Related Cases Research Articles

Relativistic effects on the Richtmyer-Meshkov instability

Theoretical and numerical analysis of the relativistic effects on the Richtmyer-Meshkov (RM) instability reveals new and potentially very useful effects. We find that, in contrast with the non- relativistic case, the growth rate of the RM instability depends strongly on the equation of state of the fluid, opening up the possibility to infer equations of state from experimental observations of the RM instability. As opposed to the non-relativistic case, we also discover that, above a critical value of the fluid velocity, the growth rate of the instability counter-intuitively decreases due to the Lorentz's factor, and vanishes in the ultrarelativistic limit, as the speed of the particles approaches the speed of light. Both effects might prove very useful for leading-edge applications, such as the study of the equation of state of quark-gluon matter, and the design of fast ignition inertial confinement fusion (ICF) schemes. We perform a linear stability analysis to characterize the instability, for an arbitrary equation of state, and implement numerical simulations to study the instability in the non-linear regime, using the equation of state of an ideal gas. Furthermore, based on the numerical results, we propose a general expression that characterizes the long term evolution of the instability.

Braneworld setup and embedding in teleparallel gravity

We construct the setup of a five-dimensional braneworld scenario in teleparallel gravity. Both cases of Minkowski and Friedmann–Robertson–Walker branes embedded in anti-de Sitter bulk are studied and the effective 4D action were studied. 4-dimensional local Lorentz invariance is found to be recovered in both cases. However, due to different junction conditions, the equations governing the 4D cosmological evolution differ from general relativistic case. Using the results of Ref. [13], we consider a simple inflationary scenario in this setup. The inflation parameters are found to be modified compared to general relativistic case.

Operator product expansion and conservation laws in non-relativistic conformal field theories

We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family tree of primaries with zero particle number and discuss the presence of conservation laws in this sector.

Fuzzy topology and geometric quantum formalism

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of geometric quantum formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty σx. It’s shown that m evolution with minimal number of additional assumptions obeys to schroedinger and dirac formalisms in norelativistic and relativistic cases correspondingly. It’s argued that particle’s interactions on such fuzzy manifold should be gauge invariant.

Linear confinement in momentum space: Singularity-free bound-state equations

Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schr\"odinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much easier to solve and yields accurate and stable solutions. To test the method's numerical efficiency, we performed a three-parameter least-squares fit of a simple linear-plus-Coulomb potential to the bottomonium spectrum.

Goldstones with extended shift symmetries

We consider scalar field theories invariant under extended shift symmetries consisting of higher order polynomials in the spacetime coordinates. These generalize ordinary shift symmetries and the linear shift symmetries of the galileons. We find Wess–Zumino Lagrangians which transform up to total derivatives under these symmetries, and which possess fewer derivatives per field and lower order equations of motion than the strictly invariant terms. In the nonrelativistic context, where the extended shifts are purely spatial, these theories may describe multi-critical Goldstone bosons. In the relativistic case, where the shifts involve the full spacetime coordinate, these theories generally propagate extra ghostly degrees of freedom.

Improving complex kinship analyses with additional STR loci.

In a standard paternity testing, mother, child, and alleged father are analyzed with STR markers using commercially available kits. Since Italian civil legislation does not have thresholds to confirm a paternity, paternity is practically proven when likelihood ratio increases prior probability of paternity to posterior, accepted by court as sufficient. However, in some cases the number of markers included in a commercial kit may be insufficient to conclusively prove or disprove a relationship between individuals, especially when complex family scenarios are suspected or indirect analyses are required. Additional genetic information can increase the values of the likelihood ratio regarding the detection of true parental relationships in a pedigree, while reducing the chances of false attributions (e.g. false paternities). In these cases the introduction of a 26Plex amplification system allows to examine 23-26 additional markers depending on the commercial kit used, thus increasing the statistical power of the kinship analysis. The PCR conditions were optimized for a multiplex amplification system and a new generation CE instrument. In order to demonstrate the utility of additional STRs markers, four complex kinship cases are presented.

Genetic polymorphism of 13 non-CODIS STR loci in three national populations from China.

The aim of this study was to investigate a 13 non-CODIS STR loci database using three national populations from China. A new multiplex PCR system that simultaneously amplified 13 loci in the same PCR reaction was developed. This multiplex system included the 13 STR markers (D3S2402, D3S2452, D3S1766, D3S4554, D3S2388, D3S3051, D3S3053, D4S2364, D4S2404, AC001348A, AC001348B, D17S975, and D17S1294), which were successfully analyzed by using 441 DNA samples from three national populations in China (154 Mongol, 177 Kazakh, and 110 Uigur). Allele frequencies and mutation rates of the 13 non-CODIS STR loci were investigated. A total of 4-10 alleles at each locus were observed and altogether 84, 88, and 87 alleles for the all selected loci were found in the Mongol, Kazakh, and Uigur, respectively. Eight mutations were detected from the 13 selected loci in 9880 meioses in kinship cases. These results indicate that this multiplex system may provide significant polymorphic information for kinship testing and relationship investigations.

Genetic polymorphism of the 26 short tandem repeat loci in the Chinese Hebei Han population using two commercial forensic kits.

We determined the allele frequencies and forensic parameters for the 26 short tandem repeat (STR) autosomal markers in two commercial kits (the Investigator HDplex and AmpFLSTR(®) Identifiler(®) systems) for 183 unrelated individuals from the Han population of the Hebei Province of China. The 26 STRs were all in Hardy-Weinberg equilibrium. No linkage disequilibrium was detected between any pair of loci. The combined power of discrimination and the combined power of exclusion for the 26 STR loci were 1-7.74E-31 and 1-1.21E-11, respectively. Six rare alleles of D10S2325 were identified and named 20, 21, 22, 23, 24, and 31. All the length of the six rare alleles were out of the range of allelic ladder. We calculated the population pairwise genetic distance based on the allele frequencies, using published population data including German, central Polish, south Dutch, northeastern Polish, south Brazilian, Korean, Sichuan Han of China, and Shanghai Han of China. Also we examined the population pairwise genetic distance of loci included in Identifiler system between Hebei Han and other ethnic population of China. These 26 autosomal STR loci could provide highly informative polymorphic data for paternity testing and forensic identification in the Hebei Han population in China. Because they are all in linkage equilibrium, they could be used together to solve deficient kinship cases or cases with mutations.

Investigator HDplex markers: allele frequencies and mutational events in a North Italian population.

Autosomal short tandem repeats (STRs) analysis represents the method of election in forensic genetics and up to now, 23 STRs are available for these purposes. However, in particular circumstances such as human identification or complex kinship cases, examination of additional STRs may be required in order to obtain reliable conclusions. For this purpose, a new multiplex STR system, namely Investigator® HDplex kit (QIAGEN) that coamplifies a set of 12 autosomal loci, 9 of which, represents novel supplementary STRs, was recently developed. A population sample of 359 unrelated healthy subjects residing in North Italy was typed to determine allele frequencies, forensic parameters and genetic distances among European populations. Furthermore, to evaluate the suitability of the HDplex kit as an auxiliary tool for paternity testing, mutation rates were estimated on 84 confirmed family trios. The 12 loci resulted highly informative with a combined power of discrimination of 0.999998 and no departures from Hardy-Weinberg equilibrium were observed with the sole exception of locus D4S2366. From the comparison of our population sample and European reference populations, a single significant difference was revealed with the Poland population at D4S2366 locus. With regard to the mutation rate study, on a total of 2,016 meioses considered, six single-step mutational events were observed and the average mutation rate calculated was of 2.94 × 10(-3) per locus per generation (95% confidence interval, 1.08 × 10(-3)-6.39 × 10(-3)).

Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M-Theory, loop quantum cosmology and Ho\v{r}ava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to high orders for the cases where the modified dispersion relation (linear or nonlinear) has only one-turning point (or zero). We obtain the general expressions for the power spectra and spectral indices of both scalar and tensor perturbations up to the third-order, at which the error bounds are $\lesssim 0.15\%$. As an application of these formulas, we calculate the power spectra and spectral indices in the slow-roll inflation with a nonlinear power-law dispersion relation. To check the consistency of our formulas, we further restrict ourselves to the relativistic case, and calculate the corresponding power spectra, spectral indices and runnings to the second-order. Then, we compare our results with the ones obtained by the Green function method, and show explicitly that the results obtained by these two different methods are consistent within the allowed errors.

Generalized dilatation operator method for non-relativistic holography

We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent z and any value of the hyperscaling violation parameter θ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton–Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.

Models and implementation for relationship problems with dropout.

Allelic dropout in relationship problems may commonly appear in areas such as disaster victim identification and the identification of missing persons. If dropout is not accounted for, the results may be incorrect interpretation of profiles, loss of valuable information and biased results. In this paper, we explore different models for dropout in kinship cases and present an efficient implementation for one of the models. The implementation allows for dropout to be handled simultaneously with phenomena like silent alleles and mutations that may also cause discordances in relationship data, in addition to subpopulation correction. The implemented dropout model is freely available in the new version of the Familias software. The concepts and methods are illustrated on real and simulated data.

Limiting energy spectrum of an electron radiation belt

AbstractTo determine the Kennel‐Petschek limiting particle flux in a planetary radiation belt in a fully relativistic regime, without assuming a predetermined form for the particle energy distribution, has been a long‐standing challenge in space physics. In this paper, for the case of whistler mode wave‐electron interaction, we meet this challenge. The limiting flux is determined by a steady state marginal stability criterion in which a convective wave gain condition is applied over all frequencies for which wave growth occurs. This condition produces an integral equation for the trapped flux. We find that in the relativistic regime the limiting electron energy spectrum varies asymptotically as 1/E, for large energy E, just as in the nonrelativistic case. However, the scaling coefficient in the relativistic case is twice that in the nonrelativistic result. We compare numerical solutions for the limiting spectra with measured energetic electron spectra at Jupiter.

Non-equilibrium transport in d-dimensional non-interacting Fermi gases

.We consider a non-interacting Fermi gas in d dimensions, both in the non-relativistic and relativistic case. The system of size Ld is initially prepared into two halves and , each of them thermalized at two different temperatures, and respectively. At time t = 0 the two halves are put in contact and the entire system is left to evolve unitarily. We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the corresponding stationary currents. In particular, in the case of non-relativistic fermions, we find a low-temperature behavior for the particle and energy currents which is independent from the dimensionality d of the system, being proportional to the difference . Only in one spatial dimension (d = 1) do the results for the non-relativistic case agree with the massless relativistic ones

Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier Penetration by a Dirac Particle

We have studied the energy band structure of a Dirac particle in presence of a generalised uncertainty principle (GUP). We start from defining a modified momentum operator and derive corresponding modified dispersion relation (MDR) and GUP. Apart from the forbidden band within the range ±m, m being the mass of the particle, we find the existence of additional forbidden bands at the both ends of the spectrum. Such band structure forbids a Dirac particle to penetrate a potential step of sufficient height (∼E P , E P being Planck energy). This is also true for massless particle. Unlike the relativistic case, a massless particle also can reflect from a barrier of sufficient height. Finally we discuss about the Klein’s paradox in presence of the GUP.

Relativistic radiative transfer in relativistic plane-parallel flows: Behavior of the Eddington factor

Abstract Relativistic radiative transfer in a relativistic plane–parallel flow which is accelerated from its base, like an accretion disk wind, is numerically examined under a fully special-relativistic treatment. We first derive relativistic formal solutions. We then iteratively solve the relativistic transfer equation for several cases such as radiative equilibrium or local thermodynamic equilibrium, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities and the Eddington factor. Moment quantities are rather different in each case, but the behavior of the Eddington factor for the plane–parallel case is quite similar in all cases. The Eddington factor generally depends on the flow velocity v as well as the optical depth τ. In the case of relativistic plane–parallel flows, in an optically thin regime of τ ≲ 1, it is slightly larger than 1/3 at very slow speed, it becomes smaller than 1/3 at mildly relativistic speed, and it again increases up to unity in the highly relativistic case. At highly relativistic speed, on the other hand, it becomes larger than 1/3 even in an optically thick regime. We find the Eddington approximation is fairly good, except for τ ≲ 1 or v/c ≳ 0.9, although the moment formalism under the Eddington approximation has some defects at $v/c=1/\sqrt{3}$.

The Linear Interaction in Noncommutative Space; Both Relativistic and Nonrelativistic Cases

We investigate the effects of the Aharonov-Bohm field and a linear interaction on the quantum dynamics of both nonrelativistic and relativistic (Dirac equation) particles in noncommutative formulation.

Holographic Lifshitz superconductors with an axion field

We use a Yang-Mills field coupled to an axion as probes of a black hole with arbitrary Lifshitz scaling to investigate, via holography, superconducting phase transitions of the dual theory with a $⟨{p}_{x}+i{p}_{y}⟩$ condensate. In the relativistic case with no axion, this phase is known to be unstable, the stable phase corresponding to condensates of the $⟨{p}_{x}⟩$ form. We investigate this stability in theories with nonrelativistic scaling. Finally we numerically compute the ``Hall'' conductivity of these black holes in the nonsuperconducting phase as a function of their Lifshitz scaling.

Calculations on polarization properties of alkali metal atoms using Dirac—Fock plus core polarization method

A semi-empirical atomic structure model method is developed in the framework of a relativistic case. This method starts from Dirac—Fock calculations using B-spline basis set. The core-valence electron correction is then treated in a semi-empirical core polarization potential. As an application, the polarization properties of alkali metal atoms, including the static polarizabilities and long-range two-body dispersion coefficients, have been calculated. Our results are in good agreement with the results obtained from ab initio relativistic many-body perturbation method and the available experimental measurements.