A direct primitive variable recovery scheme for hyperbolic conservative equations: the case of relativistic hydrodynamics

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.Comment: 19 pages, 6 figures, 2 tables. Accepted for publication in PLOS ON

A comparison of the Bering Sea, Gulf of Alaska, and Aleutian Islands large marine ecosystems through food web modeling / by K. Aydin ... [et al.]

Detailed mass balance food web models were constructed to compare ecosystem characteristics for three Alaska regions: the eastern Bering Sea (EBS), the Gulf of Alaska (GOA), and the Aleutian Islands (AI). This paper documents the methods and data used to construct the models and compares ecosystem structure and indicators across models. The common modeling framework, including biomass pool and fishery definitions, resulted in comparable food webs for the three ecosystems which showed that they all have the same apex predator—the Pacific halibut longline fishery. However, despite the similar methods used to construct the models, the data from each system included in the analysis clearly define differences in food web structure which may be important considerations for fishery management in Alaska ecosystems. The results showed that the EBS ecosystem has a much larger benthic influence in its food web than either the GOA or the AI. Conversely, the AI ecosystem has the strongest pelagic influence in its food web relative to the other two systems. The GOA ecosystem appears balanced between benthic and pelagic pathways, but is notable in having a smaller fisheries catch relative to the other two systems, and a high biomass of fish predators above trophic level (TL) 4, arrowtooth flounder and halibut. The patterns visible in aggregated food webs were confirmed in additional more detailed analyses of biomass and consumption in each ecosystem, using both the single species and whole ecosystem indicators developed here

Predictive Behavior of a Computational Foot/Ankle Model through Artificial Neural Networks

Computational models are useful tools to study the biomechanics of human joints. Their predictive performance is heavily dependent on bony anatomy and soft tissue properties. Imaging data provides anatomical requirements while approximate tissue properties are implemented from literature data, when available. We sought to improve the predictive capability of a computational foot/ankle model by optimizing its ligament stiffness inputs using feedforward and radial basis function neural networks. While the former demonstrated better performance than the latter per mean square error, both networks provided reasonable stiffness predictions for implementation into the computational model

Zero Temperature Phases of the Electron Gas

The stability of different phases of the three-dimensional non-relativistic electron gas is analyzed using stochastic methods. With decreasing density, we observe a {\it continuous} transition from the paramagnetic to the ferromagnetic fluid, with an intermediate stability range ($25\pm 5 \leq r_s\leq 35 \pm 5$) for the {\it partially} spin-polarized liquid. The freezing transition into a ferromagnetic Wigner crystal occurs at $r_s=65 \pm 10$. We discuss the relative stability of different magnetic structures in the solid phase, as well as the possibility of disordered phases.Comment: 4 pages, REVTEX, 3 ps figure

Magneto-structural transformations via a solid-state nudged elastic band method: Application to iron under pressure

We extend the solid-state nudged elastic band method to handle a non-conserved order parameter - in particular, magnetization, that couples to volume and leads to many observed effects in magnetic systems. We apply this formalism to the well-studied magneto-volume collapse during the pressure-induced transformation in iron - from ferromagnetic body-centered cubic (bcc) austenite to hexagonal close-packed (hcp) martensite. We find a bcc-hcp equilibrium coexistence pressure of 8.4 GPa, with the transition-state enthalpy of 156 meV/Fe at this pressure. A discontinuity in magnetization and coherent stress occurs at the transition state, which has a form of a cusp on the potential-energy surface (yet all the atomic and cell degrees of freedom are continuous); the calculated pressure jump of 25 GPa is related to the observed 25 GPa spread in measured coexistence pressures arising from martensitic and coherency stresses in samples. Our results agree with experiments, but necessarily differ from those arising from drag and restricted parametrization methods having improperly constrained or uncontrolled degrees of freedom.Comment: 7 pages, 7 figure

Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

Generalized Coherent States as Preferred States of Open Quantum Systems

We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.Comment: 5 pages, no figures; Significantly improved presentation, new derivation of invariant uncertainty measure via quantum Fisher information added

Human cachexia induces changes in mitochondria, autophagy and apoptosis in the skeletal muscle

Cachexia is a wasting syndrome characterized by the continuous loss of skeletal muscle mass due to imbalance between protein synthesis and degradation, which is related with poor prognosis and compromised quality of life. Dysfunctional mitochondria are associated with lower muscle strength and muscle atrophy in cancer patients, yet poorly described in human cachexia. We herein investigated mitochondrial morphology, autophagy and apoptosis in the skeletal muscle of patients with gastrointestinal cancer-associated cachexia (CC), as compared with a weight-stable cancer group (WSC). CC showed prominent weight loss and increased circulating levels of serum C-reactive protein, lower body mass index and decreased circulating hemoglobin, when compared to WSC. Electron microscopy analysis revealed an increase in intermyofibrillar mitochondrial area in CC, as compared to WSC. Relative gene expression of Fission 1, a protein related to mitochondrial fission, was increased in CC, as compared to WSC. LC3 II, autophagy-related (ATG) 5 and 7 essential proteins for autophagosome formation, presented higher content in the cachectic group. Protein levels of phosphorylated p53 (Ser46), activated caspase 8 (Asp384) and 9 (Asp315) were also increased in the skeletal muscle of CC. Overall, our results demonstrate that human cancer-associated cachexia leads to exacerbated muscle-stress response that may culminate in muscle loss, which is in part due to disruption of mitochondrial morphology, dysfunctional autophagy and increased apoptosis. To the best of our knowledge, this is the first report showing quantitative morphological alterations in skeletal muscle mitochondria in cachectic patients