Multisoliton solutions to Einstein's equations

We discuss a multisoliton solution to Einsteins equations in vacuum. The solution is interpreted as many gravitational solitons propagating and colliding on a homogeneous cosmological background. Following a previous letter, we characterize the solitons by their localizability and by their peculiar properties under collisions. Furthermore, we define an associated frame-dependent velocity field which illustrates the solitonic character of these gravitational solitons in the classical sense.

Semiclassical equations for weakly inhomogeneous cosmologies

The in-in effective action formalism is used to derive the semiclassical correction to Einsteins equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Glutamine synthesis rate in the hyperammonaemic rat brain using simultaneous localized in vivo H-1 and N-15 MRS

Objectives: Glutamine synthetase is a critical step in the glutamate-glutamine cycle, the major mechanism of glutamate neurotransmission and is implicated in the mechanism of ammonia toxicity. 15N MRS is an alternative approach to 13C MRS in studying glutamate- glutamine metabolism. 15N MRS studies allow to measure an apparent glutamine synthesis rate (Vsyn) which reflects a combination of the glutamate- glutamine cycle activity (Vnt) and net glutamine accumulation. The net glutamine synthesis (Vsyn-Vnt) can be directly measured from 1H NMR. Therefore, the aim of this study was to perform in vivo localized 1H MRS interleaved with 15N MRS to directly measure the net glutamine synthesis rate and the apparent glutamine synthesis rate under 15N labeled ammonia infusion in the rat brain, respectively. Methods: 1H and 15N MRS data were acquired interleaved on a 9.4T system (Varian/Magnex Scientific) using 5 rats. 15NH4Cl solution was infused continuously into the femoral vein for up to 10 h (4.5 mmol/h/kg).1 The plasma ammonia concentration was increased to 0.95±0.08 mmol/L (Analox GM7 analyzer). 1H spectra were acquired and quantified as described previously.2 15N unlocalized and localized spectra were acquired using the sequence;3 and quantified using AMARES and an external reference method.4 The metabolic model used to analyze the total Gln and 5-15N labeled Gln time courses is shown on Figure 1A. Results: Glutamine concentration increased from 2.5±0.3 to 15±3.3 mmol/kg whereas the total glutamate concentrations remained unchanged (Figure 1B). The linear fit of the time-evolution of the total Gln from the 1H spectra gave the net synthesis flux (Vsyn-Vnt), which was 0.021± 0.006 mmol/min per g (Figure 1D). The 5-15N Gln peak (_271 ppm) was visible in the first and all subsequent scans, whereas the 2-15N Gln/Glu peak (_342 ppm) appeared after B1.5 h (Figure 1C). From the in vivo 5-15N Gln time course, Vsyn = 0.29±0.1 mmol/min per g and a plasma NH3 fractional enrichment of 71%±6% were calculated. Vnt was 0.26±0.1 mmol/min/g, obtained assuming a negligible Gln efflux.5 Vsyn and Vnt were within the range of 13C NMR measurements.6 Conclusion: The combination of 1H and 15N NMR allowed for the first time a direct and localized measurement of Vnt and apparent glutamine synthesis rate. Vnt is approximately one order of magnitude faster than the net glutamine accumulation.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

Simultaneous determination of Pu and Am radioisotopes in environmental samples: a tool for determining origin and release date

A radiochemical procedure was developed for the sequential determination of Pu and Am radioisotopes in environmental samples. The radioisotope activities were then used to assess the origin and release date of the environmental plutonium. The radioanalytical procedure is based on the separation of Pu and Am on selective extraction chromatographic resins (Eichrom TEVA and DGA). Alpha sources were prepared by electrodeposition on stainless steel discs, and the alpha emitting radionuclides (238Pu, 239,240Pu and 241Am) were measured by alpha spectrometry. For the determination of the beta emitting 241Pu, the Pu alpha source was leached in hot concentrated nitric acid and the Pu fraction further purified by extraction chromatography on a small column of TEVA resin (100 μg of resin in a pipette tip). 241Pu is then measured by ultra low level liquid scintillation counting. Due to the lack of reference material for 241Pu, the proposed radiochemical method was nevertheless validated using four IAEA reference sediments with information values of 241Pu. The proposed method was then used to determine the 238Pu, 239,240Pu, 241Pu and 241Am activity concentrations in alpine soils of France and Switzerland. The soil is the primary receptor of the atmospheric radioactive fallout and, because of the strong binding interaction with soils particles, the isotopes are little fractionated. Therefore, the activity ratios 241Pu/239+240Pu and 238Pu/239,240Pu in soil samples were used to determine the origin (source) and date of the Pu contamination in the investigated alpine sites. The 241Pu/239,240Pu and 238Pu/239,240Pu activity ratios confirmed that the main origin of Pu in the alpine soils was the global fallout from the nuclear bomb tests (NBT) in the fifties and sixties. Furthermore, the 241Pu/241Am activity ratios were used to determine the age of the Pu contamination, which is also an important data for distinguishing the Pu sources. The estimation of the date of the contamination, by the 241Pu/241Am age-dating method, further confirmed the NBT as the Pu source. However, the 241Pu/241Am dating method was limited to samples where Pu-Am fractionation was insignificant. If any, the contribution of the Chernobyl accident in the studied sites is negligible.

Simultaneous Mendelian and clonal genome transmission in a sexually reproducing, all-triploid vertebrate.

Meiosis in triploids faces the seemingly insuperable difficulty of dividing an odd number of chromosome sets by two. Triploid vertebrates usually circumvent this problem through either asexuality or some forms of hybridogenesis, including meiotic hybridogenesis that involve a reproductive community of different ploidy levels and genome composition. Batura toads (Bufo baturae; 3n = 33 chromosomes), however, present an all-triploid sexual reproduction. This hybrid species has two genome copies carrying a nucleolus-organizing region (NOR+) on chromosome 6, and a third copy without it (NOR-). Males only produce haploid NOR+ sperm, while ova are diploid, containing one NOR+ and one NOR- set. Here, we conduct sibship analyses with co-dominant microsatellite markers so as (i) to confirm the purely clonal and maternal transmission of the NOR- set, and (ii) to demonstrate Mendelian segregation and recombination of the NOR+ sets in both sexes. This new reproductive mode in vertebrates ('pre-equalizing hybrid meiosis') offers an ideal opportunity to study the evolution of non-recombining genomes. Elucidating the mechanisms that allow simultaneous transmission of two genomes, one of Mendelian, the other of clonal inheritance, might shed light on the general processes that regulate meiosis in vertebrates.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.