Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross-Pitaevskii Equation

For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one dimensional amplitude equation that describes the slow evolution of the envelope of the initial instability. We show that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation. We also illustrate the role of dissipation in the symmetry breaking process. All analyses are confirmed by detailed numerical computations

Inverse problem for wave equation with sources and observations on disjoint sets

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted Dirichlet-to-Neumann operator $\Lambda_{\Gamma_1,\Gamma_2}$. This operator corresponds the boundary measurements when we have smooth sources supported on $\Gamma_1$ and the fields produced by these sources are observed on $\Gamma_2$. We show that when $\Gamma_1$ and $\Gamma_2$ are disjoint but their closures intersect at least at one point, then the restricted Dirichlet-to-Neumann operator $\Lambda_{\Gamma_1,\Gamma_2}$ determines the Riemannian manifold and the metric on it up to an isometry. In the Euclidian space, the result yields that an anisotropic wave speed inside a compact body is determined, up to a natural coordinate transformations, by measurements on the boundary of the body even when wave sources are kept away from receivers. Moreover, we show that if we have three arbitrary non-empty open subsets $\Gamma_1,\Gamma_2$, and $\Gamma_3$ of the boundary, then the restricted Dirichlet-to-Neumann operators $\Lambda_{\Gamma_j,\Gamma_k}$ for $1\leq j<k\leq 3$ determine the Riemannian manifold to an isometry. Similar result is proven also for the finite-time boundary measurements when the hyperbolic equation satisfies an exact controllability condition

Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations

We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is as follows: If two systems of elliptic operators generate the same set of partial Cauchy data on an arbitrary subboundary, then the coefficient matrices of the first-order and zero-order terms satisfy the prescribed system of first-order partial differential equations. The main result implies the uniqueness of any two coefficient matrices provided that the one remaining matrix among the three coefficient matrices is known

A New Seismic-Geotechnical Strong Motion Approach

We have developed a new approach to estimate site-specific strong motion due to earthquakes on specific faults or source zones. It combines seismologic and geotechnical studies. It entails obtaining records of small earthquakes at the site, both at the surface and downhole in bedrock, as well as performing geotechnical dynamic site characterization. This new approach has the dual result of providing an optimized definition of the dynamic geotechnical site properties and providing calculated free-field, strong motion estimates. The procedure is demonstrated at the Painter Street Bridge site in Rio Dell, CA, for which we provide a range of surface motions corresponding to an earthquake of magnitude 7 on the subducting plate underlying this region. These calculated motions bracket the records of the Petrolia event (M = 7) measured near the site

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

[EN] Parabolic heat equation based on Fourier's theory (FHE), and hyperbolic heat equation (HHE), has been used to mathematically model the temperature distributions of biological tissue during thermal ablation. However, both equations have certain theoretical limitations. The FHE assumes an infinite thermal energy propagation speed, whereas the HHE might possibly be in breach of the second law of thermodynamics. The relativistic heat equation (RHE) is a hyperbolic-like equation, whose theoretical model is based on the theory of relativity and which was designed to overcome these theoretical impediments. In this study, the three heat equations for modelling of thermal ablation of biological tissues (FHE, HHE and RHE) were solved analytically and the temperature distributions compared. We found that RHE temperature values were always lower than those of the FHE, while the HHE values were higher than the FHE, except for the early stages of heating and at points away from the electrode. Although both HHE and RHE are mathematically hyperbolic, peaks were only found in the HHE temperature profiles. The three solutions converged for infinite time or infinite distance from the electrode. The percentage differences between the FHE and the other equations were larger for higher values of thermal relaxation time in HHE.This work received financial support from the Spanish Government (Ministerio de Ciencia e Innovacion, Ref. TEC2011-27133-C02-01).López Molina, JA.; Rivera Ortun, MJ.; Berjano, E. (2014). Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 470:1-16. https://doi.org/10.1098/rspa.2014.0547S11647

A slip-based model for the size-dependent effective thermal conductivity of nanowires

The heat flux across a nanowire is computed based on the Guyer-Krumhansl equation. Slip conditions with a slip length depending on both temperature and nanowire radius are introduced at the outer boundary. An explicit expression for the effective thermal conductivity is derived and compared to existing models across a given temperature range, providing excellent agreement with experimental data for Si nanowires

Lack of phenotypic and evolutionary cross-resistance against parasitoids and pathogens in Drosophila melanogaster

BackgroundWhen organisms are attacked by multiple natural enemies, the evolution of a resistance mechanism to one natural enemy will be influenced by the degree of cross-resistance to another natural enemy. Cross-resistance can be positive, when a resistance mechanism against one natural enemy also offers resistance to another; or negative, in the form of a trade-off, when an increase in resistance against one natural enemy results in a decrease in resistance against another. Using Drosophila melanogaster, an important model system for the evolution of invertebrate immunity, we test for the existence of cross-resistance against parasites and pathogens, at both a phenotypic and evolutionary level.MethodsWe used a field strain of D. melanogaster to test whether surviving parasitism by the parasitoid Asobara tabida has an effect on the resistance against Beauveria bassiana, an entomopathogenic fungus; and whether infection with the microsporidian Tubulinosema kingi has an effect on the resistance against A. tabida. We used lines selected for increased resistance to A. tabida to test whether increased parasitoid resistance has an effect on resistance against B. bassiana and T. kingi. We used lines selected for increased tolerance against B. bassiana to test whether increased fungal resistance has an effect on resistance against A. tabida.Results/ConclusionsWe found no positive cross-resistance or trade-offs in the resistance to parasites and pathogens. This is an important finding, given the use of D. melanogaster as a model system for the evolution of invertebrate immunity. The lack of any cross-resistance to parasites and pathogens, at both the phenotypic and the evolutionary level, suggests that evolution of resistance against one class of natural enemies is largely independent of evolution of resistance against the other

Tissue-specific inducible expression of antimicrobial peptide genes in Drosophila surface epithelia

The production of antimicrobial peptides is an important aspect of host defense in multicellular organisms. In Drosophila, seven antimicrobial peptides with different spectra of activities are synthesized by the fat body during the immune response and secreted into the hemolymph. Using GFP reporter transgenes, we show here that all seven Drosophila antimicrobial peptides can be induced in surface epithelia in a tissue-specific manner. The imd gene plays a critical role in the activation of this local response to infection. In particular, drosomycin expression, which is regulated by the Toll pathway during the systemic response, is regulated by imd in the respiratory tract, thus demonstrating the existence of distinct regulatory mechanisms for local and systemic induction of antimicrobial peptide genes in Drosophila

The heterogeneous coma of comet 67P/Churyumov-Gerasimenko as seen by ROSINA: H <inf>2</inf> O, CO <inf>2</inf>, and CO from September 2014 to February 2016

Context. The ESA Rosetta mission has been investigating the environment of comet 67P/Churyumov-Gerasimenko (67P) since August 2014. Among the experiments on board the spacecraft, the ROSINA experiment (Rosetta Orbiter Spectrometer for Ion and Neutral Analysis) includes two mass spectrometers to analyse the composition of neutrals and ions and a COmet Pressure Sensor (COPS) to monitor the density and velocity of neutrals in the coma. Aims. We study heterogeneities in the coma during three periods starting in October 2014 (summer in the northern hemisphere) and ending in February 2016 (end of winter in the northern hemisphere). We provide a detailed description of the main volatiles dynamics (H2O, CO2, CO) and their abundance ratios. Methods. We analysed and compared the data of the Reflectron-Type Time-Of-Flight (RTOF) mass spectrometer with data from both the Double Focusing Mass Spectrometer (DFMS) and COPS during the comet escort phase. This comparison has demonstrated that the observations performed with each ROSINA sensor are indeed consistent. Furthermore, we used a Direct Simulation Monte Carlo (DSMC) model to compare modelled densitites with in situ detections. Results. Our analysis shows how the active regions of the main volatiles evolve with the seasons with a variability mostly driven by the illumination conditions; this is the case except for an unexpected dichotomy suggesting the presence of a dust layer containing water deposited in the northern hemisphere during previous perihelions hiding the presence of CO2. The influence of various parameters is investigated in detail: distance to the comet, heliocentric distance, longitude and latitude of sub-satellite point, local time, and phase angle

Relative Roles of the Cellular and Humoral Responses in the Drosophila Host Defense against Three Gram-Positive Bacterial Infections

BACKGROUND: Two NF-kappaB signaling pathways, Toll and immune deficiency (imd), are required for survival to bacterial infections in Drosophila. In response to septic injury, these pathways mediate rapid transcriptional activation of distinct sets of effector molecules, including antimicrobial peptides, which are important components of a humoral defense response. However, it is less clear to what extent macrophage-like hemocytes contribute to host defense. METHODOLOGY/PRINCIPAL FINDINGS: In order to dissect the relative importance of humoral and cellular defenses after septic injury with three different gram-positive bacteria (Micrococcus luteus, Enterococcus faecalis, Staphylococcus aureus), we used latex bead pre-injection to ablate macrophage function in flies wildtype or mutant for various Toll and imd pathway components. We found that in all three infection models a compromised phagocytic system impaired fly survival--independently of concomitant Toll or imd pathway activation. Our data failed to confirm a role of the PGRP-SA and GNBP1 Pattern Recognition Receptors for phagocytosis of S. aureus. The Drosophila scavenger receptor Eater mediates the phagocytosis by hemocytes or S2 cells of E. faecalis and S. aureus, but not of M. luteus. In the case of M. luteus and E. faecalis, but not S. aureus, decreased survival due to defective phagocytosis could be compensated for by genetically enhancing the humoral immune response. CONCLUSIONS/SIGNIFICANCE: Our results underscore the fundamental importance of both cellular and humoral mechanisms in Drosophila immunity and shed light on the balance between these two arms of host defense depending on the invading pathogen