Some new well-posedness results for continuity and transport equations, and applications to the chromatography system

We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the BV norm at the initial time. We apply these results (valid in any space dimension) to the k x k chromatography system of conservation laws and to the k x k Keyfitz and Kranzer system, both in one space dimension.Comment: 33 pages, minor change

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data

International audienceThis article is dedicated to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions, or more generally nonconstant monotonic bounded functions, as initial data. Under a uniform strict hyperbolicity assumption on the characteristic fields, we construct a multitype version of the sticky particle dynamics and obtain existence of global weak solutions by compactness. We then derive a $L^p$ stability estimate on the particle system uniform in the number of particles. This allows to construct nonlinear semigroups solving the system in the sense of Bianchini and Bressan [Ann. of Math. (2), 2005]. We also obtain that these semigroup solutions satisfy a stability estimate in Wasserstein distances of all orders, which encompasses the classical $L^1$ estimate and generalises to diagonal systems the results by Bolley, Brenier and Loeper [J. Hyperbolic Differ. Equ., 2005] in the scalar case. Our results are obtained without any smallness assumption on the variation of the data, and only require the characteristic fields to be Lipschitz continuous and the system to be uniformly strictly hyperbolic

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Theoretical Analysis of Hydrogen Bonds, Energy Distribution and Information in a 1 % Rosa damascena Mill Oil Solution

The method of Non-equilibrium Energy Spectrum (NES) was applied in measurement of hydrogen bonds energy distribution in 1% Rosa damscena L. oil solution in deionized water. Local maxima in this spectrum were identical with these obtained in investigations of other biologically active solutions and related to particular bio effects as follows: (-0.1387 eV; 8.95 µm; 1117 cm-1). This local maximum is typical for antibacterial, anti-tumor and anti-inflammatory effects. The local maxima at (-0.1212 eV; 10.23 µm; 978 cm-1) and (-0.1262 eV; 9.82 µm; 1018 cm-1) are typical for anti-inflammatory effects and this at (-0.1112 eV; 11.15 µm; 897 cm-1) is typical for effects on the nervous system and nerve conductivity. Information theoretical analysis was performed using the values of Shannon entropy and Transformational information entropy, pointing to hydrogen bonds distribution similarities between Rosa damscena L., V. myrtillus L. and Salvia divinorum Epling. The possible chemical causes of these similarities were identified as antioxidant activity and polyphenols concentration

Research on the structuring of water clusters in Chlorella vulgaris water suspension

Many bioactive compounds of natural origin have beneficial effects on human health and are used to treat different diseases. Chlorella is a genus of green algae with a high potential for producing biologically active substances. Exposure to extreme conditions can enhance its antioxidant activity and the production of concrete metabolites. C. vulgaris is cultivated in plantations. It is accessible in pharmacies and drugstores. The Health Act of 2005 in Bulgaria allows the therapeutic and prophylactic use of herbs, both independently by patients and as prescribed by a doctor. This study performed comparative spectral analyses of C. vulgaris using a 1% suspension of C. vulgaris in deionized water (v/v) by the methods of Non-equilibrium energy spectrum (NES) and Differential non-equilibrium energy spectrum (DNES). The research was performed in order to make indirect studies of the biological effects of C. vulgaris, which are connected with calcium conductivity and anti-inflammatory and anti-tumor effects. The effects of structuring of water clusters by C. vulgaris were examined. The data from spectral analyses, connected with a peak at (E =-0.1312 eV)(?=9.45 ?m) (?=1058 cm-1), revealed anti-inflammatory effects. The anti-oxidant and anti-tumor effects of C. vulgaris were shown at (E=-0.1387 eV)(?=8.95 ?m)(?=1117 cm-1). The results showed effects of improvement of calcium conductivity and anti-inflammatory, antioxidant and antitumor effects of C. vulgaris on human health

Tensor based multichannel reconstruction for breast tumours identification from DCE-MRIs

A new methodology based on tensor algebra that uses a higher order singular value decomposition to perform three-dimensional voxel reconstruction from a series of temporal images obtained using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is proposed. Principal component analysis (PCA) is used to robustly extract the spatial and temporal image features and simultaneously de-noise the datasets. Tumour segmentation on enhanced scaled (ES) images performed using a fuzzy C-means (FCM) cluster algorithm is compared with that achieved using the proposed tensorial framework. The proposed algorithm explores the correlations between spatial and temporal features in the tumours. The multi-channel reconstruction enables improved breast tumour identification through enhanced de-noising and improved intensity consistency. The reconstructed tumours have clear and continuous boundaries; furthermore the reconstruction shows better voxel clustering in tumour regions of interest. A more homogenous intensity distribution is also observed, enabling improved image contrast between tumours and background, especially in places where fatty tissue is imaged. The fidelity of reconstruction is further evaluated on the basis of five new qualitative metrics. Results confirm the superiority of the tensorial approach. The proposed reconstruction metrics should also find future applications in the assessment of other reconstruction algorithms

Molecular pathways leading to loss of skeletal muscle mass in cancer cachexia can findings from animal models be translated to humans?

Background: Cachexia is a multi-factorial, systemic syndrome that especially affects patients with cancer of the gastrointestinal tract, and leads to reduced treatment response, survival and quality of life. The most important clinical feature of cachexia is the excessive wasting of skeletal muscle mass. Currently, an effective treatment is still lacking and the search for therapeutic targets continues. Even though a substantial number of animal studies have contributed to a better understanding of the underlying mechanisms of the loss of skeletal muscle mass, subsequent clinical trials of potential new drugs have not yet yielded any effective treatment for cancer cachexia. Therefore, we questioned to which degree findings from animal studies can be translated to humans in clinical practice and research. Discussion: A substantial amount of animal studies on the molecular mechanisms of muscle wasting in cancer cachexia has been conducted in recent years. This extensive review of the literature showed that most of their observations could not be consistently reproduced in studies on human skeletal muscle samples. However, studies on human material are scarce and limited in patient numbers and homogeneity. Therefore, their results have to be interpreted critically. Summary: More research is needed on human tissue samples to clarify the signaling pathways that lead to skeletal muscle loss, and to confirm pre-selected drug targets from animal models in clinical trials. In addition, improved diagnostic tools and standardized clinical criteria for cancer cachexia are needed to conduct standardized, randomized controlled trials of potential drug candidates in the future

CXCL14, CXCR7 expression and CXCR4 splice variant ratio associate with survival and metastases in Ewing sarcoma patients

Animal science