Infinite Density Research Articles

Эзотерический подход к экспликации понятий страдания, объективированной воли (эго) и имманентной целенаправленности с позиции концептуальной идеи об эволюционной каузальной финалистичности

This study endeavors to explicate and elucidate, from an esoteric perspective, the potential, prospective, and functional content of such phenomena as suffering, objectified will (with the ego representing the referent of the psychic structure of the subject), and immanent teleology. Drawing upon the philosophical perspectives on suffering and objectified will by German philosopher A. Schopenhauer, as well as referencing the esoteric teachings of American philosopher-mystic F. Merrell-Wolff, the philosophical views on human existence by J.-P. Sartre, the spiritual concepts of Canadian psychologist E. Tolle, and the arguments posited by Aristotle in favor of the existence of a final cause, the study aims to analyze these phenomena. An attempt is made to demonstrate the interconnectedness between the claims of the objectified will, as discussed in philosophical discourse, and the ideas of theoretical physicist S. Hawking in the field of physical sciences, particularly in the evolutionary development of the universe. Through the discourse, immanent teleology, manifested in life itself as an inclination towards eternal peace, is asserted as an a priori form of understanding the world of phenomenal spatiotemporal multiplicity. In contrast, the objectified will strives for the identity of infinite energy density through possession, sole proprietary ownership, and governance over the objects of the universe. These dual directions culminate in liberation through the overcoming or destruction of enslavement, ultimately leading to the annulment of time and space.

Thermodynamically consistent flocking: from discontinuous to continuous transitions

We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C, and that it generically exhibits tricritical behavior. Self-propulsion has a non-perturbative effect on the phase diagram, yielding novel phase behaviors depending on the type of aligning interactions. For aligning interaction that increase monotonically with the density, the tricritical point diverges to infinite density reproducing the standard scenario of a discontinuous flocking transition accompanied by traveling bands. In contrast, for models where the aligning interaction is non-monotonic in density, the system can exhibit either (the nonequilibrium counterpart of) an azeotropic point, associated with a continuous flocking transition, or a state with counterpropagating bands.

Distribution in homology classes and discrete fractal dimension

In this note, we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.

Dynamical analysis of a hyperbolic solution in scale-covariant theory

In this paper, we study an isotropic flat FLRW-model in scale-covariant theory of gravity [Formula: see text] 1 which is explained in terms of ordinary and covariant differentiation of scalar field [Formula: see text]. As we know, the deceleration parameter (DP) is time-dependent, so we consider the DP q as the function of t. Using this methodology, we find all the important cosmological factors in terms of a hyperbolic function of the cosmic time t. In turn, we create the model having the behavior of the late-time universe, which is ever accelerated expanding and faces a Big Freeze at the end. The model shows the quintessence dark energy model from early to late times. We compute the constrained values of Hubble parameter [Formula: see text] and the model parameter [Formula: see text] using joint analysis of the OHD data of 77-points and Pantheon bin data. The model exhibits point-type singularity as it begins with a point of zero volume, infinite energy density and temperature. Furthermore, we obtain the present value of DP [Formula: see text]. Also, we examine the ultimate behavior of our model by the proper analysis of energy conditions (ECs), cosmographical parameters and Statefinder diagnostic. Finally, the proposed model behaves like a quintessence dark energy model.

Transition to anomalous dynamics in a simple random map.

The famous doubling map (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one, hence expanding, with a positive Lyapunov exponent and a uniform invariant density. If the slope is less than one, the map becomes contracting, the Lyapunov exponent is negative, and the density trivially collapses onto a fixed point. Sampling from these two different types of maps at each time step by randomly selecting the expanding one with probability p, and the contracting one with probability 1-p, gives a prototype of a random dynamical system. Here, we calculate the invariant density of this simple random map, as well as its position autocorrelation function, analytically and numerically under variation of p. We find that the map exhibits a non-trivial transition from fully chaotic to completely regular dynamics by generating a long-time anomalous dynamics at a critical sampling probability pc, defined by a zero Lyapunov exponent. This anomalous dynamics is characterized by an infinite invariant density, weak ergodicity breaking, and power-law correlation decay.

The formation and evolution of black holes

The concept of Black Holes was first introduced as a prediction by Eisteins Theory of General Relativity and later solved by the Schwarzschild Solution in 1915. A point of mass to great that the bend in space time as a result doesnt allow even light to escape its gravitational pull within the Event Horizon, a point of infinite density and a point at which the laws of time break down. Formation of Black Holes are of interest in many fields of not only Astrophysics but the Physics as a whole. For example it can tell us about the structure and rotation of galaxies which in turn reveals properties of Dark Matter while features such as Hawking Radiation help to further link the world of quantum mechanics to Eisteins Theory of General Relativity. Stellar Black Holes are the remains of enormous stars which has collapsed after running out of fuel for nuclear fusion to continue. These objects can be found throughout the galaxy but most importantly at the center of each galaxy lies a Supermassive Black Hole such as Sagittarius A* at the centre of the Milky Way which has a massive of 4.6 million solar masses, the process by which these Supermassive Black Holes form remain unknown till this day. Black Holes have been notoriously hard to detect due to the fact that they cannot be seen and only through the analysis of orbits of objects around it can its properties like mass be determined. Their mystical nature is exactly why Black Holes draw so much interest within the Astrophysics community today. The formation of such large celestial objects has been debated among Physicists for decades and this paper aims to review current understandings and existing research on the formation of Black Holes to provide an overview on the collapse of stars and the processes with which the core may evolve into a black hole.

Schwarzschild Black Holes in Extended Spacetime with Two Time Dimensions

Black holes are one of the most extreme phenomena in the Universe, bridging the gap between the realms of general relativity and quantum physics. Any matter that crosses the event horizon moves towards the core of the black hole, creating a singularity with infinite mass density—a phenomenon that cannot be comprehended within present theories of relativity and quantum physics. In this study, we undertake an investigation of non-rotating, non-charged Schwarzschild black holes in an extended spacetime framework with two time dimensions. To accomplish this, we extend Einstein’s field equations by one more temporal dimension. We solve the corresponding equations for a spherical central mass, which leads to an Abel-type equation for the 5D Schwarzschild metric. By exploring distinct solution classes, we present an approximate solution for the 5D metric. Our proposed solution maintains consistency with Schwarzschild’s 4D solution. Finally, we address the central black hole singularity and demonstrate a potential breakthrough, as our solution effectively avoids the singularity quandary, providing valuable insight into the fundamental properties of black holes in this augmented framework.

The dynamical analysis of a parameterized dark energy cosmological model in the f(R,G) gravity

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] both signify the Ricci scalar and Gauss–Bonnet invariant. Furthermore, in order to determine the model’s behavior, it must have the late-time universe’s behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor [Formula: see text]. The model’s actions are accelerating and expanding at the moment, and [Formula: see text]CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology [Formula: see text]CDM in late times.

Asynchronous Hyperbolic UWB Source-Localization and Self-Localization for Indoor Tracking and Navigation

Hyperbolic localization measures the time difference of arrivals (TDOAs) of signals to determine the location of a wireless source or receiver. Traditional methods depend on precise clock synchronization between nodes so that time measurements from independent devices can be meaningfully compared. Imperfect synchronization is often the dominant source of error. We propose two new message based TDOA equations for hyperbolic localization which require no synchronization and meet or exceed state-of-the-art accuracy. Our approaches leverage anchor nodes that observe each other’s packet arrival times and a novel reformulation of the TDOA equation to reduce the effect of clock drift error. Closed-form equations are derived for computing TDOA in both self-localization and source-localization modes of operation along with bounds on maximum clock drift error. Three experiments are performed including a clock drift simulation, a non-line-of-sight (NLOS) simulation, and an indoor validation experiment on custom ultra wideband (UWB) hardware all of which involved eight anchor nodes and one localizing node in a 128m3 capture volume. Our source-localization approach achieved unprecedented accuracy with lower cost equipment and trivial setup. Our self-localization matched state-of-the art accuracy but with infinite scalability and high privacy. These results could enable economical and infinite density indoor navigation and dramatically reduce the economic cost and increase the accuracy of implementing industrial and commercial tracking applications.

Fisher information and its extensions based on infinite mixture density functions

In this work, we consider the Fisher information and some of its well-known extended versions and then establish some results based on infinite mixture density functions for the proposed information measures. Specifically we introduce the Jensen-type of Fisher information (parametric-type and density-based) and generalized Fisher information measures based on infinite mixture density functions. We then show that the proposed Jensen–Fisher information measure have two representations in terms of Fisher information distance in the both parametric-type and density-based cases. We have further shown that the generalized Fisher information of an infinite mixture density can be stated based on Pearson–Vajda χk divergence. Finally, we examine the convexity property of q−Fisher information measure based on finite mixture density functions under a mild condition. Some examples related to scale mixture of skew-normal family of distributions, with emphasis on skew-normal density, are illustrated within the paper.

Non-Abelian anyons with Rydberg atoms

We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant quantum computing, have not been generated. To generate anyons with non-Abelian braiding statistics, we consider systems with mixed-boundary punctures. We obtain the topologically distinct ground states of the system numerically using the infinite Density Matrix Renormalization Group technique. We discuss how these topological states can be created using ancilla atoms of a different type. We show that a system with $2N+2$ punctures and an equal number of ancilla atoms leads to $N$ logical qubits whose Hilbert space is determined by a set of stabilizing conditions on the ancilla atoms. Quantum gates can be implemented using a set of gates acting on the ancilla atoms that commute with the stabilizers and realize the braiding group of non-Abelian Ising anyons.

Plaquette valence bond state in the spin- 12 J1−J2 XY model on the square lattice

We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at ${J}_{2}/{J}_{1}<0.50$ and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.

Bubble–particle collisions in turbulence: insights from point-particle simulations

Bubble–particle collisions in turbulence are central to a variety of processes such as froth flotation. Despite their importance, details of the collision process have not received much attention yet. This is compounded by the sometimes counter-intuitive behaviour of bubbles and particles in turbulence, as exemplified by the fact that they segregate in space. Although bubble–particle relative behaviour is fundamentally different from that of identical particles, the existing theoretical models are nearly all extensions of theories for particle–particle collisions in turbulence. The adequacy of these theories has yet to be assessed as appropriate data remain scarce to date. In this investigation, we study the geometric collision rate by means of direct numerical simulations of bubble–particle collisions in homogeneous isotropic turbulence using the point-particle approach over a range of the relevant parameters, including the Stokes and Reynolds numbers. We analyse the spatial distribution of bubble and particles, and quantify to what extent their segregation reduces the collision rate. This effect is countered by increased approach velocities for bubble–particle compared to monodisperse pairs, which we relate to the difference in how bubbles and particles respond to fluid accelerations. We found that in the investigated parameter range, these collision statistics are not altered significantly by the inclusion of a lift force or different drag parametrisations, or when assuming infinite particle density. Furthermore, we critically examine existing models and discuss inconsistencies therein that contribute to the discrepancy.

Brillouin propagation modes of cold atoms undergoing Sisyphus cooling.

An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equationsfor the phase space densities of the Zeeman ground-state sublevels. The calculations are for a J_{g}=1/2→J_{e}=3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.

A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement

Fidelity plays an important role in quantum information processing, which provides a basic scale for comparing two quantum states. At present, one of the most commonly used fidelities is Uhlmann-Jozsa (U-J) fidelity. However, U-J fidelity needs to calculate the square root of the matrix, which is not trivial in the case of large or infinite density matrices. Moreover, U-J fidelity is a measure of overlap, which has limitations in some cases and cannot reflect the similarity between quantum states well. Therefore, a novel quantum fidelity measure called quantum Tanimoto coefficient (QTC) fidelity is proposed in this paper. Unlike other existing fidelities, QTC fidelity not only considers the overlap between quantum states, but also takes into account the separation between quantum states for the first time, which leads to a better performance of measure. Specifically, we discuss the properties of the proposed QTC fidelity. QTC fidelity is compared with some existing fidelities through specific examples, which reflects the effectiveness and advantages of QTC fidelity. In addition, based on the QTC fidelity, three discrimination coefficients d <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QTC</sup> , d <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QTC</sup> , and d <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QTC</sup> are defined to measure the difference between quantum states. It is proved that the discrimination coefficient d <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QTC</sup> is a true metric. Finally, we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.

Infinite density matrix renormalization group method for solving the Ising model

Infinite density matrix renormalization group method for solving the Ising model

Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For $d$-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}4$, while dipole symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$. For $T=0$, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$ if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.

Dipole-like Field Configurations in Nonperturbative Vacuum

A model of nonperturbative vacuum in SU(2) Yang–Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to such a vacuum comes from dipole-like field configurations existing in this theory. Using an assumption of the behavior of the number density of dipole-like field configurations whose energy approaches infinity, we derive an approximate expression for the energy density of such nonperturbative vacuum symmetrical under translation that turns out to be finite, unlike the infinite energy density of perturbative vacuum. Using characteristic values of the parameters appearing in the expression for the nonperturbative energy density, it is shown that this density may be of the order of the energy density associated with Einstein’s cosmological constant. The physical interpretation of the spinor field self-coupling constant as a characteristic distance between dipole-like field configurations is suggested. The questions of experimental verification of the nonperturbative vacuum model under consideration and of determining its pressure are briefly discussed.

Design of a polyurethane underwater sound absorber based on the BP neural network and genetic algorithm

A coordinate transformation theory for the acoustic cloak design based on pentamode material was proposed by Norris in 2008. This theory avoids the problem of infinite density at the inner boundary of the inertial cloak, but the structural design of the pentamode material was difficult to be achieved. In order to solve this manufacturing problem, a design scheme of a low scattering cloak with only a few layers of polyurethane materials was proposed in this study. First, the material parameter distribution of the acoustic cloak was obtained based on the coordinate transformation theory. On this basis, the material parameter distribution in the two-dimensional annular acoustic cloak was derived by using linear mapping. Through simulation comparison between the uncovered acoustic cloak and covered acoustic cloak, the equivalent scattering characteristics of obstacles covered with the acoustic cloak were significantly reduced, which shows that anisotropic concealed materials have obvious advantages in acoustic control. When the thickness was given and the frequency was fixed, the sound pressure field of the cloak was simulated under the condition of uniform stratification. With the increase in the number of layers, the stealth effect was better, and the complexity of the preparation of metamaterials was increased. In order to obtain the cloak structure with a simple structure and good stealth performance, the BP neural network genetic algorithm and sound field finite element modeling were used. The minimum scattering area was taken as the optimization goal, and we tried to find the design scheme of a low scattering cloak with only a few layers of polyurethane materials. The optimization results show that when the target frequency is 2 KHz and the number of cloak layers is five, the optimized scattering area is 73% less than that of the uniformly layered structure. This shows that anisotropic stealth materials have obvious advantages in sound control. This study can guide the cell configuration design of polyurethane materials in different positions and greatly simplify the complexity of the manufacturing process of stealth materials.

On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles

In this paper and its sequel, we construct a set of finite energy smooth initial data for which the corresponding solutions to the compressible three-dimensional Navier-Stokes and Euler equations implode (with infinite density) at a later time at a point, and we completely describe the associated formation of singularity. This paper is concerned with existence of smooth self-similar profiles for the barotropic Euler equations in dimension $d\ge 2$ with decaying density at spatial infinity. The phase portrait of the nonlinear ODE governing the equation for spherically symmetric self-similar solutions has been introduced in the pioneering work of Guderley. It allows us to construct global profiles of the self-similar problem, which however turn out to be generically non-smooth across the associated acoustic cone. In a suitable range of barotropic laws and for a sequence of quantized speeds accumulating to a critical value, we prove the existence of non-generic $\mathcal{C}^\infty$ self-similar solutions with suitable decay at infinity. The $\mathcal{C}^\infty$ regularity is used in a fundamental way in our companion paper (part II) in the analysis of the associated linearized operator and leads, in turn, to the construction of finite energy blow up solutions of the compressible Euler and Navier-Stokes equations in dimensions $d=2,3$.