The maximal advance path constraint for the homogenization of materials with random network microstructure

This paper presents a non-affine homogenization scheme for materials with a random network microstructure. It is based on a newly developed kinematic constraint that links the microscopic deformation of the network to the macroscopic strain of the material. This relation accounts for the network functionality and is established by means of maximal advance paths that are long enough to reach the macroscopic scales of the continuous body and deform accordingly but are also composed of the microscopic fibres that follow the network deformation. The exact distribution of the variable fibre stretch is determined by the principle of minimum averaged free energy, which ultimately allows one to derive the homogenized elastic response of the network at equilibrium. Besides the general formulation, the model is presented in detail for the case of tetrafunctional networks, for which the micro–macro relation and the expression for the homogenized elastic stress are derived in a compact and interpretable tensorial form. The performance of the model as well as the convexity and stability of the obtained homogenized response of the material is examined for networks composed of two different types of fibres, namely flexible chains and stiff filaments. The qualitative behaviour of the networks predicted for the two considered cases agrees with experimentally observed phenomena for soft materials. This includes a consistent explanation for the difference in the stiffness of elastomers at uniaxial and equibiaxial extension as well as a validation of recent experimental investigations of atypical normal stress amplitudes in biopolymer gels under shear loading.     

The algebraic and geometric classification of nilpotent terminal algebras

We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 21 additional isomorphism classes (see Theorem 13). The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras (see Theorem 15). In particular, there are no rigid 4-dimensional complex nilpotent terminal algebras.     

A one-pot radiation-chemical synthesis of metal-polymeric nanohybrides in solutions of vinyltriazole containing gold ions

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Semilinear subdiffusion with memory in multidimensional domains

For , we investigate the nonlinear integro‐differential equation on a multidimensional space domain where is the Caputo fractional derivative and and are uniform elliptic operators with smooth coefficients depending on time. Under suitable conditions on the nonlinearity, the global existence and uniqueness of the classical solution to the related initial and boundary value problems are established.     

The algebraic classification of nilpotent Tortkara algebras

Abstract

We classify all complex 6-dimensional nilpotent Tortkara algebras.

Communicated by Alberto Facchini     

Triangulenes: From Precursor Design to On-Surface Synthesis and Characterization

Triangulene and its higher homologues are a class of zigzag-edged triangular graphene molecules (ZTGMs) with high-spin ground states. These open-shell molecules are predicted to host ferromagnetically coupled edge states with net spin values scaling with molecular size and are therefore considered promising candidates for future molecular spintronics applications. Unfortunately, the synthesis of unsubstituted [n]triangulenes and the direct observation of their edge states have been a long-standing challenge due to a high reactivity towards oxygen. However, recent advances in precursor design enabled the on-surface synthesis and characterization of unsubstituted [3]-, [4]-, and [5]triangulene. In this Minireview, we will highlight key aspects of this rapidly developing field, ranging from the principles of precursor design to synthetic strategies and characterization of a homologous series of triangulene molecules synthesized on-surface. We will also discuss challenges and future directions.     

An approach to optimize the design of microfluidic chips for electrophoretic separations

The precise design and operational control of the separation process of liquid matrices is key to the performance of on-chip liquid analysis. Present research attempts from the engineering point of view to investigate of the process occurring in the microfluidic channels for chip design with the best separation efficiency. An one-dimensional model of electrokinetic sample motion was developed to simulate the separation process of sample containing amino acids (tryptophan, tyrosine, proline, methionine) that migrate in a buffer solution through a straight separation channel made of poly(methyl methacrylate) within a microfluidic chip under different conditions. On the basis of the simulations by the finite-difference method the effects of the channel size, the chip material, the applied voltage difference and the test solution pH on separation rate are discussed. It was found that for the channel length of 2 cm the resolution of peaks is optimal and the fastest time of amino acids separation is 4 s.     

Partial cohomology of groups and extensions of semilattices of abelian groups

We extend the notion of a partial cohomology group $H^n(G,A)$ to the case of non-unital A and find interpretations of $H^1(G,A)$ and $H^2(G,A)$ in the theory of extensions of semilattices of abelian groups by groups.     

Solution of Equations with One Variable

Let a function f(x) C ^(r)[a,b], r 0, and take values that have different signs at the endpoints of the interval [a,b]. In the article, we propose effective methods for calculating real roots of the equation f(x)=0 on the given interval [a,b]. We substantiate this method and make a comparison between this method and the chord and Newton methods.     

Adaptive Procedures for Numerical Methods

A generalized interpolation polynomial with a base function and node coefficients , is a polynomial of the form