Large Total Variation Research Articles

RF MEMS filter based on dual liquid variations

This paper discusses the behavior of RF MEMS tunable microwave filter. We have modeled the distribution of magnetic field and electric current density in order to reveal the comportment of each device and to evaluate the relation between the frequency response and the microwave performances. From several modelling and simulations, we catch the resonance phenomenon for magnetic and electric fields at different conditions. Hence, in order to develop a reconfigurable MEMS ensuring a function of tunable band-pass filters, we have identified conditions allowing to vary the resonance frequency from Fres = 0.42 GHz to Fres = 1.85 GHz ensuring a large total variation of Tr = 340.5%. The structure is fabricated using SU-8 resin for circulating microchannels and sealing layers. The extracted parameters from measurements results and retro-simulation reveal a diminution of the total tuning range.

Non-relativistic limits and stability of composite wave patterns to the relativistic Euler equations

We are concerned with the structural stability of composite wave patterns to the Cauchy problem for the relativistic full Euler equations consisting of a large 1-shock, a large 2-contact discontinuity, and a large 3-shock. When the initial data are bounded but possibly large total variations, approximate solutions have been constructed via the wave front tracking scheme, a weighted Glimm functional has been introduced and its monotonicity has been proved on the basis of the local wave interaction estimates, and then the global stability of these wave patterns has been established. Moreover, the non-relativistic limits of such solutions can be obtained as the light speed c → +∞.

Large-scale cross-sectional study of relationships between somatic cell count and milking-time test results in different milking systems

Milking-time testing (MTT) is a method for evaluating the vacuum conditions in the teatcup during milking. The purpose is to evaluate the possible impact of the milking and milking equipment on udder health and milk quality. The method is commonly implemented by herd health advisory services, but results are interpreted empirically due to lack of scientific documentation on relationships between MTT result variables and objective measures of udder health.The current study was conducted to increase our understanding of associations between cow-level differences in composite milk somatic cell count (CMSCC) and MTT results in dairy cows milked in 3 different milking systems; automatic milking systems (AMS), milking parlors, and pipeline milking systems. Data from 7069 cows (predominantly Norwegian Red breed) in 1009 herds were used in a cross-sectional study. Multilevel linear regression models with a random intercept at herd level were used to describe relationships between CMSCC (on logarithmic scale) and the following MTT explanatory variables: average vacuum level in the short milk tube and mouthpiece chamber in the main milking and overmilking periods, the duration of these two periods, and vacuum stability, measured by sudden vacuum drops in the short milk tube. The models were corrected for the herd effect, mastitis history and differences in milk yield, lactation stage and parity between cows. Separate models were run for AMS, milking parlors, and pipeline milking systems, because this approach allowed for comparison between systems and for evaluation of the herd effect independently of milking system.The models described 8–10 % of the variation in CMSCC, indicating that MTT could only explain a relatively small proportion of a large total variation in CMSCC. In most observations, vacuum levels in the short milk tube during main milking were within the range recommended by the International Organization for Standardization. The results from our multivariable models showed decreasing CMSCC with increasing vacuum level in the short milk tube during the main milking period in AMS and milking parlors. Similarly, decreasing CMSCC was also associated with increasing duration of the main milking period in all 3 systems. These relationships are important for the interpretation of MTT results under practical conditions; finding high vacuum levels and long milking durations in a MTT is not associated with elevated CMSCC. In AMS herds, we also found indications that the relationships were different for cows where a case of mastitis had been treated before the MTT.

On finite time BV blow-up for the p-system

The paper studies the possible blowup of the total variation for entropy weak solutions of the p-system, modeling isentropic gas dynamics. It is assumed that the density remains uniformly positive, while the initial data can have arbitrarily large total variation (measured in terms of Riemann invariants). Two main results are proved. (I) If the total variation blows up in finite time, then the solution must contain an infinite number of large shocks in a neighborhood of some point in the t-x plane. (II) Piecewise smooth approximate solutions can be constructed whose total variation blows up in finite time. For these solutions the strength of waves emerging from each interaction is exact, while rarefaction waves satisfy the natural decay estimates stemming from the assumption of genuine nonlinearity.

Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic gas. Meanwhile, a transonic characteristic discontinuity appears to separate the supersonic flow behind the rarefaction wave from the static gas. In this paper, we employ a wave front tracking method to establish structural stability of such a flow pattern under non-smooth perturbations of the upcoming supersonic flow. It is an initial-value/free-boundary problem for the two-dimensional steady non-isentropic compressible Euler system. The main ingredients are careful analysis of wave interactions and construction of suitable Glimm functional, to overcome the difficulty that the strong rarefaction wave has a large total variation.

The path decomposition technique for systems of hyperbolic conservation laws

We are concerned with the problem of the global (in time) existence of weak solutions to hyperbolic systems of conservation laws, in one spatial dimension. First, we provide a survey of the different facets of a technique that has been used in several papers in the last years: the path decomposition. Then, we report on two very recent results that have been achieved by means of suitable applications of this technique. The first one concerns a system of three equations arising in the dynamic modeling of phase transitions, the second one is the famous Euler system for nonisentropic fluid flow. In both cases, the results concern classes of initial data with possibly large total variation.

Delta shocks interactions and the wave front tracking method

The subject of this paper is numerical verification of delta shock waves interaction for a pressureless gas dynamics system using the approximated Wave Front Tracking algorithm. We approach the subject in two different ways. The first way is by perturbing the system with a small pressure term. The obtained perturbed system is strictly hyperbolic. We use the new bounds on the strength of elementary waves in the Wave Front Tracking algorithm. That allows us to get a global solution for initial data with arbitrary large total variation, provided that the perturbing parameter is small enough. The second approach is by using a shadow wave solution concept. The paper ends with the comparison of the solutions obtained in these two ways.

The Slow Erosion Limit in a Model of Granular Flow

We study a 2 × 2 system of balance laws that describes the evolution of a granular material (avalanche) flowing downhill. The original model was proposed by Hadeler and Kuttler (Granul Matter 2:9–18, 1999). The Cauchy problem for this system has been studied by the authors in recent papers (Amadori and Shen in Commun Partial Differ Equ 34:1003–1040, 2009; Shen in J Math Anal Appl 339:828–838, 2008). In this paper, we first consider an initial-boundary value problem. The boundary condition is given by the flow of the incoming material. For this problem we prove the global existence of BV solutions for a suitable class of data, with bounded but possibly large total variations. We then study the “slow erosion (or deposition) limit”. We show that, if the thickness of the moving layer remains small, then the profile of the standing layer depends only on the total mass of the avalanche flowing downhill, not on the time-law describing the rate at which the material slides down. More precisely, in the limit as the thickness of the moving layer tends to zero, the slope of the mountain is provided by an entropy solution to a scalar integro-differential conservation law.

Solutions with large total variation to nonconservative hyperbolic systems

In this note we prove the existence of solutions for a class of first order non-linear hyperbolic systems. Given a possibly non conservative straight line system, we prove that all hyperbolic systems sufficiently near to the given one also admit global solutions. The total variation of the initial data is not assumed to be small. Stability estimates are also provided.

Global Existence of Large BV Solutions in a Model of Granular Flow

In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20], describing the flow of granular matter in terms of the heights of a standing layer and of a moving layer. By a suitable change of variables, the system can be written as a 2 × 2 hyperbolic system of balance laws, which we study in the one-dimensional case. The system is linearly degenerate along two straight lines in the phase plane, and therefore is weakly linearly degenerate at the point of the intersection. The source term is quadratic, consisting of product of two quantities, which are transported with strictly different speeds. Assuming that the initial height of the moving layer is sufficiently small, we prove the global existence of entropy-weak solutions to the Cauchy problem, for a class of initial data with bounded but possibly large total variation.

On a Model of Multiphase Flow

We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity, and the mass density fraction of the vapor in the fluid. For a class of initial data having large total variation we prove the global existence of solutions to the Cauchy problem.

Spectral Analysis of a Model of the Compressible Euler Equations

We construct degenerate quadratic models for the Euler equations which distinguish the stabilizing effect of an antisymmetry in the Lie structure of the Euler equations when this antisymmetry is accounted for versus when it is not. We derive a matrix, depending only on the mesh size, $N$, and the 2-wave strengths, whose powers propagate the 1- and 3-waves up to time $t$. We give sharp estimates for the magnitude of the largest eigenvalue of this matrix and conclude that the solution will decay for initial data of arbitrarily large total variation, of order the 4-th root of $N$ in the limit $N$ approaches infinity, when the antisymmetry is accounted for, and only for suffciently small total variation when it is not

Large BV solutions to the compressible isothermal Euler–Poisson equations with spherical symmetry

The Euler–Poisson equations for isothermal flows in charge transport are studied. The global weak entropy solution with spherical symmetry is constructed for arbitrarily large initial data in BV. The global solution is in BV and has large total variations. One difficulty is that the system of Euler–Poisson equations is a hyperbolic–elliptic coupled system, and the property of finite propagation speed does not hold. A modified Glimm scheme is used to construct the approximate solution of the Euler equations while the Poisson equation is approximated by an integral of the solution to the Euler equations. Other difficulties include the geometrical structure, the damping and some additional source terms, which make the analysis more complicated and difficult. To overcome these difficulties, the solution of a discrete ordinary differential equation is used to construct the approximate solution. It is proved that vacuum will not occur in the solution, which is important to obtain the compactness of the approximate solution in BV.

Well-Posedness for Hyperbolic Systems of Conservation Laws with Large BV Data

We study the Cauchy problem for a strictly hyperbolic n × n system of conservation laws in one space dimension Open image in new window assuming that the initial data Open image in new window has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problems generated by the jumps in Open image in new window we prove existence and uniqueness of a (local in time) BV solution, depending continuously on the initial data in L1loc. The last section contains an application to the 3 × 3 system of gas dynamics.

$L^1$ continuous dependence for the Euler equations of compressible fluids dynamics

We prove the $L^1$ continuous dependence of entropy solutions for the $2 \times 2$ (isentropic) and the $3\times 3$ (non-isentropic) systems of inviscid fluid dynamics in one-space dimension. We follow the approach developed by the second author for solutions with small total variation to general systems of conservation laws in [11, 14]. For the systems of fluid dynamics under consideration here, our estimates are more precise and we cover entropy solutions with large total variation.

Sharp L 1 Continuous Dependence¶of Solutions of Bounded Variation¶for Hyperbolic Systems of Conservation Laws

In this paper, we establish the sharp L 1 continuous dependence of entropy solutions of bounded variation for genuinely nonlinear hyperbolic systems of conservation laws. The sharp estimate contains quadratic and cubic dissipation terms which are precisely identified. For general systems, the results hold for solutions with small total variation. For a typical model arising in continuum physics, we can handle solutions with large total variation.

Changes in wood and stem properties of Pinus sylvestris caused by provenance transfer

Wood properties focused in forest tree breeding should be of economic importance, have a large total variation and a high heritability. The properties of interest are those that influence the strength and durability of sawn products or the amount and properties of pulp produced. The following wood properties are treated: width of the annual ring, juvenile wood, late wood content, heart wood, tracheid dimensions, basic density, stem straightness and branch diameter. The provenance variation in wood properties can be related to differences in growth phenology. In the northern part of distribution P. sylvestris (L.) provenances transferred a few degrees southwards have a high survival and yield but stem wood production is low. Trees from these provenances will be straight and with few spike knots or other injuries. The shoot elongation period will be short and the temperature sum required for wood formation sufficient. Provenances transferred southwards will form thin annual rings, few and thin branches, little early wood, high basic density and slender tracheids with thick cell walls in comparison to local provenances. An example of the effect of alternative transfers on the yield and wood properties is evaluated. In regions with deviating climatic patterns alternative provenance transfer patterns may be better. The objectives of the land owner should influence the provenance choice. The importance of integrating tree improvement with silvicultural management is discussed with reference to spacing.

The large time stability of sound waves

We demonstrate the existence of solutions to the full 3×3 system of compressible Euler equations in one space dimension, up to an arbitrary timeT>0, in the case when the initial data has arbitrarily large total variation, and sufficiently small supnorm. The result applies to periodic solutions of the Euler equations, a nonlinear model for sound wave propagation in gas dynamics. Our analysis establishes a growth rate for the total variation that depends on a new length scaled that we identify in the problem. This length scale plays no role in 2×2 systems, (or any system possessing a full set of Riemann coordinates), nor in the small total variation problem forn×n systems, the cases originally addressed by Glimm in 1965. Recent work by a number of authors has demonstrated that when the total variation is sufficiently large, solutions of 3×3 systems of conservation laws can in general blow up in finite time, (independent of the supnorm), due to amplifying instabilities created by the non-trivial Lie algebra of the vector fields that define the elementary waves. For the large total variation problem, there is an interaction between large scale effects that amplify and small scale effects that are stable, and we show that the length scale on which this interaction occurs isd. In the limitd→∞, we recover Glimm's theorem, and we observe that there exist linearly degenerate systems within the class considered for which the growth rate we obtain is sharp.

On Measures Determined by Continuous Functions that are not of Bounded Variation

In [1] it was shown that a continuous function of bounded variation on the real line determined a Method II outer measure for which the Borel sets were measurable and the measure of an open interval was equal to the total variation of f over the interval. The monotone property of measures implied that if an open interval I on which f was not of bounded variation contained subintervals on which f was of finite but arbitrarily large total variation then the measure of I was infinite. Since there are continuous functions that are not of bounded variation over any interval (e.g. the Weierstrasse nondifferentiable function) the general case was not resolved.