Related Cases Research Articles

Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view

The “metric” structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not determine a unique Galilean (i.e., compatible) connection. This subtlety is intimately related to the fact that the timelike part of the torsion is proportional to the exterior derivative of the absolute clock. When the latter is not closed, torsionfreeness and metric-compatibility are thus mutually exclusive. We will explore generalisations of Galilean connections along the two corresponding alternative roads in a series of papers. In the present one, we focus on compatible connections and investigate the equivalence problem (i.e., the search for the necessary data allowing to uniquely determine connections) in the torsionfree and torsional cases. More precisely, we characterise the affine structure of the spaces of such connections and display the associated model vector spaces. In contrast with the relativistic case, the metric structure does not single out a privileged origin for the space of metric-compatible connections. In our construction, the role of the Levi-Civita connection is played by a whole class of privileged origins, the so-called torsional Newton-Cartan geometries recently investigated in the literature. Finally, we discuss a generalisation of Newtonian connections to the torsional case.

Detection of a novel X-chromosomal short tandem repeat marker in Xq28 in four ethnic groups.

DNA testing of X-chromosomal short tandem repeat (X-STR) polymorphisms has been the focus of attention in several studies, mainly due to its applicability in the investigation of complex kinship cases. Studies of X-STR in analyses of DNA sequences, population studies and DNA testing applications have been reported. We performed detection and population genetic study of a novel tetranucleotide X-STR locus in the present study. We identified a unique X-STR locus consisting of two tetranucleotides in Xq28. Although the STR is a simple tetranucleotide, its polymorphism was comparatively high [polymorphism information content (PIC)=0.7140] in Japanese subjects. In addition, the STR varied in structure among ethnic groups. We conclude that this locus will be useful for forensic DNA testing and anthropological studies.

Quantum Vavilov-Cherenkov radiation from shearing two transparent dielectric plates

Using a fully relativistic theory we study the quantum Vavilov-Cherenkov radiation and quantum friction occurring during relative sliding of the two transparent dielectric plates with the refractive index $n$. These phenomena occur above the threshold velocity $v_c=2nc/(n^2+1)$. Close to the threshold velocity they are dominated by the contribution from $s$--polarized electromagnetic waves, which agrees with the approximate (relativistic) theory by Pendry (J. Mod. Opt. \textbf{45}, 2389 (1998)). However, in the ultra relativistic case ($v\rightarrow c$), the contributions from both polarisations are strongly enhanced in the comparison with the approximate theory, and a new contribution occurs from the mixing of the electromagnetic waves with the different polarization. The numerical results are supplemented by an analytical treatment close to the threshold velocity and the light velocity.

Quasiclassical Approximation in the Non-Relativistic and Relativistic Problems of Tunneling Ionization of a Hydrogen-Like Atom in a Uniform Electric Field

A recurrent scheme for finding the quasiclassical solution of the onedimensional equation obtained after the separation of variables in the Schrodinger equation in parabolic coordinates is derived. The method of quasiclassical localized states is developed for the Dirac equation with an arbitrary axially symmetric potential of barrier type which does not allow complete separation of the variables. By means of the proposed quasiclassical methods the non-relativistic and relativistic wavefunctions for hydrogenlike (H-like) atoms in an external uniform electrostatic field of intensity F are constructed in the classically forbidden and allowed regions. The general analytical expressions of the leading term of the asymptotic behaviour (at small F ) of the ionization rate of an H-like atom in the uniform electrostatic field are obtained for the non-relativistic and relativistic cases.

Classical and Relativistic Flux of Energy Conservation in Astrophysical Jets

The conservation of the energy flux in turbulent jets which propagate in the intergalactic medium (IGM) allows deducing the law of motion in the classical and relativistic cases. Three types of IGM are considered: constant density, hyperbolic and inverse power law decrease of density. An analytical law for the evolution of the magnetic field along the radio-jets is deduced using a linear relation between the magnetic pressure and the rest density. Astrophysical applications are made to the centerline intensity of synchrotron emission in NGC315 and to the magnetic field of 3C273.

Invariants in Relativistic MHD Turbulence

The objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants in the relativistic case and comparing them to what we know of nonrelativistic turbulence. Although much work has been done to understand the dynamics of nonrelativistic systems (mostly for ideal incompressible fluids), there is minimal literature explicitly describing the dynamics of relativistic MHD turbulence using numerical simulations. Many researchers simply assume that relativistic turbulence has the same invariants and obeys the same dynamics as non-relativistic systems our results show that this assumption may be incorrect.

Timescales in Heavy-ion Collisions

The study of high energy collisions between heavy nuclei is a field unto itself, distinct from nuclear and particle physics. A defining aspect of heavy ion physics is the importance of a bulk, self-interacting system with a rich space-time substructure. I focus on the issue of timescales in heavy ion collisions, starting with proof from low-energy collisions that femtoscopy can, indeed, measure very long timescales. I then discuss the relativistic case, where detailed measurements over three orders of magnitude in energy reveal a timescale increase that might be due to a first-order phase transition. I discuss also consistency in evolution timescales as determined from traditional longitudinal sizes and a novel analysis using shape information.

Efecto Doppler con una fuente que acelera: una simple aproximación gráfica

Se analiza el efecto Doppler producido por una fuente acelerada usando un enfoque cinemático elemental. Con este simple método se obtienen fácilmente las expresiones para la frecuencia detectada por un observador estacionario y una fuente que se aleja o acerca. También se analiza el caso relativista.

Analysis of Rapidly Mutating Y Chromosome Short Tandem Repeats (RM Y-STRs).

Rapidly mutating (RM) Y-STRs were recently identified and can help to differentiate between paternally related males in paternity and forensic casework. Normal Y-STRs are often used in casework due to their paternal inheritance, which can help to resolve kinship cases, and identify male components in male/female mixtures; however, more discriminating profiles are obtained if rapidly mutating Y-STRs are used. Previously two or three multiplex PCRs have been used to amplify 13 RM Y-STRs; here, an assay amplifying these 13 markers in a single multiplex PCR is described. Commercially available male control DNA samples have been genotyped during the validation of this assay, thus providing a tool for calibrating genotyping results. It is expected that the assay will provide a niche tool for genotyping casework samples.

Analysis of 30 Biallelic INDEL Markers Using the Investigator DIPplex(®) Kit.

Insertion/deletion polymorphisms (INDELs) are a relatively new class of a DNA marker to be used in forensic casework; used most commonly as a supplementary method to STR-based typing. INDELs, like SNPs, are particularly useful for the analysis of highly degraded DNA as the amplicon sizes are typically below 160 bp; they can also be valuable as an additional tool to help resolve kinship cases, with the advantage over STRs that they do not have high mutation rates. INDELs have an advantage over SNPs in that they are length polymorphisms and so can be analyzed by simply measuring the length of the allele(s). The Qiagen Investigator(®) DIPplex Kit is currently only one of two commercially available kits for the amplification of INDEL polymorphisms; it amplifies 30 biallelic INDEL loci and the amelogenin locus. The primers used are fluorescence labeled with 6-FAM, BTG, BTY, and BTR. This technique is robust, relatively simple, and the results are analyzed using the same capillary electrophoresis equipment and software as used for STR typing.

ADVANCED RELATIVISTIC ENERGY APPROACH TO RADIATION DECAY PROCESSES IN ATOMIC SYSTEMS

We consider the fundamental aspects of the advanced generalized energy approach to relativistic calculation of the radiative decay (transitions) probabilities in heavy neutral atomic systems and multicharged ions. The approach is based on the Gell-Mann and Low S-matrix formalism and the relativistic many-body perturbation theory (PT) with using the optimized one-quasiparticle representation and an accurate account of the relativistic and correlation. In relativistic case the Gell-Mann and Low formula expresses an energy shift through the electrodynamical scattering matrix including the interaction with as the laser field as the photon vacuum field. The last case is corresponding to definition of the traditional radiative transitions probabilities for atoms and ions.

Charge-hyperscaling violating Lifshitz hydrodynamics from black-holes

Non-equilibrium black hole horizons are considered in scaling theories with generic Lifshitz invariance and an unbroken U(1) symmetry. There is also charge-hyperscaling violation associated with a non-trivial conduction exponent. The boundary stress tensor is computed and renormalized and the associated hydrodynamic equations derived. Upon a non-trivial redefinition of boundary sources associated with the U(1) gauge field, the equations are mapped to the standard non-relativistic hydrodynamics equations coupled to a mass current and an external Newton potential in accordance with the general theory of [arXiv:1502.00228]. The shear viscosity to entropy ratio is the same as in the relativistic case.

Orbital and epicyclic frequencies around neutron and strange stars in $$R^2$$ R 2 gravity

According to various models, the orbital and the epicyclic frequencies of particles moving on a circular orbit around compact objects are related to the quasi-periodic oscillations observed in the X-ray flux of some pulsars or black hole candidates. It is expected that they originate from the inner edge of the accretion discs, deep into the gravitational field of the compact objects. Considering the planned new generation X-ray timing observatories with large collective areas, the quasi-periodic oscillations might be an excellent tool for testing gravity in strong field regime and respectively alternative gravitational theories. We examine the orbital and the epicyclic frequencies of a particle moving on a circular orbit around neutron or strange stars in $R^2$ gravity. The case of slow rotation is considered too. The $R^2$ gravity results are compared to the General Relativistic case. We comment the deviations from General Relativity, as well as the deviations due to rotation in both theories.

INFRARED TIME LAGS FOR THE PERIODIC QUASAR PG 1302-102

The optical light curve of the quasar PG 1302-102 at z = 0.278 shows a strong, smooth 5.2 year periodic signal, detectable over a period of ~20 years. Although the interpretation of this phenomenon is still uncertain, the most plausible mechanisms involve a binary system of two supermassive black holes with a subparsec separation. At this close separation, the nuclear black holes in PG 1302-102 will likely merge within ~ 10^5 years due to gravitational wave emission alone. Here, we report the rest-frame near-infrared time lags for PG 1302-102. Compiling data from WISE and Akari, we confirm that the periodic behavior reported in the optical light curve from Graham et al. is reproduced at infrared wavelengths, with best-fit observed-frame 3.4 and 4.6 µm time lags of (2219 ± 153, 2408 ± 148) days for a near face-on orientation of the torus, or (4103 ± 153, 4292 ± 148) days for an inclined system with relativistic Doppler boosting in effect. The periodicity in the infrared light curves and the light-travel time of the accretion disk photons to reach the dust glowing regions support that a source within the accretion disk is responsible for the optical variability of PG 1302-102, echoed at the farther out dusty regions. The implied distance of this dusty, assumed toroidal region is ~1.5 pc for a near face-on geometry or ~1.1 pc for the relativistic Doppler-boosted case.

Relationship inference based on DNA mixtures.

Today, there exists a number of tools for solving kinship cases. But what happens when information comes from a mixture? DNA mixtures are in general rarely seen in kinship cases, but in a case presented to the Norwegian Institute of Public Health, sample DNA was obtained after a rape case that resulted in an unwanted pregnancy and abortion. The only available DNA from the fetus came in form of a mixture with the mother, and it was of interest to find the father of the fetus. The mother (the victim), however, refused to give her reference data and so commonly used methods for paternity testing were no longer applicable. As this case illustrates, kinship cases involving mixtures and missing reference profiles do occur and make the use of existing methods rather inconvenient. We here present statistical methods that may handle general relationship inference based on DNA mixtures. The basic idea is that likelihood calculations for mixtures can be decomposed into a series of kinship problems. This formulation of the problem facilitates the use of kinship software. We present the freely available R package relMix which extends on the R version of Familias. Complicating factors like mutations, silent alleles, and θ-correction are then easily handled for quite general family relationships, and are included in the statistical methods we develop in this paper. The methods and their implementations are exemplified on the data from the rape case.

Newton-Cartan supergravity with torsion and Schrödinger supergravity

We derive a torsionfull version of three-dimensional $$ \mathcal{N}=2 $$ Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The “superconformal” theory that we start with is Schrodinger supergravity which we obtain by gauging the Schrodinger superalgebra. We present two non-relativistic $$ \mathcal{N}=2 $$ matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call “old minimal” and “new minimal” Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.

Thermodynamics of relativistic Newton—Wigner particle in external potential field

Thermodynamic properties of relativistic spinless particle described by the Klein–Gordon equation have been studied using the Newton–Wigner theory of particle in external potential field. Concept of Wiener path integral was extended on relativistic case. A new path integral Monte–Carlo method was developed for relativistic particle in external potential field. The bounds of applicability of available analytical approaches and related results have been specified by comparison with Monte–Carlo calculations. Developed path integral formalism can be directly extended on systems of many identical Newton–Wigner particles, which interact with external field and each other.

The aging problem of twins in the ellipsoidal coordinates

In this paper, we have tried to explore the twin paradox in the ellipsoidal coordinate system. We have investigated that the traveling twin travels away from the gravitational source in the first case while in the other it moves towards the source. We then tried to compare it with the special relativistic case where the static twin ages faster as compared to his traveling counterpart.

Alfven solitary waves in nonrelativistic, relativistic, and ultra-relativistic degenerate quantum plasma

Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.

Belarusian experience of the use of FamLinkX for solving complex kinship cases involving X-STR markers

Use of X-STR markers extends and gives additional possibilities to a forensic DNA expert for kinship analysis. FamLinkX is software for the calculation of likelihood ratios (LRs) for kinship cases based on X-STR DNA profiles that takes linkage and linkage disequilibrium as well as mutations of X-STR markers into account. Belarusian haplotype frequencies database of 360 unrelated Belarusian males has been uploaded to FamLinkX. LR values for 6 deficient paternity cases and 2 forensic cases involving two putative full siblings, females, were calculated with different values of lambda (λ=1, 10, 100) in order to account for uncertainties in the haplotype frequency estimation. To demonstrate the ethnic sensitivity of X-STR markers and importance of the choice of the appropriate X-STR population database for LR calculation we calculated LR values for the same kinship cases using Belarusian and Swedish X-STR databases. LR values for the same kinship case differed from each other up to 6000 times depending on the chosen database. X-STRs genotyping lets us to determine relatedness successfully in all cases whereas the results of autosomal STR profiling and mitochondrial sequencing (for the cases where only the samples of putative full-siblings were available) were not sufficient to resolve family relationships issues. LR values were considered to be high enough in all cases.