Uniform Initial Conditions Research Articles

A Topological Investigation of the Cosmic Web Formation

N-body simulations of the evolution of the large-scale structure of the universe (the Cosmic Web) were run while altering attractive gravity laws and initial conditions, in order to infer which properties of the universe are revealed by its current large-scale topology. The Cosmic Web was found to develop regardless of the gravitational alteration made. Significantly altering the initial conditions from Gaussian distribution ones was found to eliminate the Cosmic Web. Thus, we require small random perturbations in otherwise uniform initial conditions in the early universe, under an attractive gravitational force, for the Cosmic Web to develop.

Tracer dynamics in the active random average process

We investigate the dynamics of tracer particles in the random average process (RAP), a single-file system in one dimension. In addition to the position, every particle possesses an internal spin variable σ(t) that can alternate between two values, ±1, at a constant rate γ. Physically, the value of σ(t) dictates the direction of motion of the corresponding particle and, for finite γ, every particle performs non-Markovian active dynamics. Herein, we study the effect of this non-Markovian behavior in the fluctuations and correlations of the positions of tracer particles. We analytically show that the variance of the position of a tagged particle grows sub-diffusively as ∼ζqt at large times for the quenched uniform initial conditions. While this sub-diffusive growth is identical to that of the Markovian/non-persistent RAP, the coefficient ζq is rather different and bears the signature of the persistent motion of active particles through higher-point correlations (unlike in the Markovian case). Similarly, for the annealed (steady-state) initial conditions, we find that the variance scales as ∼ζat at large times, with the coefficient ζa once again different from the non-persistent case. Although both ζ q and ζa individually depart from their Markovian counterparts, their ratio ζa/ζq is still equal to 2 , a condition observed for other diffusive single-file systems. This condition turns out to be true even in the strongly active regimes, as corroborated by extensive simulations and calculations. Finally, we study the correlation between the positions of two tagged particles in both quenched uniform and annealed initial conditions. We verify all our analytical results using extensive numerical simulations.

A computational strategy for nonlinear time-fractional generalized Kawahara equation using new eighth-kind Chebyshev operational matrices

This paper presents a new method to numerically solve the nonlinear time-fractional generalized Kawahara equations (NTFGKE) with uniform initial boundary conditions (IBCs). A class of modified shifted eighth-kind Chebyshev polynomials (MSEKCPs) is introduced to satisfy the given IBCs. The proposed method is based on using the operational matrices (OMs) for the ordinary derivatives (ODs) and the fractional derivatives (FDs) of MSEKCPs. These OMs are employed together with the spectral collocation method (SCM). Our presented algorithm enables the extraction of efficient and accurate numerical solutions. The convergence of the suggested method and the error analysis have been developed. Three numerical examples are presented to demonstrate the applicability and accuracy of our algorithm. Some comparisons of the presented numerical results with other existing ones are offered to validate the efficiency and superiority of our approach. The presented tables and graphs demonstrate that the proposed approach produces approximate solutions with high accuracy.

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques

In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. Initially, a detailed qualitative analysis of the spatio-temporal model is presented. The existence, uniqueness, positivity, and boundedness of the model solution are investigated. Local asymptotical stability of the diffusive COVID-19 model at steady state is carried out using well-known criteria. Moreover, a suitable nonlinear Lyapunov functional is constructed for the global asymptotical stability of the spatio-temporal model. Further, the model is solved numerically based on uniform and non-uniform initial conditions. Two different numerical schemes named: finite difference operator-splitting and mesh-free operator-splitting based on multi-quadratic radial basis functions are implemented in the numerical study. The impact of diffusion as well as some pharmaceutical and non-pharmaceutical control measures, i.e., reducing an effective contact causing infection transmission, vaccination rate and vaccine waning rate on the disease dynamics is presented in a spatially heterogeneous environment. Furthermore, the impact of the aforementioned interventions is investigated with and without diffusion on the incidence of disease. The simulation results conclude that the random motion of individuals has a significant impact on the disease dynamics and helps in setting a better control strategy for disease eradication.

Approximate analytical solution to equation for two-dimensional soil-water movement in ponding infiltration based on numerical simulation

A simple analytical solution to two-dimensional (2D) ponding infiltration is essential for designing line-source or drip irrigation. We propose a new and simple approximate analytical method for calculating the 2D distribution of soil water with a 1-cm radius of ponding and uniform initial conditions and for estimating the horizontal and vertical distances of wetting fronts based on soil hydraulic parameters. The method assumes a semi-elliptical soil-wetting pattern and a one-dimensional profile of soil water at an arbitrary infiltration angle to solve the equation for the 2D movement of soil water and cumulative infiltration. We applied the numerical data simulated using HYDRUS-3D to validate the proposed method's parameters and evaluate the relationship between the wetting front and hydraulic parameters. The simulated results indicated that the assumptions were propitious to the fine-texture soils with air-entry suction larger than 10 cm. The ratio between the distances of the horizontal and vertical wetting fronts could be approximately predicted using the air-entry suction by analyzing the numerical results. The fitted results indicated that the parameters of the power function of the relationship between the distances of the horizontal and vertical wetting fronts and infiltration time could be described as polynomial and power functions of the diffusivity of saturated soil water. The approximate analytical solutions for the distance of the horizontal wetting front, depth of the vertical wetting front, and cumulative infiltration agreed well with other numerical simulations.

Approximate analytical solutions for one-dimensional soil water movement equation with arbitrary initial conditions

Simple analytical solutions of one-dimensional horizontal and vertical soil water movement are of great importance for the soil hydraulic parameters estimation and precision irrigation. We present the approximate analytical solutions for the problem of horizontal absorption and vertical infiltration in soil under arbitrary initial conditions and constant boundary conditions based on the principle of least action and the variational principle. The algebraic functions of soil water content (SWC) profile, cumulative infiltration, infiltration rate and infiltration time about the wetting front distance/depth (WFD) and the parameters of Brooks-Corey model are obtained. Compared with the numerical results simulated by HYDRUS-1D, the algebraic results calculated by approximate analytical solutions have high precision to predict the horizontal and vertical soil water infiltration based on the known WFD. Contrary to the linear relationship in horizontal absorption with uniform initial conditions, the relationships between cumulative infiltration and WFD, infiltration rate and reciprocal of WFD, square of WFD and infiltration time are nonlinear for the arbitrary heterogeneous initial conditions. However, the initial conditions have little effect on the relationship between infiltration rate and WFD when the initial SWCs are lower than 0.6 θs. Based on the nonlinear relationships of infiltration rate and WFD in vertical infiltration, the WFD and time of the stable infiltration are obtained.

A numerical study of COVID-19 epidemic model with vaccination and diffusion.

The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.

Time fractional advection-dispersion model to study transportation of particles with time-memory for unsteady nonequilibrium suspension in open-channel turbulent flows

In this study, the effects of time-memory on the mixing and nonequilibrium transportation of particles in an unsteady turbulent flow are investigated. The memory effect of particles is captured through a time-fractional advection-dispersion equation rather than a traditional advection-dispersion equation. The time-fractional derivative is considered in Caputo sense which includes a power-law memory kernel that captures the power-law jumps of particles. The time-fractional model is solved using the Chebyshev collocation method. To make the solution procedure more robust three different kinds of Chebyshev polynomials are considered. The time-fractional derivative is approximated using the finite difference method at small time intervals and numerical solutions are obtained in terms of Chebyshev polynomials. The model solutions are compared with existing experimental data of traditional conditions and satisfactory results are obtained. Apart from this, the effects of time-memory are analyzed for bottom concentration and transient concentration distribution of particles. The results show that for uniform initial conditions, bottom concentration increases with time as the order of fractional derivative decreases. In the case of transient concentration, the value of concentration initially decreases when T < 1 and thereafter increases throughout the flow depth. The effects of time-memory are also analyzed under steady flow conditions. Results show that under steady conditions, transient concentration is more sensitive for linear, parabolic, and parabolic-constant models of sediment diffusivity rather than the constant model.

Gravitational collapse from cold uniform asymmetric initial conditions

Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite N fluctuations and perturbations induced by the anisotropic gravitational field compete to determine the physical properties of the asymptotic quasi-stationary state. When finite N fluctuations dominate the dynamics, the particle energy distribution changes greatly and the final density profile decays outside its core as r−4 with an N-dependent amplitude. On the other hand, in the limit where the anisotropic perturbations dominate, the collapse is softer and the density profile shows a decay as r−3, as is typical of halos in cosmological simulations. However, even in this limit, convergence with N of the macroscopic properties of the virialized system, such as the particle energy distributions, the bound mass, and the density profile, is very slow and not clearly established, including for our largest simulations (with N ∼ 106). Our results illustrate the challenges of accurately simulating the first collapsing structures in standard-type cosmological models.

Approximate analytical solution and parameter estimation for one‐dimensional horizontal absorption based on the van Genuchten–Mualem model

AbstractThe van Genuchten–Mualem (VGM) model is used to describe the absorption of water by soil. The model is highly nonlinear, so developing a simple analytical or approximate method to predict the movement of soil water via the VGM model then estimating the model parameters is necessary. We present a approximate functional extremum solution (FES) for the problem of one‐dimensional horizontal absorption (1DHA) of water in soil under constant saturated boundary conditions and uniform initial conditions based on the least action and the variational principles. Simple linear relationships between the infiltration characteristics (distribution of soil water content, cumulative infiltration, infiltration rate, wetting front distance, and infiltration time) and the VGM model parameters were obtained. We developed a simple approximate analytical method for estimating the VGM model parameters by testing 1DHA. Numerical data simulated by HYDRUS‐1D were compared with the analytical results and used to verify our method's feasibility. The results indicated that the FES could accurately predict the infiltration characteristics, with relative errors between the approximate analytical and numerical solutions of 0.8 to 8.5% for the distribution of soil water content, 0.1 to 0.8% for cumulative infiltration, 1.1 to 6.4% for infiltration rate, and 0.1 to 6.9% for wetting front distance. Estimates of the parameters indicated that errors ranged from 3.2 to 28.3% for α (inverse of the mean pore diameter) and 0.4 to 8.0% for n (pore size distribution index). The proposed methods can be used to predict 1DHA and to estimate α and n in the VGM model.

The tin can method for determining moisture transport properties of concrete

Traditional methods for measuring moisture transport properties of concrete are time-consuming, especially since thick specimens are required, and steady-state methods are preferred. Non-steady state methods may be an alternative but the conditioning to uniform initial conditions is extremely difficult. The tin can method is, however, a good alternative under certain conditions and for certain concretes. Concrete is poured into a tin can and sealed cured in this way for at least a month. The can is opened, and the concrete is dried in a constant climate. Weight changes are recorded for several weeks. From these weight changes, the initial RH at start of drying, the drying climate and the desorption isotherm, the moisture transport coefficient or the moisture diffusion resistance factor are derived. The paper describes the theory behind the method and the unique conditions available for certain concretes that makes the method applicable. Examples of measurements are shown for a number of concretes and verification is done with the cup method on the very same concretes, with excellent results.

Heat-induced planar shock waves in supercritical fluids

We have investigated one-dimensional compression waves, produced by heat addition in quiescent and uniform initial conditions, in six different supercritical fluids, each taken in four states ranging from compressible pseudo-liquid fluid to ideal gas. Navier–Stokes simulations of a canonical semi-infinite domain flow problem, spanning five orders of magnitude of heating rate, are also carried out to support the theoretical analysis. Depending on the intensity of the Gaussian-shaped energy source, linear waves or shock waves due to nonlinear wave steepening are observed. A new reference heating rate parameter allows to collapse in the linear regime the whole dataset, together with the existing experimental data, thanks to its absorption of real-fluid effects. Moreover, the scaling strategy illustrates a clear separation between linear and nonlinear regimes for all fluids and conditions, offering motivation for the derivation of a unified fully predictive model for shock intensity. The latter is performed by extending the validity of previously obtained theoretical results in the nonlinear regime to supercritical fluids. Finally, thermal to mechanical power conversion efficiencies are shown to be proportional, in the linear regime, to the fluid’s Gruneisen parameter, which is the highest for compressible pseudo-liquid fluids, and maximum in the nonlinear regime for ideal gases.

Timing and shape of stochastic autocatalytic burst formation.

Chemical, physical, and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semistable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with escape time sensitive to noise. When the model is extended to include space, this leads to different points in space "escaping from zero" at different times, and uniform initial conditions nucleate into sharp peaks spreading randomly across a nearly uniform background, a phenomenon closely resembling nucleation during phase transition. We use Large Deviation Theory to determine burst shape and temporal scaling with respect to noise amplitude. These results give a prototype for a particular form of patternless symmetry breaking in the vicinity of a stability boundary and demonstrate how microscopic noise can lead to macroscopic effects in such a region.

Evidence for Cogradient Growth and Survival Between Two Geographically Distinct Stocks of Muskellunge

AbstractIntraspecific genetic variation across the distribution of Muskellunge Esox masquinongy suggests the existence of divergent stocks among major river drainages. Often, stocks differentiate in response to latitudinal variation in thermal regime. Genetic variation and thermal adaptation may drive fish to either maximize growth during brief growing seasons at higher latitudes (counter‐gradient growth) or experience longer periods of slower growth at lower latitudes (cogradient growth). The strength and direction of these genetic effects matter for fish stocked outside of their native drainage and for populations experiencing changes to regional thermal regimes. We used a replicated pond experiment with uniform initial fish size and environmental conditions to compare the survival and growth of stocked age‐0 Ohio River drainage (OH) Muskellunge with those of the more northerly upper Mississippi River drainage (MISS) stock following their first winter and a year after introduction into a common environment. Both stocks had similarly high winter survival, though the MISS stock had a slower growth rate overwinter than the OH stock. Survival during the latter spring‐to‐fall period was greatly reduced for the MISS stock, however, with the differences in growth rate persisting. These findings suggest that cogradient adaptation to temperatures experienced during early life stages in native environments results in a disadvantage for high‐latitude stocks of Muskellunge in thermal regimes warmer than those they have historically experienced in their native drainages.

Arcuate stress state in accretionary prisms from real-scale numerical sandbox experiments

The stress states in accretionary prisms are important for understanding the building and releasing of seismic energy. Numerous researchers have conducted sandbox experiments as a scaled physical analog model to understand the formation of accretionary prisms. However, measuring stress states in laboratory sandbox experiments is still practically infeasible. Here we performed real-scale numerical sandbox experiments using the discrete element method to understand the 3D stress state in the accretionary prism. Despite the nearly uniform initial conditions, macro-scale undulations of faults, which are similar to those observed in the trenches of an accretionary prism, appear. We reveal that these undulations are caused by the formation of stress arches. We show that the mechanism behind the arch formation is the discontinuous change in the stress orientation during the rearrangement of the stress chain. Furthermore, analyses demonstrate that the in-situ stress orientation from borehole data can be a signal of either the regional direction of plate convergence or the local stress orientation associated with the stress arch. The results may greatly enhance the outcome of long term monitoring in areas, such as the Nankai Trough.

Recovery of floristic diversity and basal area in natural forest regeneration and planted plots in a Costa Rican wet forest

AbstractWhen compared to planted reforestation, natural unassisted regeneration is often reported to result in slow recovery of biomass and biodiversity, especially early in succession. In some cases, naturally regenerating forests are not comparable to the community structure of primary forests after many decades. However, direct comparison of the outcomes of tropical forest restoration and natural regeneration is hindered by differences in metrics of forest recovery, inconsistency in land use histories, and dissimilarities in experimental design. We present the results of a replicated reforestation experiment comparing natural regeneration and polyculture tree planting at multiple diversity levels (3, 6, 9, or 12 native tree species), with uniform land use history and initial edaphic conditions. We compare the recovery of basal area and floristic diversity in these treatments after 5 yr of succession. Total basal area was higher in planted plots than in naturally regenerating plots, but it but did not vary among the different planted diversity levels. The basal area of woody recruits did not differ among treatments. The diversity of woody recruits increased substantially over time but did not vary among planting treatments. Species composition trajectories showed directional turnover over time, with no consistent differences among treatments. The convergence of restoration trajectories and similarity of floristic community diversity and composition across all treatments, after only 5 yr, provides evidence of the viability of natural regeneration for rapid restoration of forest biodiversity.

Application of isotopic information for estimating parameters in Philip infiltration model

Minimizing parameter uncertainty is crucial in the application of hydrologic models. Isotopic information in various hydrologic components of the water cycle can expand our knowledge of the dynamics of water flow in the system, provide additional information for parameter estimation, and improve parameter identifiability. This study combined the Philip infiltration model with an isotopic mixing model using an isotopic mass balance approach for estimating parameters in the Philip infiltration model. Two approaches to parameter estimation were compared: (a) using isotopic information to determine the soil water transmission and then hydrologic information to estimate the soil sorptivity, and (b) using hydrologic information to determine the soil water transmission and the soil sorptivity. Results of parameter estimation were verified through a rainfall infiltration experiment in a laboratory under rainfall with constant isotopic compositions and uniform initial soil water content conditions. Experimental results showed that approach (a), using isotopic and hydrologic information, estimated the soil water transmission in the Philip infiltration model in a manner that matched measured values well. The results of parameter estimation of approach (a) were better than those of approach (b). It was also found that the analytical precision of hydrogen and oxygen stable isotopes had a significant effect on parameter estimation using isotopic information.

Exact correlations in a single-file system with a driven tracer

We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial conditions and compute the two-point correlations. For quenched uniform and annealed steady-state initial conditions we show that in the large time T limit the fluctuations and the correlations of the positions of the particles grow subdiffusively as and have well-defined scaling forms under proper rescaling of the labels. We compute the corresponding scaling functions exactly for these specific initial configurations and verify them numerically. We also consider a non-translationally invariant initial condition with linearly increasing gaps where we show that the fluctuations and correlations grow superdiffusively as at large times.

Study thermal characteristics of millet grain, dried in the machine with the swirling flow of the coolant and the microwave energy supply

The article discusses the problems of determining the thermal characteristics of millet. The choice of the research object. The paper presents the principle of operation of the plant and the parameters of the standard, organic glass for measurements. Method was to study millet grains and organic glass, which are brought into contact on a common plane. The heater is brought into contact with the product and passed the constant heat flow, which passed through a layer of millet grain at different speeds. As a result, the temperature in the contact plane of the changed and recorded on the chart of the potentiometer in the form of the curve, by which you can determine the time and temperature change. The thermal diffusivity and thermal conductivity determined by empirical formulas obtained by solving a system of differential equations, made up for the system of two bodies, one of which includes the unknown thermal characteristics. Test two bodies in contact on a common plane, resulting in mathematical physics principles constitute two differential equations with uniform initial and boundary conditions of the first kind, due to the parameters of ongoing experience. It is a plot of thermal performance of the temperature and humidity. Revealed linear dependence of the physical thermal characteristics, showing that with increasing temperature the thermal diffusivity value decreases, and the thermal conductivity and specific heat capacity are increasing character. Revealed the equations describing the thermal characteristics of millet grain with a humidity in the range of 13.6–35.1% and the temperature range 293–373 K.

Synchronization and Waves in a Ring of Diffusively Coupled Memristor-Based Chua’s Circuits

In the present paper we report numerical observations of the spontaneous dynamics of N identical memristor-based Chua's circuits bidirectionally coupled in a ring geometry. Two different initial configurations are studied by varying N and the coupling strength: in the first configuration we consider only one circuit with non-zero initial conditions, in the second one all circuits have uniform random initial conditions. We observed both chaotic and non-chaotic synchronization. In the chaotic synchronized regime we identified emerging chaotic steady waves, characterized by an almost constant frequency and chaotic amplitude. Depending on the initial conditions, in the pseudo-sinusoidal oscillations regime both macroscopic quasi-periodic steady and traveling waves were observed.