Terms Of Initial Conditions Research Articles

Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

BackgroundNavier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). ResultsIt was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes.ConclusionFindings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

IMPROVED MACHINE LEARNING TECHNIQUE FOR SOLVING HAUSDORFF DERIVATIVE DIFFUSION EQUATIONS

This study aims at combining the machine learning technique with the Hausdorff derivative to solve one-dimensional Hausdorff derivative diffusion equations. In the proposed artificial neural network method, the multilayer feed-forward neural network is chosen and improved by using the Hausdorff derivative to the activation function of hidden layers. A trial solution is a combination of the boundary and initial condition terms and the network output, which can approximate the analytical solution. To transform the original Hausdorff derivative equation into a minimization problem, an error function is defined, where the coefficients are approximated by using the gradient descent algorithm in the back-propagation process. Two numerical examples are given to illustrate the accuracy and the robustness of the proposed method. The obtained results show that the improved machine learning technique is efficient in computing the Hausdorff derivative diffusion equations both from computational accuracy and stability.

On the establishment of a mutant

How long does it take for an initially advantageous mutant to establish itself in a resident population, and what does the population composition look like then? We approach these questions in the framework of the so called Bare Bones evolution model (Klebaner et al. in J Biol Dyn 5(2):147–162, 2011. https://doi.org/10.1080/17513758.2010.506041) that provides a simplified approach to the adaptive population dynamics of binary splitting cells. As the mutant population grows, cell division becomes less probable, and it may in fact turn less likely than that of residents. Our analysis rests on the assumption of the process starting from resident populations, with sizes proportional to a large carrying capacity K. Actually, we assume carrying capacities to be a_1K and a_2K for the resident and the mutant populations, respectively, and study the dynamics for Krightarrow infty . We find conditions for the mutant to be successful in establishing itself alongside the resident. The time it takes turns out to be proportional to log K. We introduce the time of establishment through the asymptotic behaviour of the stochastic nonlinear dynamics describing the evolution, and show that it is indeed frac{1}{rho }log K, where rho is twice the probability of successful division of the mutant at its appearance. Looking at the composition of the population, at times frac{1}{rho }log K +n, n in mathbb {Z}_+, we find that the densities (i.e. sizes relative to carrying capacities) of both populations follow closely the corresponding two dimensional nonlinear deterministic dynamics that starts at a random point. We characterise this random initial condition in terms of the scaling limit of the corresponding dynamics, and the limit of the properly scaled initial binary splitting process of the mutant. The deterministic approximation with random initial condition is in fact valid asymptotically at all times frac{1}{rho }log K +n with nin mathbb {Z}.

Winds and feedback from supermassive black holes accreting at low rates: hydrodynamical treatment

ABSTRACT Outflows produced by a supermassive black hole (SMBH) can have important feedback effects in its host galaxy. An unresolved question is the nature and properties of winds from SMBHs accreting at low rates in low-luminosity active galactic nuclei (LLAGNs). We performed two-dimensional numerical, hydrodynamical simulations of radiatively inefficient accretion flows on to non-spinning black holes. We explored a diversity of initial conditions in terms of rotation curves and viscous shear stress prescriptions, and evolved our models for very long durations of up to 8 × 105GM/c3. Our models resulted in powerful subrelativistic, thermally driven winds originated from the corona of the accretion flow at distances 10−100 GM/c2 from the SMBH. The winds reached velocities of up to 0.01c with kinetic powers corresponding to $0.1\!-\!1 {\,{\rm per\, cent}}$ of the rest-mass energy associated with inflowing gas at large distances, in good agreement with models of the ‘radio mode’ of AGN feedback. The properties of our simulated outflows are in broad agreement with observations of winds in quiescent galaxies that host LLAGNs, which are capable of heating ambient gas and suppressing star formation.

Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms which include local pumping and decay of particles.

Direct numerical simulations of multi-mode immiscible Rayleigh-Taylor instability with high Reynolds numbers

In this paper, we conduct the high-resolution direct numerical simulations of multimode immiscible Rayleigh-Taylor instability (RTI) with a low Atwood number (At = 0.1) using an improved phase field lattice Boltzmann method. The effect of the Reynolds number on the evolutional interfacial dynamics and bubble/spike amplitudes is first investigated by considering its wide range, from 100 up to a high value of 30 000. The numerical results show that, for sufficiently large Reynolds numbers, a sequence of distinguishing stages in the immiscible RTI can be observed, which includes the linear growth, saturated velocity growth, and chaotic development stages. At the late stage, the RTI induces a complex topology structure of the interface and a mass of dissociative drops can be significantly observed in the system. The accelerations of the bubble and spike front are also measured, and it is reported that their normalized values at the late time are, respectively, approximate to the constant values of around 0.025 and 0.027, exhibiting a terminally quadratic growth. As the Reynolds number is reduced to small ones, the multiple disturbances of the RTI are found to merge into a larger one at the initial stage. Then, the evolutional interfaces display the patterns familiar from the single-mode RTI. The phase interfaces in the whole process become very smooth without the appearance of the breakup phenomenon, and the spike and bubble velocities at the late time approach constant values. Furthermore, we also analyze the effects of the initial conditions in terms of the perturbation wavelength and amplitude, and it is found that the instability undergoes a faster growth at the intermediate stage for a larger wavelength, while the late-time bubble and spike growth rates are insensitive to the changes of the initially perturbed wavelength and amplitude.

Size diversity of old Large Magellanic Cloud clusters as determined by internal dynamical evolution

The distribution of size as a function of age observed for star clusters in the Large Magellanic Cloud (LMC) is very puzzling: young clusters are all compact, while the oldest systems show both small and large sizes. It is commonly interpreted as due to a population of binary black holes driving a progressive expansion of cluster cores. Here we propose, instead, that it is the natural consequence of the fact that only relatively low-mass clusters have formed in the last ~3 Gyr in the LMC and only the most compact systems survived and are observable. The spread in size displayed by the oldest (and most massive) clusters, instead, can be explained in terms of initial conditions and internal dynamical evolution. To quantitatively explore the role of the latter, we selected a sample of five coeval and old LMC clusters with different sizes, and we estimated their dynamical age from the level of central segregation of blue straggler stars (the so-called dynamical clock). Similarly to what found in the Milky Way, we indeed measure different levels of dynamical evolution among the selected coeval clusters, with large-core systems being dynamically younger than those with small size. This behaviour is fully consistent with what expected from internal dynamical evolution processes over timescales mainly set by the structure of each system at formation.

Учет влияния нерегулярной качки в навигационном обеспечении пусков баллистических ракет подводных лодок

The paper attempts to solve the problem of determining initial conditions in terms of submarine ballistic missile velocity by means of an optimum Wiener filter. We provide solutions for known and proposed empirical models of nonlinear ship motion. We show that for a generic pre-launch sequence it is possible to considerably increase the accuracy of solving the initial velocity determination problem by exploiting the proposed model of modified nonlinear ship motion

How Initial Size Governs Core Collapse in Globular Clusters

Abstract Globular clusters (GCs) in the Milky Way exhibit a well-observed bimodal distribution in core radii separating the so-called core-collapsed and non-core-collapsed clusters. Here, we use our Hénon-type Monte Carlo code, CMC, to explore initial cluster parameters that map into this bimodality. Remarkably, we find that by varying the initial size of clusters (specified in our initial conditions in terms of the initial virial radius, r v ) within a relatively narrow range consistent with the measured radii of young star clusters in the local universe (r v ≈ 0.5–5 pc), our models reproduce the variety of present-day cluster properties. Furthermore, we show that stellar-mass black holes (BHs) play an intimate role in this mapping from initial conditions to the present-day structural features of GCs. We identify “best-fit” models for three GCs with known observed BH candidates, NGC 3201, M22, and M10, and show that these clusters harbor populations of ∼50–100 stellar-mass BHs at present. As an alternative case, we also compare our models to the core-collapsed cluster NGC 6752 and show that this cluster likely contains few BHs at present. Additionally, we explore the formation of BH binaries in GCs and demonstrate that these systems form naturally in our models in both detached and mass-transferring configurations with a variety of companion stellar types, including low-mass main-sequence stars, white dwarfs, and sub-subgiants.

A numerical study on the dynamic response of a floating spar platform in extreme waves

The investigation of the interaction of floating structures with very high waves, also known as freak or rogue waves, is of crucial importance for the analysis of their ultimate design conditions. The representation of such waves is usually achieved through computationally intensive numerical simulations. In this paper, a deterministic approach is proposed, to represent extreme wave groups in the space–time domain. The free surface profile for a Gaussian sea is obtained by means of the Quasi-Determinism theory, and the corresponding dynamic response of a spar-type support for floating offshore wind turbines in parked rotor conditions is analyzed. The Quasi-Determinism theory and the nonlinear equation of motion of the structure are coupled through an in-house time-domain numerical code. Wave forces and structure motions in surge, heave and pitch are obtained. A parametric analysis is carried out to investigate the effects of the criteria used for the definition of the extreme wave, its position of occurrence and the initial conditions in terms of body motions. The results obtained give a clear insight into the physics of the wave–structure interaction phenomenon for extremely high waves in Gaussian seas and allow to identify a few load combinations, corresponding to the severest wave conditions for the floating structure.

Solving shallow water equations with crisp and uncertain initial conditions

Purpose This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions. Design/methodology/approach Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations. Findings Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots. Originality/value Shallow water equations with crisp and fuzzy initial conditions have been solved.

On the Self-Similar, Wright-Function Exact Solution for Early-Time, Anomalous Diffusion in Random Networks: Comparison with Numerical Results

Recently, Zhang and Padrino in (Int J Multiph Flow 92:70–81, 2017) derived an equation for diffusion in random networks consisting of junction pockets and connecting channels by applying the ensemble average method to the mass conservation principle. The resulting integro-differential equation was solved numerically using the finite volume method for the test case of one-dimensional diffusion in the half-line. For early time, they found that the numerical predictions of pocket mass density depend on the similarity variable $$x t^{-1/4}$$ , describing sub-diffusion, instead of $$x t^{-1/2}$$ as in ordinary diffusion. They argue that the sub-diffusive trend is the result of the time required to establish a linear concentration profile inside a channel. By theoretical analysis of the diffusion equation for small time, they confirmed this finding. Nevertheless, they did not present an exact solution for the small-time limit to compare with. Here, starting with their small-time leading order diffusion equation in (x, t) space, we use elements of fractional calculus to cast it into a form for which an analytical solution has been given in the literature for the same boundary and initial conditions in terms of the Wright function (Gorenflo et al. in J Comput Appl Math 118(1):175–191, 2000). This solution, in turn, is written in terms of generalized hypergeometric functions, readily available in calculus software packages. Comparing predictions from the exact solution with Zhang and Padrino’s numerical results leads to excellent agreement, serving as validation of their numerical approach.

Hanbury-Brown–Twiss correlation functions and radii from event-by-event hydrodynamics

Hanbury-Brown--Twiss correlation functions and radii from event-by-event hydrodynamics (HoTCoffeeh) is a new computational tool which determines Hanbury-Brown--Twiss (HBT) charged-pion (${\ensuremath{\pi}}^{+}$) correlation functions and radii for event-by-event hydrodynamics with fluctuating initial conditions in terms of Cooper--Frye integrals, including resonance-decay contributions. In this paper, we review the basic formalism for computing the HBT correlation functions and radii with resonance-decay contributions included and discuss our implementation of this formalism in the form of HoTCoffeeh. This tool may easily be integrated with other numerical packages [see, e.g., [Comput. Phys. Commun. 199, 61 (2016)]] for the purpose of simulating the evolution of heavy-ion collisions and thereby extracting predictions for heavy-ion observables.

Influence of Hydrological Perturbations and Riverbed Sediment Characteristics on Hyporheic Zone Respiration of CO2 and N2

AbstractRivers in climatic zones characterized by dry and wet seasons often experience periodic transitions between losing and gaining conditions across the river‐aquifer continuum. Infiltration shifts can stimulate hyporheic microbial biomass growth and cycling of riverine carbon and nitrogen leading to major exports of biogenic CO2 and N2 to rivers. In this study, we develop and test a numerical model that simulates biological‐physical feedback in the hyporheic zone. We used the model to explore different initial conditions in terms of dissolved organic carbon availability, sediment characteristics, and stochastic variability in aerobic and anaerobic conditions from water table fluctuations. Our results show that while highly losing rivers have greater hyporheic CO2 and N2 production, gaining rivers allowed the greatest fraction of CO2 and N2 production to return to the river. Hyporheic aerobic respiration and denitrification contributed 0.1–2 g/m2/d of CO2 and 0.01–0.2 g/m2/d of N2; however, the suite of potential microbial behaviors varied greatly among sediment characteristics. We found that losing rivers that consistently lacked an exit pathway can store up to 100% of the entering C/N as subsurface biomass and dissolved gas. Our results demonstrate the importance of subsurface feedbacks whereby microbes and hydrology jointly control fate of C and N and are strongly linked to wet‐season control of initial sediment conditions and hydrologic control of seepage direction. These results provide a new understanding of hydrobiological and sediment‐based controls on hyporheic zone respiration, including a new explanation for the occurrence of anoxic microzones and large denitrification rates in gravelly riverbeds.

Galaxies with Prolate Rotation in Illustris

Abstract Tens of early-type galaxies have been recently reported to possess prolate rotation of the stellar component, i.e., a significant amount of rotation around the major axis, including two cases in the Local Group. Although expected theoretically, this phenomenon is rarely observed and remains elusive. We study its origin using the population of well-resolved galaxies in the Illustris cosmological simulation. We identify 59 convincing examples of prolate rotators at the present time, more frequently among more massive galaxies, with the number varying very little with redshift. We follow their evolution back in time using the main progenitor branch galaxies of the Illustris merger trees. We find that the emergence of prolate rotation is strongly correlated with the time of the last significant merger that the galaxy experienced, although other evolutionary paths leading to prolate rotation are also possible. The transition to prolate rotation most often happens around the same time as the transition to prolate shape of the stellar component. The mergers leading to prolate rotation have slightly more radial orbits and higher mass ratios, and they occur at more recent times than mergers in the reference sample of twin galaxies we construct for comparison. However, they cover a wide range of initial conditions in terms of the mass ratio, merger time, radiality of the progenitor orbits, and relative orientations of progenitor spins with respect to the orbital angular momenta. About half of our sample of prolate rotators was created during gas-rich mergers, and the newly formed stars usually support prolate rotation.

On the self-similar, early-time, anomalous diffusion in random networks — Approach by fractional calculus

In a recent work, Zhang and Padrino (2017) derived an equation for diffusion in random networks consisting of junction pockets and connecting channels by applying the ensemble average method to the mass conservation principle. The resulting integro-differential equation was solved numerically using finite volumes for the test case of one-dimensional diffusion in the half-line. For early time, they found that the numerical predictions of pocket mass density depend on the similarity variable xt−1/4, representing sub-diffusion. They argue that the sub-diffusive behavior is a consequence of the time needed to establish a linear concentration profile inside a channel. By theoretical analysis of the diffusion equation for small time, they confirmed this finding. Nevertheless, they did not present an exact solution for the small time limit to compare with. Here, starting with their small-time leading order diffusion equation in (x,t) space, we use elements of fractional calculus to cast it into a form for which an analytical solution has been obtained in the literature for the same boundary and initial conditions in terms of the Fox H-function (Schneider and Wyss, 1989). For ease of computation, we express the solution in terms of the Meijer G-function. We compare the exact solution with Zhang and Padrino's numerical predictions, resulting in excellent agreement, thereby validating their numerical approach.

An inverse problem for a family of two parameters time fractional diffusion equations with nonlocal boundary conditions

The determination of a space‐dependent source term along with the solution for a 1‐dimensional time fractional diffusion equation with nonlocal boundary conditions involving a parameter β>0 is considered. The fractional derivative is generalization of the Riemann‐Liouville and Caputo fractional derivatives usually known as Hilfer fractional derivative. We proved existence and uniqueness results for the solution of the inverse problem while over‐specified datum at 2 different time is given. The over‐specified datum at 2 time allows us to avoid initial condition in terms of fractional integral associated with Hilfer fractional derivative.

The Einstein–Boltzmann equations revisited

The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed investigation of its mathematical properties. For this purpose, we focus on a simplified set of equations aimed at describing the broad features of the matter power spectrum. We first perform an eigenvalue analysis and study the onset of oscillations in the system signaled by the transition from real to complex eigenvalues. We then provide a stability criterion of different numerical schemes for this linear system and estimate the associated step-size. We elucidate the stiffness property of the Einstein-Boltzmann system and show how it can be characterized in terms of the eigenvalues. While the parameters of the system are time dependent making it non-autonomous, we define an adiabatic regime where the parameters vary slowly enough for the system to be quasi-autonomous. We summarize the different regimes of the system for these different criteria as function of wave number $k$ and scale factor $a$. We also provide a compendium of analytic solutions for all perturbation variables in 6 limits on the $k$-$a$ plane and express them explicitly in terms of initial conditions. These results are aimed to help the further development and testing of numerical cosmological Boltzmann solvers.

The effectiveness of TiO2 additions to mortar to maintain initial conditions in terms of its reflectance to solar radiation

Abstract Contact of facades with degradation agents and direct incidence of ultraviolet radiation on external coatings make them more opaque over time, affecting their colour and reflectance characteristics. This study evaluated the effect of adding different TiO2 contents to mortars applied in concrete substrates in order to verify the reflectance maintenance on surfaces after exposure over time. Mortar with different concentrations of TiO2 (1%, 5%, 10%) were produced in relation to the total dry premix, added as a powder and compared to unpainted mortar without TiO2 (type "A") and painted mortar without TiO2 (type "B"), both used as a reference for colour and reflectance. Exposed over 16 months to climate conditions in São Paulo, regarding the maintenance of reflectance and solar radiation, the results showed that type "B" (0%TiO2) painted mortar presented the best performance. Type "C" (1%TiO2) and type "D" (5%TiO2) unpainted mortar remained more stable. Type "A" (0%TiO2) and type "E" (10%TiO2) unpainted mortar showed greater differences according to the Just Noticeable Difference (JND) range caused by dirt pick up.

Adaptive Disturbance-Based High-Order Sliding-Mode Control for Hypersonic-Entry Vehicles

In this paper, an adaptive, disturbance-based sliding-mode controller for hypersonic-entry vehicles is proposed. The scheme is based on high-order sliding-mode theory, and is coupled to an extended sliding-mode observer, able to reconstruct online the disturbances. The result is a numerically stable control scheme, able to adapt online to reduce the error in the presence of multiple uncertainties. The transformation of a high-order sliding-mode technique into an adaptive law by using the extended sliding-mode observer is, together with the multi-input/multi-output formulation for hypersonic-entry vehicles, the main contribution of this paper. The robustness is verified with respect to perturbations in terms of initial conditions, atmospheric density variations, as well as mass and aerodynamic uncertainties. Results show that the approach is valid, leading to an accurate disturbance reconstruction, to a better transient, and to good tracking performance, improved of about 50% in terms of altitude and range errors with respect to the corresponding standard sliding-mode-control approach.