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

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

Immune-Complex Mimics as a Molecular Platform for Adjuvant-Free Vaccine Delivery

Protein-based vaccine development faces the difficult challenge of finding robust yet non-toxic adjuvants suitable for humans. Here, using a molecular engineering approach, we have developed a molecular platform for generating self-adjuvanting immunogens that do not depend on exogenous adjuvants for induction of immune responses. These are based on the concept of Immune Complex Mimics (ICM), structures that are formed between an oligomeric antigen and a monoclonal antibody (mAb) to that antigen. In this way, the roles of antigens and antibodies within the structure of immune complexes are reversed, so that a single monoclonal antibody, rather than polyclonal sera or expensive mAb cocktails can be used. We tested this approach in the context of Mycobacterium tuberculosis (MTB) infection by linking the highly immunogenic and potentially protective Ag85B with the oligomeric Acr (alpha crystallin, HspX) antigen. When combined with an anti-Acr monoclonal antibody, the fusion protein formed ICM which bound to C1q component of the complement system and were readily taken up by antigen-presenting cells in vitro. ICM induced a strong Th1/Th2 mixed type antibody response, which was comparable to cholera toxin adjuvanted antigen, but only moderate levels of T cell proliferation and IFN-γ secretion. Unfortunately, the systemic administration of ICM did not confer statistically significant protection against intranasal MTB challenge, although a small BCG-boosting effect was observed. We conclude that ICM are capable of inducing strong humoral responses to incorporated antigens and may be a suitable vaccination approach for pathogens other than MTB, where antibody-based immunity may play a more protective role

Integration concept of an Electron Cyclotron System in DEMO

The pre-conceptual layout for an electron cyclotron system (ECS) in DEMO is described. The present DEMO ECS considers only equatorial ports for both plasma heating and neoclassical tearing mode (NTM) control. This differs from ITER, where four launchers in upper oblique ports are dedicated to NTM control and one equatorial EC port for heating and current drive (H&CD) purposes as basic configuration. Rather than upper oblique ports, DEMO has upper vertical ports to allow the vertical removal of the large breeding blanket segments. While ITER is using front steering antennas for NTM control, in DEMO the antennas are recessed behind the breeding blanket and called mid-steering antennas, referred to the radially recessed position to the breeding blanket. In the DEMO pre-conceptual design phase two variants are studied to integrate the ECS in equatorial ports. The first option integrates waveguide bundles at four vertical levels inside EC port plugs with antennas with fixed and movable mid-steering mirrors that are powered by gyrotrons, operating at minimum two different multiples of the fundamental resonance frequency of the microwave output window. Alternatively, the second option integrates fixed antenna launchers connected to frequency step-tunable gyrotrons. The first variant is described in this paper, introducing the design and functional requirements, presenting the equatorial port allocation, the port plug design including its maintenance concept, the basic port cell layout, the transmission line system with diamond windows from the tokamak up to the RF building and the gyrotron sources. The ECS design studies are supported by neutronic and tokamak integration studies, quasi-optical and plasma physics studies, which will be summarized. Physics and technological gaps will be discussed and an outlook to future work will be given

Observation of an Excited Bc+ State

Using pp collision data corresponding to an integrated luminosity of 8.5 fb-1 recorded by the LHCb experiment at center-of-mass energies of s=7, 8, and 13 TeV, the observation of an excited Bc+ state in the Bc+π+π- invariant-mass spectrum is reported. The observed peak has a mass of 6841.2±0.6(stat)±0.1(syst)±0.8(Bc+) MeV/c2, where the last uncertainty is due to the limited knowledge of the Bc+ mass. It is consistent with expectations of the Bc∗(2S31)+ state reconstructed without the low-energy photon from the Bc∗(1S31)+→Bc+γ decay following Bc∗(2S31)+→Bc∗(1S31)+π+π-. A second state is seen with a global (local) statistical significance of 2.2σ (3.2σ) and a mass of 6872.1±1.3(stat)±0.1(syst)±0.8(Bc+) MeV/c2, and is consistent with the Bc(2S10)+ state. These mass measurements are the most precise to date

3D Protein structure prediction with genetic tabu search algorithm

Abstract Background Protein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task. Results In order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods. Conclusions The hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively

Quantum numbers of the X(3872)X(3872) state and orbital angular momentum in its ρ0Jψ\rho^0 J\psi decay

Angular correlations in $B^+\to X(3872) K^+$ decays, with $X(3872)\to \rho^0 J/\psi$, $\rho^0\to\pi^+\pi^-$ and $J/\psi \to\mu^+\mu^-$, are used to measure orbital angular momentum contributions and to determine the $J^{PC}$ value of the $X(3872)$ meson. The data correspond to an integrated luminosity of 3.0 fb$^{-1}$ of proton-proton collisions collected with the LHCb detector. This determination, for the first time performed without assuming a value for the orbital angular momentum, confirms the quantum numbers to be $J^{PC}=1^{++}$. The $X(3872)$ is found to decay predominantly through S wave and an upper limit of $4\%$ at $95\%$ C.L. is set on the fraction of D wave.Comment: 16 pages, 4 figure

Measurement of the inelastic pp cross-section at a centre-of-mass energy of 13TeV

The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum p > 2 GeV/c in the pseudorapidity range 2 < η < 5 is determined to be ϭ acc = 62:2 ± 0:2 ± 2:5mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section ϭ inel = 75:4 ± 3:0 ± 4:5mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7TeV is also reported