Related Cases Research Articles

Fermi gas and modified gravity

We derive the equations of state of Fermi gas by maximizing the Fermi-Dirac entropy in modified gravity in relativistic and non-relativistic case. It will be demonstrated that the microphysics must depend on a given theory of gravity in order to consistently describe a physical system at a statistical equilibrium state.

Effects of the magnetic field penetration into the metal on the Brillouin flow in a crossed-field gap

In this paper, the relativistic Brillouin flow in a crossed-field gap is investigated. For this, the case of a planar magnetron is considered. In contrast to previous studies, it is assumed that the electron discharge occurs in a timescale that is long compared to the magnetic diffusion time in the metal. It is found that the Brillouin flow properties and the overall scenario for the loss of magnetic insulation are different from the short pulse case. In particular, it is shown that two branches of equilibrium Brillouin flow solutions can coexist inside the gap region: one linearly stable and the other linearly unstable. As the parameters are varied, the two branches coalesce and cease to exist in a bifurcation that leads to a complete loss of magnetic insulation. Nevertheless, the mere existence of the unstable solution inside the gap is shown to affect the electron dynamics causing cathode–anode currents. An expression for the onset of the unstable solution is obtained and compared to the relativistic Hull cutoff condition for the short pulse case. It is found that the loss of magnetic insulation occurs for lower accelerating potentials in the present case. This effect is noticeable even for weakly relativistic cases.

Self-generated magnetic field induced by Karpman–Washimi ponderomotive force in relativistic electron plasmas

The relativistic effects on nonstationary Karpman–Washimi ponderomotive magnetization are investigated in relativistic electron plasmas. The magnetization Mp and radiation power P̄ are obtained as functions of the relativistic parameter α, scaled wave frequency ω̄, and wave number k̄. It is shown that the ponderomotive force is more likely to induce a low-frequency and small-scale magnetic field. In addition, the results indicate that the magnetization and radiation power are suppressed by the relativistic effects in the ultrarelativistic case but enhanced in the moderately and weakly relativistic cases, especially in the moderately relativistic regime.

Particle decay, Oberth effect and a relativistic rocket in the Schwarzschild background

We relate the known Oberth effect and the nonrelativistic analogue of the Penrose process. When a particle decays to two fragments, we derive the conditions on the angles under which debris can come out for such a process to occur. We also consider the decay and the Oberth effect in the relativistic case, when a particle moves in the background of the Schwarzschild black hole. This models the process when a rocket ejects fuel. Different scenarios are analyzed depending on what data are fixed. The efficiency of the process is found, in particular, near the horizon and for a photon rocket (when the ejected particle is massless). We prove directly that the most efficient process occurs when fuel is ejected along the rocket trajectory. When this occurs on the horizon, the efficiency reaches 100% for a photon rocket. We compare in two ways how a rocket can reverse its direction of motion to a black hole near the event horizon by restoring the initial energy-to-mass ratio: (i) by a single ejection or (ii) in the two-step process when it stops and moves back afterwards. For a nonphotonic rocket, in case (ii) a larger mass can be taken out from the vicinity of a horizon. For a photonic one, there is no difference between (i) and (ii) in this respect. We also consider briefly the scenario when a rocket hangs over a black hole due to continuous ejection of fuel. Then, the fuel mass decays exponentially with the proper time.

Quantum clocks, gravitational time dilation, and quantum interference

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.

Частица Штюкельберга во внешнем магнитном поле. Нерелятивистское приближение. Точные решения

The St¨uckelberg equation for a particle with two spin states, S = 1 and S = 0, is studied in the presence of an external uniform magnetic field. In relativistic case, the particle is described by an 11-component wave function. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, we derive a system for 11 functions depending on one variable. We perform the nonrelativistic approximation in this system. For this we apply the known method of deriving nonrelativistic equations from relativistic ones, which is based on projective operators related to the matrix Γ0 of the relativistic equation. The nonrelativistic wave function turns out to be 4-dimensional. We derive the system for 4 functions. It is solved in terms of confluent hypergeometric functions. There arise three series of energy levels with corresponding solutions. This result agrees with that obtained for the relativistic St¨uckelberg equation.

Structure and evolution of ultra-massive white dwarfs in general relativity

Context. Ultra-massive white dwarfs (M⋆ ≳ 1.05 M⊙) are of utmost importance in view of the role they play in type Ia supernovae explosions, merger events, the existence of high-magnetic -field white dwarfs, and the physical processes in the super asymptotic giant branch phase. Aims. We aim to present the first set of constant rest-mass ultra-massive oxygen-neon white dwarf cooling tracks with masses of M⋆ > 1.29 M⊙ which fully take into account the effects of general relativity on their structural and evolutionary properties. Methods. We computed the full evolution sequences of 1.29, 1.31, 1.33, 1.35, and 1.369 M⊙ white dwarfs with the La Plata stellar evolution code, LPCODE. For this work, the standard equations of stellar structure and evolution have been modified to include the effects of general relativity. Specifically, the fully general relativistic partial differential equations governing the evolution of a spherically symmetric star are solved in a way so that they resemble the standard Newtonian equations of stellar structure. For comparison purposes, the same sequences have been computed for the Newtonian case. Results. According to our calculations, the evolutionary properties of the most massive white dwarfs are strongly modified by general relativity effects. In particular, the resulting stellar radius is markedly smaller in the general relativistic case, being up to 25% smaller than predicted by the Newtonian treatment for the more massive ones. We find that oxygen-neon white dwarfs more massive than 1.369 M⊙ become gravitationally unstable with respect to general relativity effects. When core chemical distribution due to phase separation on crystallization is considered, such instability occurs at somewhat lower stellar masses, ≳1.36 M⊙. In addition, cooling times for the most massive white dwarf sequences are about a factor of two smaller than in the Newtonian case at advanced stages of evolution. Finally, a sample of white dwarfs have been identified as ideal candidates to test these general relativistic effects. Conclusions. We conclude that the general relativity effects should be taken into account for an accurate assessment of the structural and evolutionary properties of the most massive white dwarfs. These new ultra-massive white dwarf models constitute a considerable improvement over those computed in the framework of the standard Newtonian theory of stellar interiors.

Blood Groups ABO and Rh System Among Paternity and Kinship Cases of Iraqi Medical Legal Directorate

ABO and Rh are the most important blood group systems with various distributions reported for different populations. Traditional ABO blood group and Rh serology is based on the immunoreactivity of antisera with the carbohydrate A, B and H antigens on Red Blood Cells (RBC). Due to its medical importance in relation to different diseases, pursuing a line of investigation on the ABO and Rh blood group systems has been of significance for years. It is well known that these blood group systems are of great importance in blood transfusion and organ transplantation. Furthermore, the susceptibility to several diseases has been associated with the ABO phenotype, but such correlation remains controversial. Progress in the molecular biology of the ABO system has recognized the molecular basis of the red blood cell antigens and has provided a genetic model for ABO polymorphism at the molecular level. The ABH antigens are not primary gene product, but they are the enzymatic reaction product of enzymes called glycosyltransferases. After the ABO system, the Rh (Rhesus) blood group system is regarded as the second most important blood group system, as some of the severe hemolytic transfusion reactions and most hemolytic disease of the fetus and new born (HDFN) cases are associated with antibodies to the Rh group antigens. Objectives: To determine ABO blood group and Rh factor phenotype antigens frequency, distribution, and document among paternity cases of Iraqi Medical Legal Directorate / Clinical Forensic Department / paternity and kinship division. Materials and Methods: The material and methods were used ABO and Rh kits for detection phenotype antigens of this blood types, the principle of test is one step immunological reaction. Total samples (1997) were referred to medical Legal Directorate (MLD). Out of the total participants there were 1815 (98.4%) of samples complete information for inclusion criteria. the sample were used for estimation of phenotypic distribution of ABO, Rh. ABO blood group serology was performed at MLD, Paternity and Kinship Division using commercially available monoclonal Anti-A, Anti-B, reagents according to the national blood bank standard operating procedures. The Method principle is based on antigen antibody reaction (agglutination) some tests were confirmed under microscope examination to see weak reaction. Results: The most common blood group was O (52.3%) and the least common was AB (3.18%).97.7% of the blood participants were Rh Positive and the rest were Rh Negative. Most participants were young adults, representing the age group of 19 – 29. Most participants were male (88.1%). Conclusion: Blood group O and Rh+ factor was dominant in both sexes, Up-to-date knowledge of the distribution of blood types in a local setting is critical to the functioning of any national health service. To date, there has been a lack of data in Iraqi population.

The general solution for the relativistic and nonrelativistic Schrödinger equation for the δ(n)-function potential in 1-dimension using cutoff regularization, and the fate of universality

A general method has been developed to solve the Schrödinger equation for an arbitrary derivative of the [Formula: see text]-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative [Formula: see text] is an even number from the one when [Formula: see text] is an odd number. A general gap equation for each case has been derived. The case of [Formula: see text]-function potential has been used as an example. The results from the relativistic case show that the [Formula: see text]-function system behaves exactly like the [Formula: see text]-function and the [Formula: see text]-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result, the evidence of universality of contact interactions has been extended further to include the [Formula: see text]-function potential.

Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The second order in rotation

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals.

Spectral actions for q-particles and their asymptotics

For spectral actions consisting of the average number of particles and arising from open systems made of general free q-particles (including Bose, Fermi and classical ones corresponding to q = ±1 and 0, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and non relativistic massive particles, where the natural cut-off is 1/β = k B T and , respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also treat in some detail the relativistic massive case for which the natural cut-off is again 1/β. We then consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium, by also discussing the appearance of condensation phenomena occurring for Bose-like q-particles, q ∈ (0, 1]. We then compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).

The massless thermal field and the thermal fermion bosonization in two dimensions

We come back to the issue of bosonization of fermions in two spacetime dimension and give a new costruction in the steady state case where left and right moving particles can coexist at two different temperatures. A crucial role in our construction is played by translation invariant infrared states and the corresponding field operators which are naturally linked to the infrared behaviour of the correlation functions. We present two applications: a simple new derivation in the free relativistic case of a formula by Bernard and Doyon and a full operator solution of the massless Thirring model in the steady state case where the left and right movers have two distinct temperatures.

Resolving the recombination pattern of 38 X-STRs from Chinese Han three-generation pedigrees

X-chromosomal markers have been proved as a useful tool for solving complex kinship cases due to its sex-linked inheriting feature. Among these markers, tightly linked X-STR clusters forming haplotypes are highly informative. The analysis of the haplotypes requires determination of linkage disequilibrium. In this study, genetic linkage, recombination fractions and mutation rates of 38 X-STR loci in 177 three-generation pedigrees were investigated. Genetic linkage analysis and calculation of recombination fractions were performed within each pair of markers and clusters. Then mutation rates were calculated. The results showed that, a) 22 recombination events happened within the tightly linked X-STR clusters, which span<1.0 Mb; b) significantly linked marker pairs were observed with the LOD (logarithm of the odds) scores > 2.0 (2.0104 to 54.8316); c) the average mutation rate of the 38 X-STR loci was 1.32 × 10−3 per meiosis in the Chinese Han population, with DXS10135 and DXS8377 presenting notably high mutation rate (6.5 × 10−3). Our results confirmed that meiotic recombination was not a simple function of physical distance, so that whether recombination occurred at the closely clustered X-STRs or not should be assumed cautiously considering the stability of haplotypes in inheritance process for kinship analysis. This study supplemented the existing database and laid an experimental foundation for the future study on genetic characteristics, recombination, and mutation of the X-STRs.

Conserved relativistic Ertel’s current generating the vortical and thermodynamic aspects of space–time

Motivated by Aoki et al.’s recent research on conserved charges and entropy current, we reinvestigated the conservation of relativistic Ertel’s current, which has received little attention outside the field of geophysical fluid dynamics. Ertel’s charge is an important indicator of the correlation between vortex vectors and entropy gradient fields in Earth’s meridional heat transport. We first show that in the generalized Hamiltonian structure of baroclinic fluids, the duality between the total energy and the Casimir as a function of Ertel’s charge plays an important role in the nonrelativistic case. Then, by extending the result to relativistic cases, we show that this finding has far-reaching implications not only for space–time issues in cosmology but also for the foundation of quantum field theory. An especially important finding is that, as an unreported dual form of the Einstein field equation, we identify a special equation satisfied not only by the vortex tensor field generated by the conserved charge but also by the Weyl tensor in interpreting the physical nature of the metric tensor [Formula: see text], which appears in the cosmological term [Formula: see text].

The symplectic geometrical formulation of quantum hydrodynamics

Quantum hydrodynamics described by Madelung equations is analyzed in the framework of symplectic geometry i.e. in covariant phase space approach to geometric field theory. The pre-symplectic manifolds providing the phase spaces describing the Hamiltonian dynamics of quantum fluid are constructed from the set of all solutions of Madelung equations and their corresponding Lagrangian densities. The Madelung equations under consideration are the Madelung equations associated to Schroedinger equations (in the nonrelativistic case) and Madelung equations associated to Klein–Gordon equations (in the relativistic case). The cases where the coupling with electromagnetic fields is present are also considered here. Our symplectic formulation is different from that of [M. Spera, Moment map and gauge geometric aspects of the Schrodinger and Pauli equations, Int. J. Geom. Methods Mod. Phys. 13 (2016) 1–36] in the choice of fundamental fields or variables. Here we regard density function [Formula: see text] and phase function [Formula: see text] not as canonical pair but as the fundamental fields of the theory. The Hamiltonian vector fields corresponding to an observable are obtained from the Hamiltonian equation generated by the observable. The Poisson bracket of two observables then is determined by the Hamiltonian vector fields associated to each observable. In general, the Poisson bracket of two observables is not unique due to the fact that every observable has more than one corresponding Hamiltonian vector field. It is pointed out that the Poisson bracket has a unique value over a certain subset of the set of all observables defined on the pre-symplectic manifold of the Madelung equation under consideration.

Extended population genetic analysis of 12 X-STRs – Exemplified using a Norwegian population sample

The use of X-chromosomal markers to resolve questions of relatedness has experienced a significant increase during the last years in forensic genetics. Perhaps primarily due to the emergence of commercial kits, but equally important due to an increased awareness of the utility of those markers. The X-chromosomal inheritance pattern entails that some cases, for instance paternal half-sisters, can potentially be resolved using a few X-chromosomal markers alone. For the statistical assessment in kinship cases it is of importance to have relevant population frequency data. In the present study 631 unrelated males from a Norwegian population sample are analyzed. The resulting haplotypes are compared to previously studied population samples and a deeper analysis of the linkage disequilibrium (LD) structure is conducted. We demonstrate that the power to detect LD will be low when few males, say below 300, are analyzed. We use entropy to describe the degree of LD between multiallelic loci and describe how this measure varies between different studied populations. Large population frequency databases have been recommended when using X-chromosomal markers, and we show that by combining reference databases from genetically similar populations, more precise haplotype frequency estimates can be obtained for rare haplotypes which improves the statistical assessment of the weight of evidence. In addition, we promote the use of simulations to assess the utility of STR markers in contrast to standard forensic parameters. Specifically we perform extensive simulations on cases where X-chromosomal markers are important and illustrate how the results can be used to infer the information gained from these markers.

The spectral line asymmetry of the Doppler effect in relativistic plasmas

In this work, we present a comparative study between the relativistic and non-relativistic Doppler effects on spectral line profiles in ultra-hot plasmas in a laboratory system. We have established an exact formula of the relativistic Doppler profile in ultra-high-temperature plasma that is not a Gaussian one (unlike the non-relativistic Doppler profile that is Gaussian). We have also derived a new FWHM (Full Width at Half Maximum) formula of the corresponding profile that is different from the non-relativistic FWHM (). We have also shown that, in the relativistic case, Doppler broadening exhibits an asymmetry of spectral line profile (non-Gaussian profile). To ensure the validity of our investigation, we have compared our theoretical calculation with the experimental results and found a good agreement.

Density Perturbation and Cosmological Evolution in the Presence of Magnetic Field in f R Gravity Models

In this paper, we have investigated the density perturbations and cosmological evolution in the FLRW universe in the presence of a cosmic magnetic field, which may be assumed to mimic primordial magnetic fields. Such magnetic fields have sufficient strength to influence galaxy formation and cluster dynamics, thereby leaving an imprint on the CMB anisotropies. We have considered the FLRW universe as a representative of the isotropic cosmological model in the 1 + 3 covariant formalism for f R gravity. The propagation equations have been determined and analyzed, where we have assumed that the magnetic field is aligned uniformly along the x -direction, resulting in a diagonal shear tensor. Subsequently, the density perturbation evolution equations have been studied, and the results have been interpreted. We have also indicated how these results change in the general relativistic case and briefly mentioned the expected change in higher-order gravity theories.

A semi-analytical solution to the forward–reverse shock hydrodynamics of the gamma-ray burst afterglow

ABSTRACT We extend the standard model of forward–reverse shock (FS–RS) for gamma-ray burst (GRB) afterglow to more general cases. On one hand, we derive the analytical solution to the hydrodynamics of the shocks in two limiting cases, i.e. an ultrarelativistic reverse shock case and a Newtonian reverse shock case. Based on the asymptotic solutions in these two limiting cases, we constitute a semi-analytical solution for the hydrodynamics of the shocks in the generic case, covering the mildly relativistic reverse shock case. On the other hand, we derive the evolution of the system taking into account the condition of energy conservation which is not satisfied in the standard FS–RS model. A generic solution of semi-analytical expressions is also given. In both the extended standard FS–RS model (satisfying pressure balance condition) and the model satisfying energy conservation, we find that the results in the ultrarelativistic reverse shock case and in the early stage of the Newtonian reverse shock case are different from those in the standard FS–RS model by only a factor that close to one while the same initial conditions adopted. However, the asymptotic solutions in the limiting cases are not good approximations to those in the intermediate case. Our semi-analytical results agree well with the numerical results for a large range of model parameters, and hence can be easily employed to diagnose the physical quantities of the GRB shell and circumburst environment.

Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations

It is shown that a constant external magnetic field, generally speaking, is not able to prevent breaking (loss of smoothness) of relativistic plasma oscillations, even if they are arbitrarily small perturbations of the zero steady-state. This result sharply differs from the non-relativistic case, for which it is possible to suppress the breaking of oscillations at any initial deviations by increasing the intensity of the magnetic field \cite {RCharx}. Nevertheless, even in the relativistic case, there are subclasses of solutions corresponding to solutions that are globally smooth in time.