Mechanics of composites with two families of finitely extensible fibers undergoing large deformations

Motivated by experimental measurements of the uniaxial response of collagen fibers, a new strain energy-density function for a solid which is finitely extensible along a preferred direction is proposed. Next, by application of a homogenization technique, the macroscopic strain energy-density function of composites with one and two families of fibers of this material embedded in a neo-Hookean matrix are determined. The resulting explicit expressions for the macroscopic strain energy-density functions are given in terms of the behaviors of the individual phases and their volume fractions. The responses of a few specific composites are investigated, revealing the lock-up surfaces of these composites. Finally, we examine the ability of the macroscopic model to capture experimentally measured stress-strain curves for the medial layer of a human abdominal aorta.     

Some mappings of pfriodic groups

For the rational integera and the rational primeb, letP(a,b) be the set of primesp such that . A natural integerq satisfies (i) iffq is a power product fromP(a,b). In the (additively written) Abelian groupG, g→ag permutes the elements ofG ^# in cycles whose lengths are multiples ofb, but not ofb ², iffG is aπ-group withπ⊂P (a,b). The casea=−2,b=2 has combinational applications.     

Mobility edge phenomenon in a Hubbard chain: A mean field study

We show that a tight-binding one-dimensional chain composed of interacting and non-interacting atomic sites can exhibit multiple mobility edges at different values of carrier energy in presence of external electric field. Within a mean field Hartree–Fock approximation we numerically calculate two-terminal transport by using Green?s function formalism. Several cases are analyzed depending on the arrangements of interacting and non-interacting atoms in the chain. The analysis may be helpful in designing mesoscale switching devices.     

Two graph isomorphism polytopes

The convex hull ψ_n,n of certain (n!)² tensors was considered recently in connection with graph isomorphism. We consider the convex hull ψ_n of the n! diagonals among these tensors. We show: 1. The polytope ψ_n is a face of ψ_n,n. 2. Deciding if a graph G has a subgraph isomorphic to H reduces to optimization over ψ_n. 3. Optimization over ψ_n reduces to optimization over ψ_n,n. In particular, this implies that the subgraph isomorphism problem reduces to optimization over ψ_n,n.     

Nitrones-III: Reaction of 3,4-dihydroisoquinoline n-oxide with phosphonoylids

Reaction of 3,4-dihydroisoquinoline N-oxide 1 with diethyl cyanomethylphosphonate 2 gave the enaminonitrile 1-cyanomethylene-1,2,3,4-tetrahydroisoquinoline 3. Reaction of 1 with trialkyl phosphonoacetate 4 gave 5, the fused aziridine derivative 7 - exo - carbethoxy -1 - aza - 4,5 - benzo - bicyclo[4.1.0]heptene - 4, and the enaminoester 1-carbalkoxymethylene-1,2,3,4-tetrahydroisoquinoline 6. The ratio of 5:6 depends on the reaction conditions. While using 1,2-dimethoxyethane the aziridine 5 is the major product; using alcoholic solvents the yield of 6 increases at the expense of 5 with increasing acidity of the solvent.     

Effect of an energy reservoir on the atmospheric propagation of laser-plasma filaments

The ability to select and stabilize a single filament during propagation of an ultrashort, high-intensity laser pulse in air makes it possible to examine the longitudinal structure of the plasma channel left in its wake. We present the first detailed measurements and numerical 3-D simulations of the longitudinal plasma density variation in a laser-plasma filament after it passes through an iris that blocks the surrounding energy reservoir. Since no compensation is available from the surrounding background energy, filament propagation is terminated after a few centimeters. For this experiment, simulations indicate that filament propagation is terminated by plasma defocusing and ionization loss, which reduces the pulse power below the effective self-focusing power. With no blockage, a plasma filament length of over a few meters was observed.     

The correlation dimension of rat hearts in an experimentally controlled environment

The electric response of several isolated rat hearts in a controlled environment was studied experimentally. The correlation dimension D(2) was estimated and was found to be between 4 and 6.5 when the response was nearly periodic. The variation of D(2) with the concentration of calcium was studied and a general trend of its increase with increasing concentration was found. Two types of ventricular fibrillation (VF) were observed, one that corresponds to a stochastic signal where D(2) is unbounded and the other to a low dimensional dynamical system with 3.5相似文献