Minimal loading conditions for higher-order numerical homogenisation schemes

The present study deals with the formulation of minimal loading conditions for microscale applications in numerical two-scale modelling (FE²) approaches. From the homogenisation concept, a set of volume average rules constrains the microscale PDE to be solved. They are considered to be the minimal set of loading conditions and can be specified by additional polynomial or periodic assumptions, for example, on the microscale displacement field. Whereas the resulting volume integrals can be transformed into surface integrals for so-called first-order homogenisation schemes, this is not possible for a second-order homogenisation of second gradient or micromorphic effective media substituting a heterogeneous microcontinuum represented by a volume element on the microscale. Several numerical examples compare the minimal loading condition concept with standard techniques discussed in literature.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

A Robust Algorithm for Roots Selection and Saturation Pressure Calculation for Cubic Equations of State

Journal of Solution Chemistry - In this work, a robust and rigorous procedure for roots calculation and selection for a Cubic Equation of State is presented. Roundoff errors are detected and...     

Role of NMDA receptor subtypes in different forms of NMDA-dependent synaptic plasticity

Background  

The involvement of different NMDA receptor (NMDAR) subunits has been implicated in several forms of synaptic plasticity. However, it is still controversial to what extent the involvement is specific, and little is known about the role of NMDAR subunits in certain "non-conventional" forms of plasticity. In this study we used subunit-specific blockers to test the roles of NR2A- and NR2B-containing NMDARs in a type of chemical long-term depression (LTD) induced by brief bath application of the NMDAR agonist NMDA to hippocampal slices from 12–18 days old rats. For comparison, we also examined other forms of plasticity, including a "slow LTD" induced by 0.1 Hz stimulation under low Mg²⁺ conditions as well as long-term potentiation (LTP).     

Fabrication and characterization of n-ZnO on p-SiC heterojunction diodes on 4H-SiC substrates

We report on the growth and characterization of n-ZnO/p-4H-SiC heterojunction diodes. Our n-ZnO layers were grown with radical-source molecular beam epitaxy (RS-MBE) on p-4H-SiC epilayers, which was previously prepared in a horizontal hot-wall reactor by chemical vapour deposition (CVD) on the n-type 4H-SiC wafers. Details on the n-ZnO growth on 8-off 4H-SiC wafers, the quality of the layers and the nature of realized p–n structures are discussed. Mesa diode structures were fabricated. Al was sputtered through a circle mask with diameter 1 mm and annealed to form Ohmic contacts to p-SiC. Ohmic contacts to the n-ZnO were formed by 30 nm/300 nm Ti/Au sputtered by electron beam evaporation. Electrical properties of the structures obtained have been studied with Hall measurements, and current–voltage measurements (I–V). I–V measurements of the device showed good rectifying behavior, from which a turn-on voltage of about 2 V was obtained.     

Insights into LiAlH4 Catalyzed Imine Hydrogenation

Commercial LiAlH₄ can be used in catalytic quantities in the hydrogenation of imines to amines with H₂. Combined experimental and theoretical investigations give deeper insight in the mechanism and identifies the most likely catalytic cycle. Activity is lost when Li in LiAlH₄ is exchanged for Na or K. Exchanging Al for B or Ga also led to dramatically reduced activities. This indicates a heterobimetallic mechanism in which cooperation between Li and Al is crucial. Potential intermediates on the catalytic pathway have been isolated from reactions of MAlH₄ (M=Li, Na, K) and different imines. Depending on the imine, double, triple or quadruple imine insertion has been observed. Prolonged reaction of LiAlH₄ with PhC(H)=NtBu led to a side-reaction and gave the double insertion product LiAlH₂[N]₂ ([N]=N(tBu)CH₂Ph) which at higher temperature reacts further by ortho-metallation of the Ph ring. A DFT study led to a number of conclusions. The most likely catalyst for hydrogenation of PhC(H)=NtBu with LiAlH₄ is LiAlH₂[N]₂. Insertion of a third imine via a heterobimetallic transition state has a barrier of +23.2 kcal mol⁻¹ (ΔH). The rate-determining step is hydrogenolysis of LiAlH[N]₃ with H₂ with a barrier of +29.2 kcal mol⁻¹. In agreement with experiment, replacing Li for Na (or K) and Al for B (or Ga) led to higher calculated barriers. Also, the AlH₄⁻ anion showed very high barriers. Calculations support the experimentally observed effects of the imine substituents at C and N: the lowest barriers are calculated for imines with aryl-substituents at C and alkyl-substituents at N.     

Recombination induced hypergraphs: A new approach to mutation-recombination isomorphism

Natural selection acts on genetic variation that comes from two principal sources: mutation and recombination. Because of the inherent differences between mutation and recombination, it is often assumed that they are qualitatively different ways to explore the genotype space. In this paper a new way of constructing recombination spaces is introduced and the topological features of the resulting hypergraphs are analyzed. It is shown that types which are neighbors in the point mutation space are also neighbors in the recombination space, i.e., mutation and recombination spaces are homomorphic. This implies that the shapes of the fitness functions explored by mutation and recombination are similar. However, the potential of one- and two-point recombination operators to explore the fitness landscape may differ dramatically from uniform recombination operators or mutation operators because of the limited number of recombinant types they can produce. © 1996 John Wiley & Sons, Inc.