A scaling method for modelling the crashworthiness of novel roadside barrier designs

In this paper, a novel method for modelling a scaled vehicle–barrier crash test similar to the 20◦ angled barrier test specified in EN 1317 is reported. The intended application is for proof-of-concept evaluation of novel roadside barrier designs, and as a cost-effective precursor to full-scale testing or detailed computational modelling. The method is based on the combination of the conservation of energy law and the equation of motion of a spring mass system representing the impact, and shows, for the first time, the feasibility of applying classical scaling theories to evaluation of roadside barrier design. The scaling method is used to set the initial velocity of the vehicle in the scaled test and to provide scaling factors to convert the measured vehicle accelerations in the scaled test to predicted full-scale accelerations. These values can then be used to calculate the Acceleration Severity Index score of the barrier for a full-scale test. The theoretical validity of the method is demonstrated by comparison to numerical simulations of scaled and full-scale angled barrier impacts using multibody analysis implemented in the crash simulation software MADYMO. Results show a maximum error of 0.3% ascribable to the scaling method.

Modified crack closure integral technique for extraction of SIFs in meshfee methods

A new approach for extracting stress intensity factors (SIFs) by the element-free Galerkin (EFG) class of methods through a modified crack closure integral (MCCI) scheme is proposed. Its primary feature is that it allows accurate calculation of mode I and mode II SIFs with a relatively simple and straightforward analysis even when a coarser nodal density is employed. The details of the adoption of the MCCI technique in the EFG method are described. Its performance is demonstrated through a number of case studies including mixed-mode and thermal problems in linear elastic fracture mechanics (LEFM). The results are compared with published theoretical solutions and those based on the displacement method, stress method, crack closure integral in conjunction with local smoothing (CCI–LS) technique, as well as the M-integral method. Its advantages are discussed.

Stiffness analysis of polymeric composites using the finite element method

The ability to predict the mechanical behavior of polymer composites is crucial for their design and manufacture. Extensive studies based on both macro- and micromechanical analyses are used to develop new insights into the behavior of composites. In this respect, finite element modeling has proved to be a particularly powerful tool. In this article, we present a Galerkin scheme in conjunction with the penalty method for elasticity analyses of different types of polymer composites. In this scheme, the application of Green's theorem to the model equation results in the appearance of interfacial flux terms along the boundary between the filler and polymer matrix. It is shown that for some types of composites these terms significantly affect the stress transfer between polymer and fillers. Thus, inclusion of these terms in the working equations of the scheme preserves the accuracy of the model predictions. The model is used to predict the most important bulk property of different types of composites. Composites filled with rigid or soft particles, and composites reinforced with short or continuous fibers are investigated. For each case, the results are compared with the available experimental results and data obtained from other models reported in the literature. Effects of assumptions made in the development of the model and the selection of the prescribed boundary conditions are discussed.

Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems

The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e. g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

A simple method to determine the water activity of ethanol-containing samples

The water activity (a(w)) of microbial substrates, biological samples, and foods and drinks is usually determined by direct measurement of the equilibrium relative humidity above a sample. However, these materials can contain ethanol, which disrupts the operation of humidity sensors. Previously, an indirect and problematic technique based on freezing-point depression measurements was needed to calculate the a(w) when ethanol was present. We now describe a rapid and accurate method to determine the a(w) of ethanol-containing samples at ambient temperatures. Disruption of sensor measurements was minimized by using a newly developed, alcohol-resistant humidity sensor fitted with an alcohol filter. Linear equations were derived from a(w) measurements of standard ethanol-water mixtures, and from Norrish's equation, to correct sensor measurements. To our knowledge, this is the first time that electronic sensors have been used to determine the a(w) of ethanol- containing samples.

Applications of the generalized Langevin equation: Towards a realistic description of the baths

The generalized Langevin equation (GLE) method, as developed previously [L. Stella et al., Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalizes toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.

GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

New results on stability analysis of delayed recurrent neural networks based on the integral quadratic constraints approach

This paper is concerned with the analysis of the stability of delayed recurrent neural networks. In contrast to the widely used Lyapunov–Krasovskii functional approach, a new method is developed within the integral quadratic constraints framework. To achieve this, several lemmas are first given to propose integral quadratic separators to characterize the original delayed neural network. With these, the network is then reformulated as a special form of feedback-interconnected system by choosing proper integral quadratic constraints. Finally, new stability criteria are established based on the proposed approach. Numerical examples are given to illustrate the effectiveness of the new approach.

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Electron-impact ionization of diatomic molecules using a configuration-average distorted-wave method

Electron-impact ionization cross sections for diatomic molecules are calculated in a configuration-average distorted-wave method. Core bound orbitals for the molecular ion are calculated using a single-configuration self-consistent-field method based on a linear combination of Slater-type orbitals. The core bound orbitals are then transformed onto a two-dimensional (r,θ) numerical lattice from which a Hartree potential with local exchange is constructed. The single-particle Schrödinger equation is then solved for the valence bound orbital and continuum distorted-wave orbitals with S-matrix boundary conditions. Total cross section results for H2 and N2 are compared with those from semiempirical calculations and experimental measurements.

Design Method for Circularly Polarized Frequency Selective Surfaces

This paper proposes a design method for the realisation of circularly polarised frequency selective surfaces (CP FSS). An equivalent circuit model for a capacitive asymmetric loop FSS is proposed. For this model a set of nonlinear design equation for CP operation is obtained. Based on space mapping of the model and full-wave simulation, a fast converging design method for CP FSS synthesis is demonstrated for the first time. 

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant EFG method

A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported.