Standard Initial Conditions Research Articles

Regulating star formation in a magnetized disc galaxy

ABSTRACT We use high-resolution magnetohydrodynamic simulations of isolated disc galaxies to investigate the co-evolution of magnetic fields with a self-regulated, star-forming interstellar medium (ISM). The simulations are conducted using the ramses adaptive mesh refinement code on the standard agora initial condition, with gas cooling, star formation, and feedback. We run galaxies with a variety of initial magnetic field strengths. The fields evolve and achieve approximate saturation within 500 Myr, but at different levels. The galaxies reach a quasi-steady state, with slowly declining star formation due to both gas consumption and increase in the field strength at intermediate ISM densities. We connect this behaviour to differences in the gas properties and overall structure of the galaxies. Stronger magnetic fields limit supernova bubble sizes. Different cases support the ISM using varying combinations of magnetic pressure, turbulence, and thermal energy. Initially, $\gtrsim\!\! 1\ \mu \mathrm{ G}$ magnetic fields evolve modestly and dominate support at all radii. Conversely, initially weaker fields grow through feedback and turbulence but never dominate the support. This is reflected in the stability of the gas disc. This interplay determines the overall distribution of star formation in each case. We conclude that an initially weak field can grow to produce a realistic model of a local disc galaxy, but starting with typically assumed field strengths ($\gtrsim\!\! 1\ \mu \mathrm{ G}$) will not.

Heating and Evaporation of Sessile Droplets: Simple and Advanced Models.

New advanced and simple two-dimensional (2D) models of sessile droplet heating and cooling and evaporation are suggested. In contrast to the earlier developed one-dimensional (1D) model, based on the assumption that heat supplied from the supporting surface is homogeneously and instantaneously spread throughout the droplet, both new 2D models consider the spatial distribution of this heat. The advanced 2D model is based on the numerical solution to the equations of conservation of mass, momentum, vapor mass fraction, and energy with standard boundary and initial conditions, using COMSOL Multiphysics code. Simple 2D and 1D models assume that droplets retain their truncated spherical shapes during the evaporation process. In the 1D model, the analytical solution to the 1D heat conduction equation inside the droplet is implemented into a numerical code. In the simple 2D model, the 2D version of this equation is solved numerically using COMSOL Multiphysics code. Droplet deformation, temperature gradients along the droplet surface, and the Marangoni effect are not considered in this model. The predictions of all three models are validated using in-house experimental data obtained from studies of sessile droplets of distilled water with initial volumes of 5.2, 3.2, and 2.2 μL, at an ambient temperature of 298.15 K, and at atmospheric pressure. The observed values of normalized droplet radii squared are shown to be close to those predicted by all three models. This allows us to recommend the application of the simplest 1D model for predicting this parameter. The time dependences of the droplet average surface temperature predicted by the advanced 2D model are shown to be close to those observed experimentally. The simple 2D and 1D models can correctly predict the initial rapid decrease in droplet average surface temperature followed by its gradual increase, in agreement with experimental data.

The Metastable State of Fermi–Pasta–Ulam–Tsingou Models

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan-Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a "metastable" state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi-Pasta-Ulam-Tsingou (FPUT) models. We treat both the α-FPUT and β-FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure-the spectral entropy (η)-and show that this measure has the power to quantify the distance from equipartition. For the α-FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state tm in the α-FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the P1-Q1 plane. Applying this procedure gives us a power-law scaling for tm, with the important result that the power laws for different system sizes collapse down to the same exponent as Eα2→0. We examine the energy spectrum E(k) over time in the α-FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the "wave turbulence" theory. We next apply a similar approach to the β-FPUT model. Here, we explore in particular the different behavior for the two different signs of β. Finally, we describe a procedure for calculating tm in the β-FPUT model, a very different task than for the α-FPUT model, because the β-FPUT model is not a truncation of an integrable nonlinear model.

Simple lessons from complex learning: what a neural network model learns about cosmic structure formation.

We train a neural network model to predict the full phase space evolution of cosmological N-body simulations. Its success implies that the neural network model is accurately approximating the Green's function expansion that relates the initial conditions of the simulations to its outcome at later times in the deeply nonlinear regime. We test the accuracy of this approximation by assessing its performance on well-understood simple cases that have either known exact solutions or well-understood expansions. These scenarios include spherical configurations, isolated plane waves, and two interacting plane waves: initial conditions that are very different from the Gaussian random fields used for training. We find our model generalizes well to these well-understood scenarios, demonstrating that the networks have inferred general physical principles and learned the nonlinear mode couplings from the complex, random Gaussian training data. These tests also provide a useful diagnostic for finding the model's strengths and weaknesses, and identifying strategies for model improvement. We also test the model on initial conditions that contain only transverse modes, a family of modes that differ not only in their phases but also in their evolution from the longitudinal growing modes used in the training set. When the network encounters these initial conditions that are orthogonal to the training set, the model fails completely. In addition to these simple configurations, we evaluate the model's predictions for the density, displacement, and momentum power spectra with standard initial conditions for N-body simulations. We compare these summary statistics against N-body results and an approximate, fast simulation method called COLA (COmoving Lagrangian Acceleration). Our model achieves percent level accuracy at nonlinear scales of , representing a significant improvement over COLA.

ЧИСЛЕННОЕ РЕШЕНИЕ НАЧАЛЬНО-КОНЕЧНОЙ ЗАДАЧИ ДЛЯ НЕСТАЦИОНАРНЫХ СИСТЕМ ЛЕОНТЬЕВСКОГО ТИПА

The main purpose of the paper is to prove the convergence of a numerical solution to a nonstationary Leontief-type system with an initial-final condition. Non-stationary Leontief-type systems are used in the study of dynamic balance models of the economy. Nonstationarity of systems is described using a scalar function, which is multiplied by one of the matrices of the system. The distinctive feature of Leontief-type systems is the matrix singularity at the derivative with time, which is due to the fact that some types of resources of economic systems cannot be stored. In the article, the initial-final condition is used instead of the standard initial condition, which for economic systems can be interpreted as taking into account indicators not only at the initial moment of time, but also indicators that will be achieved at the final moment of time. Previously, the solution of such a problem was studied and described using contour integrals. However, this type of solution is not very convenient for largedimensional systems, so this article proposes a description of the numerical solution without the use of contour integrals, and also examines the convergence of this numerical solution.

Complex Ginzburg-Landau equations with a delayed nonlocal perturbation

We consider an initial boundary value problem of the complex Ginzburg-Landau equation with some delayed feedback terms proposed for the control of chemical turbulence in reaction diffusion systems. We consider the equation in a bounded domain \(\Omega\subset\mathbb{R}^{N}\) (\(N\leq3\)), $$ \frac{\partial u}{\partial t}-(1+i\epsilon)\Delta u +(1+i\beta) | u| ^2u-(1-i\omega) u=F(u(x,t-\tau)) $$ for t>0, with $$ F(u(x,t-\tau)) =e^{i\chi_0}\big\{ \frac{\mu}{| \Omega| }\int_{\Omega}u(x,t-\tau) dx+\nu u(x,t-\tau) \big\} , $$ where \(\mu\), \(\nu\geq0\), \(\tau>0\) but the rest of real parameters \(\epsilon\), \(\beta\), \(\omega\) and \(\chi_0\) do not have a prescribed sign. We prove the existence and uniqueness of weak solutions of problem for a range of initial data and parameters. When \(\nu=0\) and \(\mu>0\) we prove that only the initial history of the integral on \(\Omega\) of the unknown on \((-\tau,0)\) and a standard initial condition at t=0 are required to determine univocally the existence of a solution. We prove several qualitative properties of solutions, such as the finite extinction time (or the zero exact controllability) and the finite speed of propagation, when the term \(|u| ^2u\) is replaced by \(|u| ^{m-1}u\), for some \(m\in(0,1)\). We extend to the delayed case some previous results in the literature of complex equations without any delay.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/40/abstr.html

Modified initial power spectrum and too big to fail problem

ABSTRACT The galactic scale challenges of dark matter such as ‘missing satellite’ problem and ‘too big to fail’ problem are the main caveats of standard model of cosmology. These challenges could be solved either by implementing the complicated baryonic physics or it could be considered as an indication to a new physics beyond the standard model of cosmology. The modification of collisionless dark matter models or the standard initial conditions are two promising venues for study. In this work, we investigate the effects of the deviations from scale invariant initial curvature power spectrum on number density of dark matter haloes. We develop the non-Markov extension of the excursion set theory to calculate the number density of dark matter substructures and dark matter halo progenitor mass distribution. We show that the plausible solution to ‘too big to fail’ problem could be obtained by a Gaussian excess in initial power in the scales of k* ∼ 3 h Mpc−1 that is related to the mass scale of M* ∼ 1011 M⊙. We show that this deviation leads to the decrement of dark matter subhaloes in galactic scale, which is consistent with the current status of the non-linear power spectrum. Our proposal also has a prediction that the number density of Milky Way-type galaxies must be higher than the standard case.

English

This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $$\{P_i\}=_{i=1}^\infty$$ generated by a three-term recurrence relation Pi(x) + Q1(x)Pi−1(x) + Q2(x)Pi−2(x) = 0 with the standard initial conditions P0(x) = 1, P−1(x) = 0, where Q1(x) and Q2(x) are arbitrary real polynomials.

Normal-mode-based theory of collisionless plasma waves

The Van Kampen normal-mode method is applied in a comprehensive study of the linear wave perturbations of a homogeneous, magnetized and finite-temperature plasma, described by the collisionless Vlasov–Maxwell system in its non-relativistic version. The analysis considers a stable, Maxwellian background, but is otherwise completely general in that it allows for arbitrary wave propagation direction relative to the equilibrium magnetic field, multiple plasma species and general polarization states of the perturbed electromagnetic fields. A convenient formulation is introduced whereby the generator of the time advance is a Hermitian operator, analogous to the Hamiltonian in the Schrödinger equation of quantum mechanics. This guarantees a real frequency spectrum and complete bases of normal modes. Expansions in these normal-mode bases yield immediately the solutions of initial-value problems for general initial conditions. With standard initial conditions and propagation direction parallel to the equilibrium magnetic field, all the familiar results obtained following Landau’s Laplace transform approach are recovered. Considering such parallel propagation, the present work shows also explicitly and provides an example of how to construct special initial conditions that result in different, damped but otherwise arbitrarily prescribed time variations of the macroscopic variables. The known dispersion relations for perpendicular propagation are also recovered.

On the structure of linear dislocation field theory

Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is illustrated by a specific example that clarifies the use of the plasticity formulation in the study of classical dislocation theory. Stationary, quasi-static, and dynamical problems for continuous dislocation distributions are investigated subject not only to standard boundary and initial conditions, but also to prescribed dislocation density. In particular, the dislocation density field can represent a single dislocation line.It is only in the static and quasi-static traction boundary value problems that such data are sufficient for the unique determination of stress. In other quasi-static boundary value problems and problems involving moving dislocations, the plastic and elastic distortion tensors, total displacement, and stress are in general non-unique for specified dislocation density. The conclusions are confirmed by the example of a single screw dislocation.

Refinement of two-dimensional electrophoresis for vitreous proteome profiling using an artificial neural network.

Despite technological advances, two-dimensional electrophoresis (2DE) of biological fluids, such as vitreous, remains a major challenge. In this study, artificial neural network was applied to optimize the recovery of vitreous proteins and its detection by 2DE analysis through the combination of several solubilizing agents (CHAPS, Genapol, DTT, IPG buffer), temperature, and total voltage. The highest protein recovery (94.9% ± 4.5) was achieved using 4% (w/v) CHAPS, 0.1% (v/v) Genapol, 20mM DTT, and 2% (v/v) IPG buffer. Two iterations were required to achieve an optimized response (580 spots) using 4% (w/v) CHAPS, 0.2% (v/v) Genapol, 60mM DTT, and 0.5% (v/v) IPG buffer at 35kVh and 25°C, representing a 2.4-fold improvement over the standard initial conditions of the experimental design. The analysis of depleted vitreous using the optimized protocol resulted in an additional 1.3-fold increment in protein detection over the optimal output, with an average of 761 spots detected in vitreous from different vitreoretinopathies. Our results clearly indicate the importance of combining the appropriate amount of solubilizing agents with a suitable control of the temperature and voltage to obtain high-quality gels. The high-throughput of this model provides an effective starting point for the optimization of 2DE protocols. This experimental design can be adapted to other types of matrices. Graphical abstract.

Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations

We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the solution is specified at an initial moment of time). We then show how our method applies in fluid mechanics. More specifically, we present a complete solution to the problem of long waves run-up in inclined bays of arbitrary shape with nonzero initial velocity.

Solution to the Initial-Final Value Problem for a Non-Stationary Leontief Type System

The article is devoted to the construction of a solution to the initial-final value problem for a non-stationary Leontief type system. Such systems take place in dynamic balance models of the economy. A distinctive feature of Leontief type systems is the degeneracy of the matrix at the time derivative, due to the fact that some types of resources of economic systems cannot be stored. In addition, dynamic balance systems of the economy are often described using time-dependent coefficients. We use resolving streams of matrices to construct solutions for such systems. In addition, the initial-final value condition is used instead of the standard initial condition. For economic systems, the initial-final value condition can be interpreted as taking into account not only indicators at the initial moment of time, but also indicators that are achieved at the final moment of time.

Black hole formation from the gravitational collapse of a nonspherical network of structures

We examine the gravitational collapse and black hole formation of multiple non--spherical configurations constructed from Szekeres dust models with positive spatial curvature that smoothly match to a Schwarzschild exterior. These configurations are made of an almost spherical central core region surrounded by a network of "pancake-like" overdensities and voids with spatial positions prescribed through standard initial conditions. We show that a full collapse into a focusing singularity, without shell crossings appearing before the formation of an apparent horizon, is not possible unless the full configuration becomes exactly or almost spherical. Seeking for black hole formation, we demand that shell crossings are covered by the apparent horizon. This requires very special fine-tuned initial conditions that impose very strong and unrealistic constraints on the total black hole mass and full collapse time. As a consequence, non-spherical non-rotating dust sources cannot furnish even minimally realistic toy models of black hole formation at astrophysical scales: demanding realistic collapse time scales yields huge unrealistic black hole masses, while simulations of typical astrophysical black hole masses collapse in unrealistically small times. We note, however, that the resulting time--mass constraint is compatible with early Universe models of primordial black hole formation, suitable in early dust-like environments. Finally, we argue that the shell crossings appearing when non-spherical dust structures collapse are an indicator that such structures do not form galactic mass black holes but virialise into stable stationary objects.

Constraints from Dust Mass and Mass Accretion Rate Measurements on Angular Momentum Transport in Protoplanetary Disks

Abstract In this paper, we investigate the relation between disk mass and mass accretion rate to constrain the mechanism of angular momentum transport in protoplanetary disks. We find a correlation between dust disk mass and mass accretion rate in Chamaeleon I with a slope that is close to linear, similar to the one recently identified in Lupus. We investigate the effect of stellar mass and find that the intrinsic scatter around the best-fit – and – relations is uncorrelated. We simulate synthetic observations of an ensemble of evolving disks using a Monte Carlo approach and find that disks with a constant α viscosity can fit the observed relations between dust mass, mass accretion rate, and stellar mass but overpredict the strength of the correlation between disk mass and mass accretion rate when using standard initial conditions. We find two possible solutions. In the first one, the observed scatter in and is not primordial, but arises from additional physical processes or uncertainties in estimating the disk gas mass. Most likely grain growth and radial drift affect the observable dust mass, while variability on large timescales affects the mass accretion rates. In the second scenario, the observed scatter is primordial, but disks have not evolved substantially at the age of Lupus and Chamaeleon I owing to a low viscosity or a large initial disk radius. More accurate estimates of the disk mass and gas disk sizes in a large sample of protoplanetary disks, through either direct observations of the gas or spatially resolved multiwavelength observations of the dust with ALMA, are needed to discriminate between both scenarios or to constrain alternative angular momentum transport mechanisms such as MHD disk winds.

Impact of early stage non-equilibrium dynamics on photon production in relativistic heavy ion collisions

In this study we discuss our results on the spectrum of photons emitted from the quark-gluon plasma produced in heavy ion collisions at RHIC energies. Simulating the space-time evolution of the fireball by solving the relativistic Boltzmann transport equation and including two-particle scattering processes with photon emission allows us to make a first step in the description of thermal photons from the QGP as well as of those produced in the pre-equilibrium stage. Indeed, we consider not only a standard Glauber initial condition but also a model in which quarks and gluons are produced in the very early stage through the Schwinger mechanism by the decay of an initial color-electric field. In the latter approach relativistic kinetic equations are coupled in a self-consistent way to field equations. We aim at spotting the impact of early stage non-equilibrium dynamics on the photon production.

Order and chaos in the one-dimensional ϕ4 model: N-dependence and the Second Law of Thermodynamics

We revisit the equilibrium one-dimensional ϕ4 model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit positive Lyapunov exponents! The periodic orbits confine every particle in a periodic chain to trace out either the same or a mirror-image trajectory in its two-dimensional phase space. These “computationally stable” sets of pairs of single-particle orbits are either symmetric or antisymmetric to the very last computational bit. In such a periodic chain the odd-numbered and even-numbered particles’ coordinates and momenta are either identical or differ only in sign. “Positive Lyapunov exponents” can and do result if an infinitesimal perturbation breaking a perfect two-dimensional antisymmetry is introduced so that the motion expands into a four-dimensional phase space. In that extended space a positive exponent results.We formulate a standard initial condition for the investigation of the microcanonical chaotic number dependence of the model. We speculate on the uniqueness of the model’s chaotic sea and on the connection of such collections of deterministic and time-reversible states to the Second Law of Thermodynamics.

Mathematical modelling of fractional order circuit elements and bioimpedance applications

In this work a classical derivation of fractional order circuits models is presented. Generalised constitutive equations in terms of fractional Riemann–Liouville derivatives are introduced in the Maxwell’s equations for each circuit element. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. It is shown that from basic properties of Fractional Calculus, a fractional differential equation model with Caputo derivatives is obtained. Thus standard initial conditions apply. Finally, models for bioimpedance are revisited.

Effect of gaseous oxidizer composition on the detonability of isooctane–air sprays

Experimental and numerical study of the detonation has been conducted in heterogeneous reactive two-phase media made of liquid isooctane sprays dispersed in gaseous oxidizing atmospheres. Influence of the oxidizer composition on conditions of detonation formation and propagation regimes, with particular attention on the existence of the so-called cellular structure, has been studied.Experiments have been performed under standard initial conditions of temperature and pressure (293 K, 1 bar) in a 4-m long vertical, square cross-section (53 × 53 mm2) detonation tube. The mean isooctane droplet size was of about 30 µm. When oxidizing mixture was made of air (O2 + βN2 with β = 3.76), three detonation regimes have been observed with increasing equivalence ratio: a spinning regime, a marginal one with half a cell structure, and a normal multi-headed detonation regime. At smaller dilution ratio (β = 2 and 1), only the multi-headed detonation regime was observed, with smaller cell size. When nitrogen is replaced by argon as inert diluent, the detonation structure is multi-headed; the cellular structure is more regular and the cell size is smaller than with nitrogen.Numerical simulations have been performed with the EFAE code, with taking in consideration the chemical composition of the oxidizing phase and the effects of the two-phase mixture richness. Results of 2D and 3D numerical simulations, as a function of the equivalence ratio and the dilution, display propagation regimes and detonation cell sizes in reasonable agreement with the experimental results.

Regularity for a generalized jeffrey's integral model for viscoelastic fluids

We prove a local existence of a strong solution υ: Ω × T → R3 for a system of nonlinear integrodifferential equations describing motion of an incompressible viscoelastic fluid using standard mathematical tools. The problem is considered in a bounded, smooth domain Ω R3 with a Dirichlet boundary condition and a standard initial condition.