Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is non-standard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case

Nonlinear ER effects in an ac applied field

The electric field used in most electrorheological (ER) experiments is usually quite high, and nonlinear ER effects have been theoretically predicted and experimentally measured recently. A direct method of measuring the nonlinear ER effects is to examine the frequency dependence of the same effects. For a sinusoidal applied field, we calculate the ac response which generally includes higher harmonics. In is work, we develop a multiple image formula, and calculate the total dipole moments of a pair of dielectric spheres, embedded in a nonlinear host. The higher harmonics due to the nonlinearity are calculated systematically.Comment: Presented at Conference on Computational Physics (CCP2000), held at Gold Coast, Australia from 3-8, December 200

Gaming with eutrophication: Contribution to integrating water quantity and quality management at catchment level

The Metropolitan Region of Sao Paulo (MRSP) hosts 18 million inhabitants. A complex system of 23 interconnected reservoirs was built to ensure its water supply. Half of the potable water produced for MRSP's population (35 m3/s) is imported from a neighbour catchment, the other half is produced within the Alto Tietê catchment, where 99% of the population lives. Perimeters of land use restriction were defined to contain uncontrolled urbanization, as domestic effluents were causing increasing eutrophication of some of these reservoirs. In the 90's catchment committees and sub committees were created to promote discussion between stakeholders and develop catchment plans. The committees are very well structured "on paper". However, they are not very well organised and face a lack of experience. The objective of this work was to design tools that would strengthen their discussion capacities. The specific objective of the AguAloca process was to integrate the quality issue and its relation to catchment management as a whole in these discussions. The work was developed in the Alto Tietê Cabeceiras sub-catchment, one of the 5 sub catchments of the Alto-Tietê. It contains 5 interconnected dams, and presents competitive uses such as water supply, industry, effluent dilution and irrigated agriculture. A RPG was designed following a companion modelling approach (Etienne et al., 2003). It contains a friendly game-board, a set of individual and collective rules and a computerized biophysical model. The biophysical model is used to simulate water allocation and quality processes at catchment level. It articulates 3 modules. A simplified nutrient discharge model permits the estimation of land use nutrient exportation. An arc-node model simulates water flows and associated nutrient charges from one point of the hydrographical network to another. The Vollenweider model is used for simulating specific reservoir dynamics. The RPG allows players to make individual and collective decisions related to water allocation and the management of its quality. Impacts of these decisions are then simulated using the biophysical model. Specific indicators of the game are then updated and may influence player's behaviour (actions) in following rounds. To introduce discussions on the management of water quality at a catchment level, an issue that is rarely explicitly dealt with, four game sessions were implemented involving representatives of basin committees and water and sanitation engineers. During the game session, the participants took advantage of the water quality output of the biophysical model to test management alternatives such as rural sewage collection or effluent dilution. The biophysical model accelerated calculations of flows and eutrophication rates that were then returned to the game board with explicit indicators of quantity and quality. Players could easily test decisions impacting on qualitative water processes and visualize the simulation results directly on the game board that was representing a friendly, virtual and simplified catchment. The Agualoca game proved its ability to turn complex water processes understandable for a non totally initiated public. This experience contributed to a better understanding of multiple-use water management and also of joint management of water quality and quantity. (Résumé d'auteur

Nonlinear alternating current responses of graded materials

When a composite of nonlinear particles suspended in a host medium is subjected to a sinusoidal electric field, the electrical response in the composite will generally consist of alternating current (AC) fields at frequencies of higher-order harmonics. The situation becomes more interesting when the suspended particles are graded, with a spatial variation in the dielectric properties. The local electric field inside the graded particles can be calculated by the differential effective dipole approximation, which agrees very well with a first-principles approach. In this work, a nonlinear differential effective dipole approximation and a perturbation expansion method have been employed to investigate the effect of gradation on the nonlinear AC responses of these composites. The results showed that the fundamental and third-harmonic AC responses are sensitive to the dielectric-constant and/or nonlinear-susceptibility gradation profiles within the particles. Thus, by measuring the AC responses of the graded composites, it is possible to perform a real-time monitoring of the fabrication process of the gradation profiles within the graded particles.Comment: 18 pages, 4 figure

Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems

We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and find that our eigenvalue expansions agree with those of Rayleigh/Schrodinger theory, whereas our wave functions more accurately capture the more-rapid-than-gaussian decay. For the quartic oscillator our results strongly suggest that the ground state energy eigenvalue expansion and its associated wave function expansion are Borel summable to yield natural candidates for the actual exact ground state solution and its energy. Our techniques for proving the existence of the crucial `fundamental solution' to the relevant Hamilton Jacobi equation admit infinite dimensional generalizations. In a parallel project we shall show how this construction can be carried out for the Yang-Mills equations in Minkowski spacetime

Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

Nonlinear ac response of anisotropic composites

When a suspension consisting of dielectric particles having nonlinear characteristics is subjected to a sinusoidal (ac) field, the electrical response will in general consist of ac fields at frequencies of the higher-order harmonics. These ac responses will also be anisotropic. In this work, a self-consistent formalism has been employed to compute the induced dipole moment for suspensions in which the suspended particles have nonlinear characteristics, in an attempt to investigate the anisotropy in the ac response. The results showed that the harmonics of the induced dipole moment and the local electric field are both increased as the anisotropy increases for the longitudinal field case, while the harmonics are decreased as the anisotropy increases for the transverse field case. These results are qualitatively understood with the spectral representation. Thus, by measuring the ac responses both parallel and perpendicular to the uniaxial anisotropic axis of the field-induced structures, it is possible to perform a real-time monitoring of the field-induced aggregation process.Comment: 14 pages and 4 eps figure

Transport of Proteins into Mitochondria

The mitochondrial ADP/ATP carrier is an integral transmembrane protein of the inner membrane. It is synthesized on cytoplasmic ribosomes. Kinetic data suggested that this protein is transferred into mitochondria in a posttranslational manner. The following results provide further evidence for such a mechanism and provide information on its details. 1. In homologous and heterologous translation systems the newly synthesized ADP/ATP carrier protein is present in the postribosomal supernatant. 2. Analysis by density gradient centrifugation and gel filtration shows, that the ADP/ATP carrier molecules in the postribosomal fraction are present as soluble complexes with apparent molecular weights of about 120000 and 500000 or larger. The carrier binds detergents such as Triton X-100 and deoxycholate forming mixed micelles with molecular weights of about 200000–400000. 3. Incubation of a postribosomal supernatant of a reticulocyte lysate containing newly synthesized ADP/ATP carrier with mitochondria isolated from Neurospora spheroplasts results in efficient transfer of the carrier into mitochondria. About 20–30% of the transferred carrier are resistant to proteinase in whole mitochondria. The authentic mature protein is also largely resistant to proteinase in whole mitochondria and sensitive after lysis of mitochondria with detergent. Integrity of mitochondria is a prerequisite for translocation into proteinase resistant position. 4. The transfer in vitro into a proteinase-resistant form is inhibited by the uncoupler carbonyl-cyanide m-chlorophenylhydrazone but not the proteinase-sensitive binding. These observations suggest that the posttranslational transfer of ADP/ATP carrier occurs via the cytosolic space through a soluble oligomeric precursor form. This precursor is taken up by intact mitochondria into an integral position in the membrane. These findings are considered to be of general importance for the intracellular transfer of insoluble membrane proteins. They support the view that such proteins can exist in a water-soluble form its precursors and upon integration into the membrane undergo a conformational change. Uptake into the membrane may involve the cleavage of an additional sequence in some proteins, but this appears not to be a prerequisite as demonstrated by the ADP/ATP carrier protein

Simplifying the clinical classification of polymerase gamma (POLG) disease based on age of onset; studies using a cohort of 155 cases

Background: Variants in POLG are one of the most common causes of inherited mitochondrial disease. Phenotypic classification of POLG disease has evolved haphazardly making it complicated and difficult to implement in everyday clinical practise. The aim of our study was to simplify the classification and facilitate better clinical recognition. / Methods: A multinational, retrospective study using data from 155 patients with POLG variants recruited from seven European countries. / Results: We describe the spectrum of clinical features associated with POLG variants in the largest known cohort of patients. While clinical features clearly form a continuum, stratifying patients simply according to age of onset—onset prior to age 12 years; onset between 12 and 40 years and onset after the age of 40 years, permitted us to identify clear phenotypic and prognostic differences. Prior to 12 years of age, liver involvement (87%), seizures (84%), and feeding difficulties (84%) were the major features. For those with onset between 12 and 40 years, ataxia (90%), peripheral neuropathy (84%), and seizures (71%) predominated, while for those with onset over 40 years, ptosis (95%), progressive external ophthalmoplegia (89%), and ataxia (58%) were the major clinical features. The earlier the onset the worse the prognosis. Patients with epilepsy and those with compound heterozygous variants carried significantly worse prognosis. / Conclusion: Based on our data, we propose a simplified POLG disease classification, which can be used to guide diagnostic investigations and predict disease course

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe