Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes occurring in the internal heterogeneous structure. These models tend to be intensive from the computational point of view as they adopt an “a priori” discretization anchored to the major material heterogeneities (e.g. grains in particulate materials and aggregate pieces in cementitious composites) and this hampers their use in the numerical simulations of large systems. In this work, this problem is addressed by formulating a general multiple scale computational framework based on classical asymptotic analysis and that (1) is applicable to any discrete model with rotational degrees of freedom; and (2) gives rise to an equivalent Cosserat continuum. The developed theory is applied to the upscaling of the Lattice Discrete Particle Model (LDPM), a recently formulated discrete model for concrete and other quasi-brittle materials, and the properties of the homogenized model are analyzed thoroughly in both the elastic and the inelastic regime. The analysis shows that the homogenized micropolar elastic properties are size-dependent, and they are functions of the RVE size and the size of the material heterogeneity. Furthermore, the analysis of the homogenized inelastic behavior highlights issues associated with the homogenization of fine-scale models featuring strain-softening and the related damage localization. Finally, nonlinear simulations of the RVE behavior subject to curvature components causing bending and torsional effects demonstrate, contrarily to typical Cosserat formulations, a significant coupling between the homogenized stress–strain and couple-curvature constitutive equations.     

Molecular Dynamics,Phase Transition and Frequency‐Tuned Dielectric Switch of an Ionic Co‐Crystal

Dielectric switches that can be converted between high and low dielectric states by thermal stimuli have attracted much interest owing to their many potential applications. Currently one main drawback for practical application lies in the non‐tunability of their switch temperatures (T_S). We report here an ionic co‐crystal (Me₃NH)₄[Ni(NCS)₆] that contains a multiply rotatable Me₃NH⁺ ion and a solely rotatable one due to a more spacious supramolecular cage for the former one. This compound undergoes an isostructural order–disorder phase transition and it can function as a frequency‐tuned dielectric switch with highly adjustable T_S, which is further revealed by the variable‐temperature structure analyses and molecular dynamics simulations. In addition, the distinct arrangements and molecular dynamics of two coexisting Me₃NH⁺ ions confined in different lattice spaces as well as the notable offset effect on the promoting/hindering of dipolar reorientation after dielectric transition provide a rarely observed but fairly good model for understanding and modulating the dipole motion in crystalline environment.     

Strain rate effects on compressive behavior of covalently bonded CNT networks

In this study, strain rate effects on the compressive mechanical properties of randomly structured carbon nanotube (CNT) networks were examined. For this purpose, three-dimensional atomistic models of CNT networks with covalently-bonded junctions were generated. After that, molecular dynamics (MD) simulations of compressive loading were performed at five different strain rates to investigate the basic deformation characteristic mechanisms of CNT networks and determine the effect of strain rate on stress–strain curves. The simulation results showed that the strain rate of compressive loading increases, so that a higher resistance of specimens to deformation is observed. Furthermore, the local deformation characteristics of CNT segments, which are mainly driven by bending and buckling modes, and their prevalence are strongly affected by the deformation rate. It was also observed that CNT networks have superior features to metal foams such as metal matrix syntactic foams (MMSFs) and porous sintered fiber metals (PSFMs) in terms of energy absorbing capabilities.     

Strain gradient plasticity analysis of elasto-plastic contact between rough surfaces

From a microscopic point of view, the real contact area between two rough surfaces is the sum of the areas of contact between facing asperities. Since the real contact area is a fraction of the nominal contact area, the real contact pressure is much higher than the nominal contact pressure, which results in plastic deformation of asperities. As plasticity is size dependent at size scales below tens of micrometers, with the general trend of smaller being harder, macroscopic plasticity is not suitable to describe plastic deformation of small asperities and thus fails to capture the real contact area and pressure accurately. Here we adopt conventional mechanism-based strain gradient plasticity (CMSGP) to analyze the contact between a rigid platen and an elasto-plastic solid with a rough surface. Flattening of a single sinusoidal asperity is analyzed first to highlight the difference between CMSGP and J₂ isotropic plasticity. For the rough surface contact, besides CMSGP, pure elastic and J₂ isotropic plasticity analysis is also carried out for comparison. In all cases, the contact area A rises linearly with the applied load, but with a different slope which implies that the mean contact pressures are different. CMSGP produces qualitative changes in the distributions of local contact pressures compared with pure elastic and J₂ isotropic plasticity analysis, furthermore, bounded by the two.     

A Study on Photoacoustic Phase Spectra of Rare Earth Complexes with Oxine

Photoacoustic phase is the time delay that occurs from light to acoustic signal. the phase includes two components: one is the time delay that occurs during the process in which light absorbed by a sample converts into heat; the other is the time delay caused from heat to acoustic signal. a modified formula of PA phase is presented based on the R-G theory considering the phase caused by non-radiative relaxation processes. the phase is associated with absorption coefficient (β), thermal diffusion length of sample (μ_s), the longest lifetime of all excited states (r), and the ratio of rapid to slow heat component (R). When the photoacoustic signal is saturated the phase is associated with only T and R. the effect of different rare earth ions on the PA phase spectra of the ligand (oxine) in the rare earth complexes are reported and are well explained by using the phase formula of PA saturation.     

The Effect of Selenium Supplementation on the NMR Proton Relaxation Time T1 in Plasma

Selenium has been identified as an essential dietary trace e1ementQ)which is a component of glutathione peroxidase (GSH-Px)(₂)and a cytochrome C-like protein(₃), The enzyme,the four subunits of which each contain one atom of selenium in the form of selenocysteine, the selenium containing active centre being amenable to chemical modification, catalyses the reduction of H,O,and organic hydroperoxides to water.In this way GSH-Px plays an important role in the protection of the cell from oxidative stresses such as the superoxide anion,organic hydroperoxides and H₂O₂     

Concentration Dependence of NMR T1 in Agar Solutions

In this study, in order to explain solvent proton relaxation mechanism, the spin-lattice relaxation time (T1) of agar solutions was measured as a function of agar concentration. Relaxation measurements were carried out by a FT-NMR spectrometer operating at 60 MHz and inversion recovery pulse squence was used. Relaxation rate(1/T1a) was linearly proportional to concentration of agar solution (C), and the T1 mechanism of solvent water protons in agar solutions should be caused by the chemical exchange of water protons between free and bound water.     

Dielectric barrier discharge in needle-to-plane configuration: Model of surface charge relaxation

Relaxation process of surface charge owing to dielectric barrier discharge (DBD) in “needle – air gap – polyethylene terephthalate film – plane” configuration is considered. Experimental data of the surface charge relaxation (SCR) are obtained by means of the rotating capacitive probe. Taking into account Gaussian radial distribution of accumulated charge density, effective surface and volume electrical conductivities of a barrier dielectric, phenomenological model of SCR for any dielectric thickness is proposed and exact solutions are obtained. The adequacy of the model is confirmed by the numerical computation. There is a good agreement between the experimental results and the model calculations.     

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.