, we investigate the temporal evolution of arbitrary, simple, closed two-dimensional (2D) and three-dimensional (3D) interfaces under motion driven by mean curvature up to a singularity. To facilitate this investigation, we propose a novel Allen–Cahn (AC) model with a time-dependent interfacial thickness parameter. The original AC equation was developed to model the phase separation of a binary mixture. It is well known that a level set or interface of the solution of the AC equation obeys the dynamics of motion by curvature as the interfacial thickness parameter approaches zero. Generally, it is difficult to find a closed-form analytic solution of the AC equation with any initial condition. Therefore, we need to estimate the solution of the AC equation through computational approaches such as finite difference method (FDM), finite element method (FEM), Fourier-spectral method (FSM), and finite volume method (FVM). Any simple, closed curves and convex surfaces eventually shrink to a point due to motion by mean curvature. Therefore, it becomes necessary to use adaptive mesh techniques to resolve this small size problem. However, even though we use adaptive mesh techniques, we still confront the relatively thick interfacial transition layer when the curves or interfaces become very small. To avoid this problem, we can start with a very small mesh size for a small value of the interfacial parameter, which results in an extremely high computational cost even when using adaptive mesh techniques. To resolve these issues, we present the AC equation with a time-dependent interfacial parameter and develop an adaptive mesh refinement system. To show the superior performance of the proposed mathematical equation and its computational algorithm, we present various numerical experiments and investigate the motion by mean curvature up to the singularity of curves in 2D space and interfaces in 3D space.

Threshold and Upper Bound for The Controller’s Designed Parameter of Fokker Planck Kolmogorov Probability Density Function with Applications to Cryptocurrency

This work is the first in literature to tackle the difficult open problem of determining the upper bound and threshold theorem for the TDCDP (time-dependent controller parameter) of the (Fokker Planck Kolmogorov) probability density function. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to information theory, graph theory, data science, finance, economics, and beyond. So, this by default adds more taste and credibility to this study. This leads by nature to introducing a different flavor to this ground-breaking research by highlighting the impact of Fokker Planck Kolmogorov(FPK) to revolutionize crypocurrency,which have received its name because it uses encryption to verify transactions, a new debatable digital payment system that doesn't rely on banks to verify transactions. It’s a peer-to-peer system that can enable anyone anywhere to send and receive payments. The paper ends with closing remarks combined with some challenging open problems and the next phase of research

The thixotropic characteristics of rheological parameters of waste stone-tailings cemented paste backfill and the time effect of pipeline resistance

The cemented paste backfill (CPB) involves the optimal combination of one or more solid materials with water to prepare a paste-like slurry with certain stability, fluidity, and plasticity. The paste flows as a piston flow under external force (pumping pressure) or gravity through pipelines into the underground goaf to complete backfilling operations. In order to improve the performance of the CPB, coarse aggregate is added to the CPB to form a coarse aggregate cemented paste backfill (C-CPB). The C-CPB belonged to non-Newtonian fluids and exhibited thixotropic behavior as its rheological parameters determined its flow characteristics. During the initial stage of pipeline transportation, the rheological parameters of the paste material were influenced by its thixotropic behavior and exhibited a certain degree of time dependence. The present study employed the stress relaxation method for thixotropy test to ascertain the rheological parameters of the C-CPB with respect to shear time. The results indicated that the yield stress decreased with increasing shear time with a negative exponential growth trend. A mathematical function describing the variation of yield stress with time for the paste material was established, and an estimation method for thixotropic equilibrium time of the yield stress was proposed. A Gaussian distribution function describing the variation of plastic viscosity with shear time was developed, and the thixotropic stabilization time of plastic viscosity was estimated. On this basis, a pipeline transportation resistance model considering the time-dependent rheological parameters of the C-CPB was established. Subsequently, a formula for calculating the boundary layer thickness during the initial stage of pipeline transportation was derived. The establishment of the model enables a better understanding of the resistance characteristics of the paste during the initial stage of pipeline transportation, as well as the process and patterns of boundary layer formation, which is of great significance.

String Viscous Fluid Cosmological Model in the Framework of Sen-Dunn Theory of Gravitation

Objective: To present a new solution to the field equations for higher-dimensional Bianchi type-III string viscous fluid cosmological model in the context of the Sen-Dunn theory of gravity. Methods: To obtain definite solution of the field equations, we consider a power law relation between the scale factor and scalar field, and we take into account two distinct scale factors, and , in which , are positive constants. This produces a time-dependent deceleration parameter. We analyse the model with constant bulk viscosity constant to explain the current accelerated expansion of the universe. Findings: Spatial volume of the model increases with cosmic time, which shows that universe is spatially expanding. Also, the model possesses a point-type singularity. It is noted that these models depict the universe's accelerated expansion. Novelty: We obtained new solution to the field equations for higher dimensional Bianchi type-III generated by means of a cloud of strings with bulk viscous fluid in Sen-Dunn theory by using quadratic form. Keywords: Bianchi type-III, Cosmic string, Bulk viscosity, Sen-Dunn Theory

A simulation-based performance evaluation model for decision support on drone location and delivery scheduling

PurposeThis paper aims to propose a simulation-based performance evaluation model for the drone-based delivery of aid items to disaster-affected areas. The objective of the model is to perform analytical studies, evaluate the performance of drone delivery systems for humanitarian logistics and can support the decision-making on the operational design of the system – on where to locate drone take-off points and on assignment and scheduling of delivery tasks to drones.Design/methodology/approachThis simulation model captures the dynamics and variabilities of the drone-based delivery system, including demand rates, location of demand points, time-dependent parameters and possible failures of drones’ operations. An optimization model integrated with the simulation system can update the optimality of drones’ schedules and delivery assignments.FindingsAn extensive set of experiments was performed to evaluate alternative strategies to demonstrate the effectiveness for the proposed optimization/simulation system. In the first set of experiments, the authors use the simulation-based evaluation tool for a case study for Central Florida. The goal of this set of experiments is to show how the proposed system can be used for decision-making and decision-support. The second set of experiments presents a series of numerical studies for a set of randomly generated instances.Originality/valueThe goal is to develop a simulation system that can allow one to evaluate performance of drone-based delivery systems, accounting for the uncertainties through simulations of real-life drone delivery flights. The proposed simulation model captures the variations in different system parameters, including interval of updating the system after receiving new information, demand parameters: the demand rate and their spatial distribution (i.e. their locations), service time parameters: travel times, setup and loading times, payload drop-off times and repair times and drone energy level: battery’s energy is impacted and requires battery change/recharging while flying.

Lax-type pairs in the theory of bivariate orthogonal polynomials

Sequences of bivariate orthogonal polynomials written as vector polynomials of increasing size satisfy a couple of three term relations with matrix coefficients. In this work, introducing a time-dependent parameter, we analyze a Lax-type pair system for the coefficients of the three term relations. We also deduce several characterizations relating the Lax-type pair, the shape of the weight, Stieltjes function, moments, a differential equation for the weight, and the bidimensional Toda-type systems.

Understanding route choice behaviors' impact on traffic throughput in a dynamic transportation network

Route planning is one of the most important and attractive topics in complex networks, geographical information science (GIS) and logistics. Travelers' route choice behaviors may affect the actual throughput of a transportation network. This study aims to analyze the influence of travelers' route choice behaviors on network traffic throughput. Two kinds of route choice behaviors, called continuous optimization behavior and hybrid optimization behavior, are defined. Based on this, two traffic scenarios are constructed to describe these behaviors and examine their effect on the network's actual traffic throughput. The application of our approach to urban street networks, Barabási-Albert scale-free network and Erdös-Rényi random network demonstrates that if all travelers choose optimal paths constraint with time from the start, network throughput is insensitive to the continuous optimization behavior but depends on the relationship between time and distance in the routing algorithm. Besides, network throughput is sensitive to the hybrid optimization behavior that the more travelers choose time-dependent optimal paths, the higher the throughput. The results indicate that the choice of initial paths and the time dependence of routing algorithms can directly affect the network's actual throughput which is enhanced >50 % when the time dependence parameter is >0.2 or the proportion of time-dependent shortest paths in initial paths is >0.2. Our findings provide supports for exploring efficient routing algorithms to enhance the throughput of urban street networks and other kinds of networks.

Endogenous thrombin potential and time-dependent thrombin generation parameters are independent risk factors for mortality in the general population

BackgroundThrombin generation (TG) is used as a global test of coagulation and is an indicator of thrombosis and bleeding risk. Until now, data on the association of TG and mortality are inconclusive. ObjectivesWe investigated the association between TG and mortality in the prospective Moli-sani cohort (n = 21 920). MethodsTG was measured using calibrated automated thrombinography using PPP-Reagent Low. Lag time (LT), endogenous thrombin potential (ETP), peak height, time-to-peak (TTP), and velocity index were quantified. The association of TG and mortality was studied by Cox regression and adjusted for sex, age, body mass index, smoking, contraceptives, and medical history (cardiovascular diseases, hypertension, hypercholesterolemia, diabetes, and cancer). ResultsLT and TTP were 4.1 ± 1.0 minutes and 6.6 ± 1.5 minutes, on average. The peak height was 364 ± 88 nM, velocity index was 163 ± 63 nM/min, and ETP was 1721 ± 411 nM·min. ETP was negatively associated with all-cause mortality (hazard ratio [HR], 0.86; 95% CI, 0.81-0.92; P < .001). Subjects in the lowest quintile of the ETP (ETPQ1) had a 1.3-fold higher mortality rate. Additionally, a high TTP/LT ratio was negatively associated with mortality (HR, 0.71; 95% CI, 0.57-0.89; P = .003). Individuals in quintile 1 of the TTP/LT ratio had a 1.4-fold higher mortality rate compared with the remainder of the cohort. Subjects that were both in ETPQ1 and TTP/LTQ1 had a 1.8-fold higher mortality rate, regardless of whether they reported history of cardiovascular disease at baseline (HR, 1.61 [CI: 1.07-2.42]) or not (HR, 1.89 [CI: 1.51-2.36]). ConclusionLow ETP and TTP/LT ratios are independent risk factors for all-cause mortality in the general population.

Characteristics and standards of severe sagittal imbalance in adult patients with spinal deformities: a retrospective analysis

ObjectiveTo analyze the characteristics of “severe” dynamic sagittal imbalance (DSI) in patients with adult spinal deformity (ASD) and establish criteria for them.MethodsWe retrospectively analyzed 102 patients with ASD presenting four cardinal signs of lumbar degenerative kyphosis. All patients underwent deformity corrective surgery and were divided into three groups according to the diagnostic criteria based on the Oswestry disability index and dynamic features (△Timewalk: time until C7 sagittal vertical axis [C7SVA] reaches ≥ 20 cm after the start of walking) of sagittal imbalance. The paravertebral back muscles were analyzed and compared using T2-weighted axial imaging. We performed a statistically time-dependent spinopelvic sagittal parameter analysis of full standing lateral lumbar radiographs. Lumbar flexibility was analyzed using dynamic lateral lumbar radiography.ResultsThe patients were classified into the mild (△Timewalk ≥ 180 s, 35 patients), moderate (180 s > △Timewalk ≥ 30 s, 38 patients), and severe (△Timewalk < 30 s, 29 patients) groups. The back muscles in the severe group exhibited a significantly higher signal intensity (533.4 ± 237.5, p < 0.05) and larger area of fat infiltration (35.2 ± 5.4, p < 0.05) than those in the mild (223.8 ± 67.6/22.9 ± 11.9) and moderate groups (294.4 ± 214.7/21.6 ± 10.6). The analysis of lumbar flexibility revealed significantly lower values in the severe group (5.8° ± 2.5°, p < 0.05) than in the mild and moderate groups (14.2° ± 12.4° and 11.4° ± 8.7°, respectively). The severe group had significantly lower lumbar lordosis (LL, 25.1° ± 22.7°, p < 0.05) and Pelvic incidence-LL mismatch (PI-LL, 81.5° ± 26.6°, p < 0.001) than those of the mild (8.2° ± 16.3°/58.7° ± 18.8°) and moderate (14.3° ± 28.6°/66.8° ± 13.4°) groups. On receiver operating characteristic curve analysis, PI-LL was statistically significant, with an area under the curve of 0.810 (95% confidence interval) when the baseline was set at 75.3°. The severe group had more postoperative complications than the other groups.ConclusionsOur results suggest the following criteria for severe DSI: C7SVA > 20 cm within 30 s of walking or standing, a rigid lumbar curve < 10° on dynamic lateral radiographs, and a PI-LL mismatch > 75.3°.Level of evidence3.

Stochastic transmission in epidemiological models.

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

Analytical Studies of Fluid Conveying Pipes on Viscoelastic Foundation Using Differential Transforms Method

This study presents an analytical investigation of the vibration of fluid-conveying pipes on viscoelastic foundations using the differential transform method. The effects of a new time dependent viscosity parameter in the modified Winkler viscoelastic foundation is studied and analyzed. The governing equation is a fourth-order partial differential equation with pinned-pinned boundary conditions, which required a special analytical method for solution. The differential transform method was applied to obtain the solution of the governing partial differential equation for the fluid-conveying pipes on viscoelastic foundations. The time-dependent viscosity parameter in the modified Winkler viscoelastic model was implemented and simulated to determine the behavior of the viscoelastic foundation. The obtained analytical solution was validated with Runge-Kutta order four numerical method. The effects of foundation stiffness , coefficient of foundation damping and the frequency mass ratio on the governing model equation were investigated. In addition, the bending and deflection of the pipe on a viscoelastic foundation are compared with those on an elastic foundation. The analytical and the numerical solutions are in good agreement. From the study, it is observed that an increase in the foundation stiffness results in increase in the pipe inherent frequencies. Furthermore, the vibration of the pipe on a viscoelastic foundation shows better control and reduction compared with its vibration on an elastic foundation.

Research of nonstationary dynamic models of the organizational and technological process of railway transport technical vehicles repair

The problems of analytical and computer research of dynamic models of repair and operation of technical vehicles used in railway transport are among the urgent problems related to ensuring safety and stability of traffic, with the development of digital twins and the improvement of monitoring and diagnostic systems. The analysis of models described by various types of multidimensional nonlinear differential equations requires the use of modern methods of dynamical systems theory, numerical optimization and computer algebra. The purpose of the article is to conduct a qualitative and numerical analysis of mathematical models of organizational and technological processes (OTP) in railway transport, as well as the synthesis of new controlled OTP models. Nonstationary generalizations of a two-dimensional dynamic model describing the repair process of railway transport equipment are proposed. Various cases of using constant and time-dependent parameters are considered. The case of linear and exponential dependences of parameters on time is studied. For the studied models, trajectories are obtained taking into account the variation of constant parameters and taking into account the choice of parametric dependencies, a comparative analysis of the results is presented. The formulation of the problem of optimal control of the number of repaired and repaired railway wagons is proposed. Promising methods for solving this problem using numerical optimization methods, including those inspired by nature, are described. The results can be used in the tasks of constructing and analyzing mathematical models of dynamic systems, in the tasks of numerical modeling of transport systems and technological processes, in the tasks of optimizing the number of vehicles and improving the transportation process, as well as in the tasks of creating digital counterparts in the transport industry.

Time behavior of hubble parameter by torsion

Consequences of the consistent exact solution of Einstein–Cartan equation on the time dependence of Hubble parameter are discussed. The torsion leads to a space and time-dependent expansion parameter which results into nontrivial windows of Hubble parameter between diverging behavior. Only one window shows a period of decreasing followed by increasing time dependence. Provided a known cosmological constant and the present values of Hubble and deceleration parameter this changing time can be given in the past as well as the ending time of the windows or universe. The comparison with the present experimental data allows to determine all parameters of the model. Large-scale spatial periodic structures appear. From the metric with torsion outside matter, it is seen that torsion can feign dark matter.

Quality of Mixedness Using Information Entropy in a Counter-Current Three-Phase Bubble Column

Knowledge of mixing phenomena is of great value in the mineral and other chemical and biochemical industries. This work aims to analyze the quality of mixedness (QM), the intrinsic mass transfer (MT) number, and the MT efficiency based on information entropy theory in the counter-current microstructured slurry bubble column. A thorough analysis is conducted to assess the effects of particle loading, gas and slurry velocity, and axial variation on the QM. The range of gas velocity, slurry velocity, particle size, and particle loading was 0.011–0.075 m/s, 0.018–0.058 m/s, 242.72–408.31 μm, and 15.54–88.94 kg/m3, respectively. QM is a time-dependent parameter, and the concept of contact time has been used for scale-up purposes. The maximum QM was achieved at dimensionless times of 0.40 × 10−3, 0.15 × 10−3, and 0.85 × 10−3 for the maximum superficial gas velocity, particle loading, and axial height, respectively. The gas velocity positively influenced both the intrinsic MT number and its efficiency. In contrast, the slurry velocity and particle loading had a negative effect. The present theoretical analysis will pave the path for industrial process intensification in counter-current flow systems.

A weakly turbulent solution to the cubic nonlinear harmonic oscillator on ℝ2 perturbed by a real smooth potential decaying to zero at infinity

We build a smooth real potential V(t, x) on ( t 0 , + ∞ ) × R 2 decaying to zero as t → ∞ and a smooth solution to the associated perturbed cubic noninear harmonic oscillator whose Sobolev norms blow up logarithmically as t → ∞ . Adapting the method of Faou and Raphael for the linear case, we modulate the Solitons associated to the nonlinear harmonic oscillator by time-dependent parameters solving a quasi-Hamiltonian dynamical system whose action grows up logarithmically, thus yielding logarithmic growth for the Sobolev norm of the solution.