Steady Distribution Research Articles

Statistical laws of a one-dimensional model of turbulent flows subject to an external random force

This paper provides mathematical and numerical analysis of a one-dimensional model of turbulent flow generating the anomalous cascade of the inviscid conserved quantity. The model is based on the generalized Constantin–Lax–Majda–DeGregorio (gCLMG) equation with viscous dissipation under a large-scale forcing. Suppose that the forcing function and the initial data are random variables defined on a certain probability space. Then, the equation is regarded as a random partial differential equation. We prove the global existence of a unique solution to the gCLMG equation, from which a stochastic process is defined. In addition, by approximating the solutions numerically by Galerkin approximation of random variables with generalized polynomial chaos, we confirm the existence of a steady distribution. We find that the steady distribution reproduces qualitatively the same cascades of the energy and the enstrophy spectra as those of a turbulent flow generated by randomly moving pulse (Matsumoto and Sakajo 2016 Phys. Rev. E 93 053101). We also investigate the structure functions, showing intermittency.

Pengaruh Personal Selling dan Display terhadap Intensi Pembelian Produk Distro di Kediri

This study aimed to analyze the influence of personal selling and display of the product purchase intentions in steady distributions store. The research data was obtained from questionnaires (primary) of the product in store steady distributions. The findings showed that personal selling and display simultaneously (simultaneous) positive effect on purchase intentions, partial (t test) is obtained that display variable and dominant positive effect on purchase intentions. Of 29.8% variable purchase intention can be explained by the independent variable while the remaining 70.2% is explained by other variables outside of this study.

Investigation of flow distribution in energy intensive aluminium production reduction cells: An exploratory study

The process of making aluminium often involves electrolytic cells, also known as reduction cells. The reduction cell exhaust manifolds must achieve a steady distribution of exhaust from each cell in the network. This will prevent fugitive pollutants, which are harmful to both human and environmental health. While ducts are adjusted to achieve appropriate flow rates, they become asymmetrical over time. A few case studies available in the literature that discuss the flow distribution in an electrolytic cell, and almost none provide insight into the operational flow distribution of reduction cells in service. As part of this study, the operating flow distribution in service reduction cells is examined, determined which factors contribute to poor gas patterns produced by reduction line cells and analysed the flow conditions that result in sediment deposition within the ducting that connects the reduction cells to the superstructure, which is the novelty of this case study. Various instruments were used to record the temperature and pressure of a smelting facility. Flow information for each cell was collected using Pitot traverses. Infrared thermography of the ducts was used to locate temperature anomalies and possible areas of particle build-up. These tests indicated a number of probable contributing causes that have contributed to the inadequate airflow pattern from each reduction cell.

Generalized User Equilibrium for Coordination of Coupled Power-Transportation Network

The increasing proliferation of electric vehicles (EVs) tightens the interaction between urban power distribution network (PDN) and transportation network (TN). This paper proposes the generalized user equilibrium (GUE) method for the coupled power-transportation network (CPTN) operation. First, the GUE concept is proposed to describe the steady traffic flow distribution as an extension of user equilibrium (UE), which could no longer exist due to the constraints placed by PDN operation on TN. Second, the GUE-based coordination model is established for CPTN with PDN generation scheduled and TN traffic assigned simultaneously. Finally, a decomposition method is developed to solve the model efficiently, which is converted into a master problem and a series of feasible/optimal path generation subproblems for individual origin-destination (O-D) pairs. The case studies on a real-world network have verified the effectiveness of the proposed model and method. The results demonstrate the necessity of GUE and its potential in improving the CPTN operation.

Analogy between streamers in sinking spheroids, gyrotactic plumes and chemotactic collapse

In a dilute suspension where sinking spheroids or motile gyrotactic micro-organisms are modelled as orientable and negatively buoyant particles, we have found analytical solutions to their steady distributions under any arbitrary continuous vertical shear flow. The two-way coupling between their distribution and the vertical flow is nonlinear, enabling the uniform base state to bifurcate into a structure reminiscent of the streamers in settling spheroid suspensions and gyrotactic plumes. This bifurcation depends on a single parameter that is proportional to the average number of particles on a horizontal cross-section. In a three-dimensional axisymmetric system, the plume structure blows up when the parameter is above a threshold. We discuss how this singularity is analogous to the chemotactic collapse of a Keller–Segel model, and the significance that this analogy entails.

Time evolution of electron distributions to bimodal steady states for electrons dilutely dispersed in theinert gases Ar, Kr, and Xe with deep Ramsauer Townsend minima in themomentum transfer cross section

The current paper considers the thermalization of an ensemble of electrons under the influence of an external electric field and dilutely dispersed in one of the inert gas moderators, Argon, Krypton or Xenon for which the electron momentum transfer cross sections have deep Ramsauer-Townsend minima. As a consequence, the steady state electron distribution functions are bimodal over a small range of external electric field strengths. The current work is directed towards the time evolution of the electron distribution function determined from the numerical solution of the Fokker-Planck equation. The kinetic theory of electrons dilutely dispersed in a heat bath of atoms at temperature T b has a very long history. The solution of the Fokker-Planck equation can be expressed as a sum of exponentials of the form where λ n are the eigenvalues of the Fokker-Planck operator. Alternatively, a finite difference algorithm is used to solve the time dependent Fokker-Planck equation to give the time dependent electron energy distribution function. We demonstrate the evolution of the initial Maxwellian into a nonequilibrium bimodal distribution which cannot be rationalized with either the Gibbs-Boltzmann entropy or the Tsallis nonextensive entropy. Instead, the time dependent approach of an initial Maxwellian to the bimodal distribution is described in terms of the Kullback-Leibler entropy. We also demonstrate the inapplicability of the Boltzmann entropy nor the Tsallis entropy for a model system with a power law momentum transfer cross section of the form, σ(x) = σ 0/x p , where is the reduced speed. This model with p = 2 is also employed to demonstrate a steady-state Kappa distribution which features prominently in space physics and other fields. For p > 2, we show distribution functions that increase without bound analogous to runaway electrons. The steady nonequilibrium distributions are interpreted as solutions of a Pearson ordinary differential equation.

Asymptotic solutions to nonlinear Hawkes processes: A systematic classification of the steady-state solutions

Hawkes point processes are first-order non-Markovian stochastic models of intermittent bursty dynamics with applications to physical, seismic, epidemic, biological, financial, and social systems. While accounting for positive feedback loops that may lead to critical phenomena in complex systems, the standard linear Hawkes process only describes excitative phenomena. To describe the co-existence of excitatory and inhibitory effects (or negative feedbacks), extensions involving nonlinear dependences of the intensity as a function of past activity are needed. However, such nonlinear Hawkes processes have been found hitherto to be analytically intractable due to the interplay between their non-Markovian and nonlinear characteristics, with no analytical solutions available. Here, we present various exact and robust asymptotic solutions to nonlinear Hawkes processes using the field master equation approach. We report explicit power law formulas for the steady state intensity distributions $P_{\mathrm{ss}}(\lambda)\propto \lambda^{-1-a}$, where the tail exponent $a$ is expressed analytically as a function of parameters of the nonlinear Hawkes models. We present three robust interesting characteristics of the nonlinear Hawkes process: (i) for one-sided positive marks (i.e., in the absence of inhibitory effects), the nonlinear Hawkes process can exhibit any power law relation either as intermediate asymptotics ($a\leq 0$) or as true asymptotics ($a>0$) by appropriate model selection; (ii) for distribution of marks with zero mean (i.e., for balanced excitatory and inhibitory effects), the Zipf law ($a\approx 1$) is universally observed for a wide class of nonlinear Hawkes processes with fast-accelerating intensity map; (iii) for marks with a negative mean, the asymptotic power law tail becomes lighter with an exponent increasing above 1 ($a>1$) as the mean mark becomes more negative.

Study of thermal variation in a longitudinal exponential porous fin wetted with [formula omitted]/ hexanol hybrid nanofluid using hybrid residual power series method

This study aims to inspect the steady state thermal distribution and heat transfer within a longitudinal porous fin of exponential profile wetted with hybrid nanoliquid. The aggregate influence of conduction, radiation, and convection causes heat transfer in the fin. The Darcy model and the Fourier law of heat conduction are used for modeling the governing ordinary differential equation (ODE) that represents the corresponding fin problem. Through the use of non-dimensional terms, the formulated equation is further simplified into a dimensionless equation along with suitable boundary condition. The arising nonlinear dimensionless equation is solved analytically using the improved residual power series method with the Pade approximant (Hybrid residual power series method/HRPSM). The consequences of various dynamic thermal parameters on thermal behavior are explored using graphical portrayal. As per the observations of this investigation, the surface wet condition by hybrid nonliquid and porous nature of the exponential fin will have a significant effect on the temperature distribution. More specifically, as the values of these corresponding parameters increase, the rate of heat transfer intensifies. Finally, the obtained HRPSM results are compared with previous investigations, and a high level of consistency is observed.

Dynamics and length distributions of microtubules with a multistep catastrophe mechanism

Regarding the experimental observation that microtubule (MT) catastrophe can be described as a multistep process, we extend the Dogterom–Leibler model for dynamic instability in order to discuss the effect that such a multistep catastrophe mechanism has on the distribution of MT lengths in the two regimes of bounded and unbounded growth. We show that in the former case, the steady state length distribution is non-exponential and has a lighter tail if multiple steps are required to undergo a catastrophe. If rescue events are possible, we detect a maximum in the distribution, i.e. the MT has a most probable length greater than zero. In the regime of unbounded growth, the length distribution converges to a Gaussian distribution whose variance decreases with the number of catastrophe steps. We extend our work by applying the multistep catastrophe model to MTs that grow against an opposing force and to MTs that are confined between two rigid walls. We determine critical forces below which the MT is in the bounded regime, and show that the multistep characteristics of the length distribution are largely lost if the growth of an MT in the unbounded regime is restricted by a rigid wall. All results are verified by stochastic simulations.

On opto-thermally excited parametric oscillations of microbeam resonators. I

The present article is the first part of the work devoted to investigation of the nonlinear dynamics of parametrically excited flexural vibrations of a clamped-clamped microbeam - the basic sensitive element of a promising class of microsensors of various physical quantities - under laser thermooptical action in the form of periodically generated pulses acting on a certain part of the surface of the beam element. An analytical solution of the heat transfer problem is found for the steady harmonic distribution of temperature in the volume of the resonator. The static and dynamic components of temperature-induced axial force and bending moment are determined. Using the Galerkin method, the discretization of nonlinear coupled partial differential equations describing the longitudinal-flexural oscillations of the resonator is performed. Using the asymptotic method of multiple time-scales, an approximate analytical solution is obtained for the nonlinear dynamics problem under the conditions of primary parametric resonance.

Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation

Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation

Stochastic localization and non-Boltzmann distribution

We investigate the microscopical root and macroscopical representation of the stochastic localization, which is a nonergodic motion in oppositive to the other limit of ballistic diffusion. In order to produce such anomalous kinetics, we consider that a tagged particle is linearly coupled to a series connection bath or the terminal of a coupled-oscillator-chain. By means of generalized Langevin equation formalism, we obtain the coordinate autocorrelation function. The localization emerged of a particle at finite temperature, is due to the spectrum of driving noise diverging at zero frequency. Consequently, the steady distribution of system depends on its initial coordinate preparation.

Applications of distributed fiber Bragg gratings to the measurements of in-tube fluid temperature distribution

The temperature distribution information of the two-phase fluid inside a tube can effectively reflect the heat transfer of the fluid, which is the key information in the study of the heat transfer of flowing fluid in a tube. This article aims to develop a method for measuring the temperature distribution of fluid inside a tube based on distributed fiber Bragg gratings (DFBGs). It is more convenient than traditional measurement methods using thermocouples that are impossible to be installed to the inner tube of a double tube heat exchanger. By using a stainless steel seamless tube, ϕ1.0 × 0.2 mm in size, and a hose to seal and protect the optical fiber with Bragg grating sensors inside, we successfully shielding the stress effects from the thermal effects, and also enhance the durability of the fiber. Since the seal leads to extra thermal resistance to the DFBGs, obtaining the response performance of the sealed DFBGs to a temperature change is essential for reliable applications. The performance characterization shows that the temperature measurement repeatability of the sealed DFBGs is within 0.2 °C for a period up to 35 months. The time constants of the DFBGs are not longer than 0.25 s, capable of measuring the temperature oscillations with frequency less than 2 Hz. Comparison with commercial thermocouples supports the feasibility and the reliability that the sealed DFBGs can be used as temperature sensors. To obtain the equivalent thermal conductivity between the tube that sealed the fiber and the fiber, κ¯air, the response to a temperature jump was also calculated based on a simplified model, which can comprehensively reflect the heat transfer of the air inside the sealed tube and provide the reference for design optimization of a sealed FBG for dynamic measurements. Finally, the capillary tube with sealed DFBGs was placed in the condenser tube of a two-phase circulation loop to exhibit the feasibility of the steady and dynamic temperature distribution measurements of the fluid inside a tube.

Effective dust growth in laminar circumplanetary discs with magnetic wind-driven accretion

ABSTRACT It has been considered that large satellites around gas planets form in situ circumplanetary discs (CPDs). However, dust particles supplied into CPDs drift toward the central planets before they grow into satellitesimals, building blocks of the satellites. We investigate the dust growth in laminar CPDs with magnetic wind-driven accretion. In such laminar discs, dust particles can settle on to the mid-plane and grow large by mutual collision more efficient than in classical turbulent CPDs. First, we carry out 3D local MHD simulations of a CPD including all the non-ideal MHD effects (Ohmic resistivity, Hall effect, and ambipolar diffusion). We investigate if the disc accretion can be governed by magnetic wind-driven accretion and how laminar the disc can be, in a situation where the magnetic disc wind can be launched from the disc. Secondly, we model 1D steady CPDs consistent with the results of the MHD simulations and calculate the steady radial distributions of the dust profiles in the modelled discs, taking account of the collisional growth, radial drift, fragmentation, and vertical stirring by the Kelvin–Helmholtz instability. We show that satellitesimals can form in such CPDs if the dust-to-gas mass ratio of the inflow to the discs is larger than 0.02, which is 50 times smaller than the critical value in turbulent CPDs. This condition can be satisfied when enough amount of dust piles up at the gas pressure bump created by the planets. This result shows that satellitesimals would form in laminar CPDs with magnetic wind-driven accretion.

Stochastic behaviors of an improved Gompertz tumor growth model with coupled two types noise

In this work, an improved Gompertz tumor growth model has been introduced. The expressions of steady probability distributions (SPD) of stochastic Gompertz tumor growth models are studied by using the technique of Fokker-Planck equation (FPE), and their dynamic behaviors are also further investigated. Moreover, the expressions for mean, variance, skewness, as well as the mean first-passage time (MFPT) also have been derived. And the influence of noise intensity, correlation coefficient, and noise correlation time of SPD are further analyzed. It is worthy noting that the colored noise intensity has an important impact on SPD. Furthermore, adjusting birth and death parameters also significantly impact SPD, MFPT, mean, variance as well as skewness.

Migration of non-Brownian particles localized inside sheared droplets

• Particles inside sheared droplets migrate along the vorticity direction. • The migration direction depends on the viscosity ratio. • The migration kinetics depends on Ca, interfacial tension and particle concentration. • VOF simulations provide velocity and shear rate distribution in a particle-free droplet. • Shear-induced migration plays a major role. The migration of non-Brownian particles inside a droplet subjected to shear flow is investigated. The viscosity ratio, particle concentration, particle to droplet size ratio and capillary number are systematically varied. It was observed that particles migrate in the vorticity direction either towards or away from the equatorial plane. The main factor determining the migration direction is the viscosity ratio. The particle concentration and applied capillary number have no influence on the equilibrium distribution and only affect the time necessary to reach this distribution. In order to identify the flow profile, both velocity and shear rate magnitudes to which the particles inside the droplet are subjected, are numerically simulated using the Volume-of-Fluid method in a particle-free droplet/matrix system. The numerical predictions of the flow are used to evaluate the presence of possible driving mechanisms for cross-streamline particle motion, such as particle inertia and shear rate gradients. Depending on the conditions, the simulations reveal significant differences in the streamline profiles and shear rate gradients within the droplet. The observed steady state particle distributions can partially be explained by shear-induced migration towards zones of low shear rates and/or low streamline curvature. However, in complex flows, such as inside a deformed droplet, different migration mechanisms can occur simultaneously. Hence, confinement inside the droplet and potential secondary flows may also play a role.

Thermal-structural reduced order models for unsteady/dynamic response of heated structures in large deformations

This paper focuses on applications of recently developed thermoelastic reduced order models (ROMs) for the geometrically nonlinear response and temperature of heated structures. In these ROMs, both displacements and temperature fields with respect to the undeformed, unheated configuration are expressed in a reduced order modeling format, i.e., as modal-type expansions of the spatial and temporal variables with constant basis functions. Accordingly, the time varying generalized coordinates of the response and temperature expansions satisfy a generic set of coupled nonlinear differential equations derived from finite deformations thermoelasticity using a Galerkin approach. Finally, the coefficients of these governing equations, which characterize the structure considered and its loading conditions, are determined from structural and thermal finite element models non intrusively so that commercial finite element software can be used. This approach is considered here for the prediction of the displacements and stress fields in the presence of unsteady temperature distributions to enrich previous investigations limited to steady temperature distributions. Specifically considered here are: (i) a panel undergoing rapid heating and (ii) an oscillating flux on a panel. These problems not only demonstrate the extension of the thermal-structural reduced order framework to unsteady problems but also show the importance of the selection of the basis functions. It is also noted that the temperature dependence of the linear stiffness coefficients on temperature can induce in the unsteady situation the existence of a parametric-type excitation of the structure. This behavior is studied in the oscillating flux example and a strong sub-harmonic resonance is in particular found. The computational benefit of using ROMs is discussed and demonstrated.

Immersed Interface and Diffuse-Domain Approach for Current-Potential Distributions and Electrodeposition Problems

Several numerical approaches are being developed to solve the moving boundary models which predict the morphological evolution of the electrode surface during electrodeposition. Despite these significant research efforts over a broad range of materials, scales, and purposes, the prediction of the shape evolution of the electrodes over time is still a challenging problem. One needs to solve these moving boundary problems, as the potential and current distributions within the cell get affected by the geometry.1-2 In this work, we will demonstrate a recently developed numerical framework based on the diffused domain approach using phase-field models for two classical example, Hull cell and copper deposition in trenches.3 The original model equation was carefully reformulated as a diffuse-domain/immerse domain approach for steady state current-potential distribution problems.4-5 Then the shape change problem is cast as a transient phase-field problem to predict the shape changes of the electrode during electrodeposition. A comparative analysis has also been performed for the efficiency, accuracy, speed, and convergence of the present solutions for the Hull cell with other available numerical and even analytical methods. It can be stated that the present phase-field model is robust and efficient for predicting the shape changes of the electrode over time without oscillations. Acknowledgments This research was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy (DoE) through the Advanced Battery Materials Research Program (Battery500 Consortium) References V. R. Subramanian, and R. E. White, J. Electrochem. Soc, 149(10) C498 (2002).R. Alkire, T. Bergh, and R. L. Sani, J. Electrochem. Soc., 125, 1981 (1978).T. Jang, L. Mishra, S. A. Roberts, A. Subramaniam, M. Uppaluri, M. P. Gururajan, J. Zhang, and V. R. Subramanian, “BattPhase – A convergent, non-oscillatory, efficient algorithm and code for predicting shape changes in lithium metal batteries using phase-field models – 1. Secondary Current Distribution,” ECSarXiv (2022), doi:10.1149/osf.io/k2vu6C. S. Peskin, Acta Numer., 11, 479 (2003).X. Li, J. Lowengrub, A. Ratz and A. Voigt, Commun. Math. Sci., 7, 81 (2009).

Electrochemical Properties of Coumarin 500 Encapsulated in a Liquid Crystal Guided Electrospun Fiber Core and Their Supercapacitor Application

Here, we first report a study on coumarin 500 and liquid crystal including polyacrylonitrile nanofibers in terms of synthesis, characterizations, and supercapacitor performances. SEM, POM, FTIR, and DSC measurements showed that liquid crystal was inserted into the fine polyacrylonitrile nanofibers successfully. Because a strong molecular interaction took place between coumarin 500 and liquid crystal and coumarin 500 was sensitive to the polarity of the medium, the liquid crystal behaved as a guide material for coumarin 500, and it was expected that coumarin 500 was oriented by the director of the liquid crystal along the core of the fiber. The average polyacrylonitrile nanofiber size was between 0.19 to 0.25 μm, and liquid-crystal-doped and liquid-crystal+coumarin-500-doped fibers exhibited a similar distribution, which is approximately in the 0.30 to 0.60 μm interval. This proved that the fibers maintained their structure after modifications. Electrochemical evaluation of the different composite nanofibers showed that there was not a significant current increase upon liquid crystal addition into polyacrylonitrile nanofibers at voltammograms. Cs values were enhanced after the coumarin 500 addition into liquid-crystal-doped nanofiber and obtained as 410.60 F/g with a specific energy value of 57.03 Wh/kg. Additionally, the long-term charge–discharge test of the liquid-crystal+coumarin-500-doped polyacrylonitrile graphite electrode showed a very steady distribution between 100th and the 2500th cycles with a 14.12% Cs deviation. This is attributed to the stable and robust network of the PAN nanofiber and the synergetic effect between liquid crystal and coumarin 500 in the nanofiber net.

Correlated continuous-time random walk with stochastic resetting

It is known that the introduction of stochastic resetting in an uncorrelated random walk process can lead to the emergence of a stationary state, i.e. the diffusion evolves towards a saturation state, and a steady Laplace distribution is reached. In this paper, we turn to study the anomalous diffusion of the correlated continuous-time random walk considering stochastic resetting. Results reveal that it displays quite different diffusive behaviors from the uncorrelated one. For the weak correlation case, the stochastic resetting mechanism can slow down the diffusion. However, for the strong correlation case, we find that the stochastic resetting cannot compete with the space-time correlation, and the diffusion presents the same behaviors with the one without resetting. Meanwhile, a steady distribution is never reached.