Search Results (15)

This study introduces a novel methodology for assessing ice-jam flood hazards along river channels. It employs empirical equations that relate non-dimensional ice-jam stage to discharge, enabling the generation of an ensemble of longitudinal profiles of ice-jam backwater levels through Monte-Carlo simulations. These simulations produce non-exceedance probability profiles, which indicate the likelihood of various flood levels occurring due to ice jams. The flood levels associated with specific return periods were validated using historical gauge records. The empirical equations require input parameters such as channel width, slope, and thalweg elevation, which were obtained from bathymetric surveys. This approach is applied to assess ice-jam flood hazards by extrapolating data from a gauged reach at Fort Simpson to an ungauged reach at Jean Marie River along the Mackenzie River in Canada’s Northwest Territories. The analysis further suggests that climate change is likely to increase the severity of ice-jam flood hazards in both reaches by the end of the century. This methodology is applicable to other cold-region rivers in Canada and northern Europe, provided similar fluvial geomorphological and hydro-meteorological data are available, making it a valuable tool for ice-jam flood risk assessment in other ungauged areas. Full article

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. Full article

We present a new perspective on the symmetries that govern the formation of large-scale structures across the Universe, particularly focusing on the transition from the seeds of galaxy clusters to the seeds of galaxies themselves. We address two main features of cosmological fluid dynamics pertaining to both the linear and non-linear regimes. The linear dynamics of cosmological perturbations within the Hubble horizon is characterized by the Jeans length, which separates stable configurations from unstable fluctuations due to the gravitational effect on sufficiently large (and therefore, massive enough) overdensities. On the other hand, the non-linear dynamics of the cosmological fluid is associated with a turbulent behavior once the Reynolds numbers reach a sufficiently high level. This turbulent regime leads to energy dissipation across smaller and smaller scales, resulting in a fractal distribution of eddies throughout physical space. The proposed scenario suggests that the spatial scale of eddy formation is associated with the Jeans length of various levels of fragmentation from an original large-scale structure. By focusing on the fragmentation of galaxy cluster seeds versus galaxy seeds, we arrived at a phenomenological law that links the ratio of the two structure densities to the number of galaxies in each cluster and to the Hausdorff number of the Universe matter distribution. Finally, we introduced a primordial magnetic field and studied its influence on the Jeans length dynamics. The resulting anisotropic behavior of the density contrast led us to infer that the main features of the turbulence could be reduced to a 2D Euler equation. Numerical simulations showed that the two lowest wavenumbers contained the major energy contribution of the spectrum. Full article

In this paper, we introduce the “Walk on Equations” (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method is particularly effective for large matrices, both real- and complex-valued, and shows significant improvements over traditional methods. Our comprehensive comparison with the Gauss–Seidel method highlights the WE algorithm’s superior performance, especially in reducing relative errors within fewer iterations. We also introduce a unique dominancy number, which plays a crucial role in the algorithm’s efficiency. A pivotal outcome of our research is the convergence theorem we established for the WE algorithm, demonstrating its optimized performance through a balanced iteration matrix. Furthermore, we incorporated a sequential Monte Carlo method, enhancing the algorithm’s efficacy. The most-notable application of our algorithm is in solving a large system derived from a finite-element approximation in constructive mechanics, specifically for a beam structure problem. Our findings reveal that the proposed WE Monte Carlo algorithm, especially when combined with sequential MC, converges significantly faster than well-known deterministic iterative methods such as the Jacobi method. This enhanced convergence is more pronounced in larger matrices. Additionally, our comparative analysis with the preconditioned conjugate gradient (PCG) method shows that the WE MC method can outperform traditional methods for certain matrices. The introduction of a new random variable as an unbiased estimator of the solution vector and the analysis of the relative stochastic error structure further illustrate the potential of our novel algorithm in computational mathematics. Full article

In this article, we apply the formalism of (classical) Extended Irreversible Thermodynamics (EIT) to the dynamics of density fluctuations for a self-gravitating fluid in a static Universe, considering only bulk viscosity. The problem is characterized by gravitational instability, for which the Jeans criterion is shown to hold. However, both the relaxation time in the constitutive equation and the viscosity itself affect the behavior of both stable and unstable modes. In particular, the stable scenario features three modes, two of them corresponding to damped oscillations which decay faster that in the CIT scene. The third mode, inexistent in the CIT, corresponds to a very quickly decaying mode. In the unstable case, growing modes are observed in both EIT and CIT theories, for which the slowest growth is the one predicted by the CIT theory followed by the EIT, while the non-dissipative case corresponds to the fastest one. Full article

The general idea of this paper is to study the effect of mass variation of a test particle on periodic orbits in the restricted three-body model. In the circular restricted three-body problem (cr3bp), two bigger bodies (known as primary and secondary or sometime only primaries) are placed at either side of the origin on abscissa while moving in circular orbits around their common center of mass (here origin), while the third body (known as smallest body or infinitesimal body or test particle) is moving in space and varies its mass according to Jeans law. Using the Lindstedt–Poincaré method, we determine equations of motion and their solutions under various perturbations. The time-series and halo orbits around one of the collinear critical points of this model are drawn under the effects of the solar radiation pressure of the primary and the oblateness of the secondary. In general, these two dynamical properties are symmetrical. Full article

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as “Lie group thermodynamics” then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau’s cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain’s PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain’s works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie–Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation. Full article

The predicted size of dark matter substructures in kilo-parsec scales is model-dependent. Therefore, if the correlations between dark matter mass densities as a function of the distances between them are measured via observations, we can scrutinize dark matter scenarios. In this paper, we present an assessment procedure of dark matter scenarios. First, we use Gaia’s data to infer the single-body phase-space density of the stars in the Fornax dwarf spheroidal galaxy. The latter, together with the Jeans equation, after eliminating the gravitational potential using the Poisson equation, reveals the mass density of dark matter as a function of its position in the galaxy. We derive the correlations between dark matter mass densities as a function of distances between them. No statistically significant correlation is observed. Second, for the sake of comparison with the standard cold dark matter, we also compute the correlations between dark matter mass densities in a small halo of the Eagle hydrodynamics simulation. We show that the correlations from the simulation and from Gaia are in agreement. Third, we show that Gaia observations can be used to limit the parameter space of the Ginzburg–Landau statistical field theory of dark matter mass densities and subsequently shrink the parameter space of any dark matter model. As two examples, we show how to leave limitations on (i) a classic gas dark matter and (ii) a superfluid dark matter. Full article

The post-Newtonian Jeans equation for stationary self-gravitating systems is derived from the post-Newtonian Boltzmann equation in spherical coordinates. The Jeans equation is coupled with the three Poisson equations from the post-Newtonian theory. The Poisson equations are functions of the energy-momentum tensor components which are determined from the post-Newtonian Maxwell–Jüttner distribution function. As an application, the effect of a central massive black hole on the velocity dispersion profile of the host galaxy is investigated and the influence of the post-Newtonian corrections are determined. Full article

This paper uses the Kolmogorov–Smirnov test to perform a fitting analysis on the mass data of Saturn’s regular moons and found that the lognormal distribution is its best-fitting distribution with an extremely high p-value of 0.9889. Moreover, novel dynamic equations for the variable-mass restricted three-body problem are established based on the newly discovered distribution of mass data, rather than the empirical Jeans’ law, and the Lindstedt–Poincaré perturbation method was used to give the approximate analytical periodic orbits near the Lagrangian point $L_3$. Furthermore, this paper also discusses the influence of the three-body gravitational interaction parameter, the variable-mass parameter of the third body, and the scale parameter in the statistical results on the periodic orbits and the position of the Lagrangian point $L_3$ through numerical simulation. Full article

I deal with an alienation problem for the system of two fundamental Cauchy functional equations with an unknown function f mapping a ring X into an integral domain Y and preserving binary operations of addition and multiplication, respectively. The resulting syzygies obtained by adding (resp. multiplying) these two equations side by side are discussed. The first of these two syzygies was first examined by Jean Dhombres in 1988 who proved that under some additional conditions concering the domain and range rings it forces f to be a ring homomorphism (alienation phenomenon). The novelty of the present paper is to look for sufficient conditions upon f solving the other syzygy to be alien. Full article

This paper considers the Schrödinger–Newton (SN) equation with a Yukawa potential, introducing the effect of locality. We also include the interaction of the self-gravitating quantum matter with a radiation background, describing the effects due to the environment. Matter and radiation are coupled by photon scattering processes and radiation pressure. We apply this extended SN model to the study of Jeans instability and gravitational collapse. We show that the instability thresholds and growth rates are modified by the presence of an environment. The Yukawa scale length is more relevant for large-scale density perturbations, while the quantum effects become more relevant at small scales. Furthermore, coupling with the radiation environment modifies the character of the instability and leads to the appearance of two distinct instability regimes: one, where both matter and radiation collapse together, and others where regions of larger radiation intensity coincide with regions of lower matter density. This could explain the formation of radiation bubbles and voids of matter. The present work extends the SN model in new directions and could be relevant to astrophysical and cosmological phenomena, as well as to laboratory experiments simulating quantum gravity. Full article

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study. Full article

In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the $SL\left(2R\right)$ type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved. Full article

A reliability approach referred to as the point estimate method (PEM) is presented to assess the uncertainty of a two-dimensional hydraulic model. PEM is a special case of numerical quadrature based on orthogonal polynomials, which evaluates the statistical moments of a performance function involving random variables. When applied to hydraulic problems, the variables are the inputs to the hydraulic model, and the first and second statistical moments refer to the mean and standard deviation of the model’s output. In providing approximate estimates of the uncertainty, PEM appears considerably simpler and requires less information and fewer runs than standard Monte Carlo methods. An example of uncertainty assessment is shown for simulated water depths in a 46 km reach of the Richelieu River, Canada. The 2D hydraulic model, H2D2, was used to solve the shallow water equations. Standard deviations around the mean water depths were estimated by considering the uncertainties of three main input variables: flow rate, Manning’s coefficient and topography. Results indicate that the mean standard deviation is <27 cm for the considered flow rates of 759, 824, 936, 1113 ${\mathrm{m}}^3/\mathrm{s}$ . Higher standard deviations were obtained upstream of the topographic shoal at the municipality of Saint-Jean-sur-Richelieu. The PEM method adds further value to the H2D2 model predictions as it indicates the magnitude and the spatial variation in uncertainties. The effort required to complete an uncertainty analysis using the PEM method is minimal and the resulting insight is meaningful. This knowledge should be incorporated into decision-making in the context of flood risk assessment. Full article