Theory and Experimental Observation of Scattering by a Space-Time Corner.

In anomaly-free quantum field theories the integrand in the bosonic functional integral—the exponential of the effective action after integrating out fermions—is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-theory the E 8-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions. In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction of heterotic M-theory on cylinders.

Thermal barrier coatings (TBCs) have been investigated both experimentally and through simulation for mixing controlled combustion (MCC) concepts as a method for reducing heat transfer losses and increasing cycle efficiency, but it is still a very active research area. Early studies were inconclusive, with different groups discovering obstacles to realizing the theoretical potential. Nuanced papers have shown that coating material properties, thickness, microstructure, and surface morphology/roughness all can impact the efficacy of the thermal barrier coating and must be accounted for. Adding to the complexities, a strong spatial and temporal heat flux inhomogeneity exists for mixing controlled combustion (diesel) imposed onto the surfaces from the impinging flame jets. In support of the United States Department of Energy SuperTruck II program goal to achieve 55% brake thermal efficiency on a heavy-duty diesel engines, this study sought to develop a deeper insight into the inhomogeneous heat flux from mixing controlled combustion on thermal barrier coatings and to infer concrete guidance for designing coatings. To that end, a co-simulation approach was developed that couples high-fidelity computational fluid dynamics (CFD) modeling of in-cylinder processes and combustion, and finite element analysis (FEA) modeling of the thermal barrier-coated and metal engine components to resolve spatial and temporal thermal boundary conditions. The models interface at the surface of the combustion chamber; FEA modeling predicts the spatially resolved surface temperature profile, while CFD develops insights into the effect of the thermal barrier coating on the combustion process and the boundary conditions on the gas side. The paper demonstrates the capability of the framework to estimate cycle impacts of the temperature swing at the surface, as well as identify critical locations on the piston/thermal barrier coating that exhibit the highest charge temperature and highest heat fluxes. In addition, the FEA results include predictions of thermal stresses, thus enabling insight into factors affecting coating durability. An example of the capability of the framework is provided to illustrate its use for investigating novel coatings and provide deeper insights to guide future coating design.

From Eq. (5.2.2), a linear operation equation such as involved in potential problems may be solved using the Best Approximation Method by use of the inner product $$\rm(u,v)= \ \int\limits_\Gamma \ uvd\Gamma + \ \int\limits_\Omega \ Lu \ Lv \ d\Omega$$ (7.1.1) where the integration over Γ includes both the spatial and temporal boundary conditions (i.e., initial conditions in a diffusion problem).

There is no unique stationary scattering theory. We distinguish the main versions by analyzing the different idealizations (spatial or temporal boundary conditions - SBC and TBC, respectively) implied by different orders of taking the limits of infinite volume and of sharp initial conditions. The relations of the different representations are discussed in detail. The equivalence of the Schrödinger and Heisenberg dynamical pictures, as well as the hermiticity of the Hamiltonian fail for SBC but can be applied in TBC. However, when using TBC the scattering wave does not behave as an eigenfunction of the Hamiltonian. The evaluation of transition rates and rates of change of observables is described for the different approaches. We also distinguish the meaning of two types of invariants of the motion by resolving the temporal variation of the observables as an "internal" production rate plus a term representing the flux across the boundary of the scattering region.

Inhomogeneously broadened lasers have weak spectral narrowing and can generate potentially ultrashort laser pulses. However, the coherence of the actively mode-locked pulses depends on the modulation strength and often is not guaranteed. In this paper an analysis of the pulse coherence property of actively mode-locked inhomogeneously broadened lasers using the space-time analogy in optics is presented. The analytic formulation determines the coherence property of the actively mode-locked laser pulses, and theoretical calculations are in agreement with experimental observations.

Finite element analyses of multi-dimensional, partial differential equations require accurate and complete boundary condition assignments. However, continuous temporal and spatial values along physical boundaries are rarely available when solving realistic problems based on field data. To mitigate this situation a neural network system was developed and coupled with an interpolation routine. This innovative computational utility was used to provide continuous boundary condition information in time and space along physical boundaries of interest. The neural network was trained to predict the time response at discrete boundary locations based on field measurements at those locations. Once trained the neural network system was capable of providing a continuous time history for those locations. This system was then linked to an interpolation routine which handled the spatial component of the boundary condition specifications. These coupled routines facilitated rapid deployment and testing of various finite element representations. Further, the neural network system captured the transient physics of the situation more accurately than interpolation routines used previously.

We study the manifestly exotic tetraquark D •• s0 ´cu s dµ and the scalar tetraquark f 0 ´ud ū dµ in SU(3) c anisotropic quenched lattice QCD.We adopt the O´aµ-improved Wilson (clover) fermion compact 4Q resonance is almost unchanged.In HBC, we find a nontrivial 4Q resonance state about 100 MeV below the two-meson threshold in some quark-mass region.Its chiral behavior largely differs from a two-meson scattering state.The scalar tetraquark f 0 ´ud ū dµ is found to have the mass of about 1.1GeV after chiral extrapolation, and seems to correspond to f 0 ´980µ.Then, the manifestly exotic tetraquark D •• s0 ´cu s dµ would exist around 1GeV in the idealized SU(4) f chiral limit.Finally, MEM analysis is applied to obtain the spectral function of the 4Q system.

Collapse of wave fronts in reaction-diffusion systems

As a western boundary current, the Kuroshio is closely related to the large-scale oceanic circulation and at the same time, is greatly influenced by the local topography because of its narrow width. Numerical studies of the Kuroshio are usually confined to portions of it in different geographical regions since the computer execution time required to run a numerical model of the Pacific using a sufficiently fine grid to resolve adequately the flow structure of the Kuroshio is enormous. In order to circumvent the problems of multiple spatial scales and consistent boundary conditions, nested models are employed in which a coarse grid model of the Pacific is used to supply the open boundary conditions for a finer grid model of the northwestern Pacific to simulate the flow and temperature fields of the Kuroshio in summer and winter. The major features of the Kuroshio have in general been successfully simulated by the nested models.

Nonlinear mixed boundary conditions in BVPs of Logistic type with spatial heterogeneities and a nonlinear flux on the boundary with arbitrary sign. The case [formula omitted

Motivated by the unique physical properties of biological active matter, e.g., cytoskeletal dynamics in eukaryotic cells, we set up effective two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin active gels with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions (K. Kruse et al., Eur. Phys. J. E 16, 5 (2005); A. Basu et al., Eur. Phys. J. E 27, 149 (2008)) for thin active-gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the activity or nonequilibrium drive.

The reliability and accuracy of numerical models and computer simulations to study aerosol deposition in the human respiratory system is investigated for a patient-specific tracheobronchial tree geometry. A computational fluid dynamics (CFD) model coupled with discrete elements methods (DEM) is used to predict the transport and deposition of the aerosol. The results are compared to experimental and numerical data available in the literature to study and quantify the impact of the modeling parameters and numerical assumptions. Even if the total deposition compares very well with the reference data, it is clear from the present work how local deposition results can depend significantly upon spatial discretization and boundary conditions adopted to represent the respiratory act. The modeling of turbulent fluctuations in the airflow is also found to impact the local deposition and, to a minor extent, the flow characteristics at the inlet of the computational domain. Using the CFD-DEM model, it was also possible to calculate the airflow and particles splitting at bifurcations, which were found to depart from the assumption of being equally distributed among branches adopted by some of the simplified deposition models. The results thus suggest the need for further studies towards improving the quantitative prediction of aerosol transport and deposition in the human airways.

In this paper we study the two dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value problem in two situations: the space-periodic problem and the case of a bounded domain with spatial Dirichlet boundary conditions on the Eulerian velocity and the cross product of the director field with its time derivative. We also show that the speed of propagation of the director field is finite and give an upper bound for it.

Analysis and numerical solution of singularly perturbed partial differential equations with large spatial delays and integral boundary conditions: applications in chemical and catalytic systems

The Po Valley (Italy) model inter-comparison exercise (POMI) has been carried out in order to explore the changes in air quality in response to changes in emissions. The starting point was the evaluation of the simulated particulate matter and ozone (O3) modelled concentrations against observations for the year 2005 of the six participating chemical transport models. As models were run with the same configuration in terms of spatial resolution, boundary condition, emissions and meteorology, the differences presented in the models’ results are only related to their formulation. As described in the paper, significant efforts have been made to improve the accuracy of the anthropogenic emissions and meteorological input data. Nevertheless, none of the models using the proposed meteorology succeeded to fulfil the quality performance criteria set in the 2008 Air Quality Directive and in the literature for particulate matter, while also for ozone the results are not very satisfying. Although the overall performances look better for O3 than for particulate matter with an aerodynamic diameter smaller than 10 μm (PM10), the models tend to exhibit a similar behaviour and show the largest model variability in locations where concentrations are the highest (urban areas for PM10 and suburbs and hilly areas for O3). While differences are significant in terms of standard deviation and bias, the correlation remains quite similar among models indicating that models generally capture well the main temporal variations, especially the seasonal ones. Possible explanations for this common behaviour and a discussion of the differences among models’ results are presented in this paper.