Micromechanical Modeling of the Effective Viscoelastic Properties of Inhomogeneous Materials Using Fraction-exponential Operators

A new analytical approach for’ micromechanical modeling of the effective viscoelastic behavior of a’ composite material is presented. Fractionexponential operators are. used to describe the viscoelastic properties of the constituents. To construct the corresponding elastic solution, effective field method is used. Effective viscoelastic operators are obtained from the Volter ra’s elasticity-viscoelasticity correspondence principle. Incompatible deformation that often occurs during the manufacturiig process is taken intp account. All the formulas are obtained in explicit ready-to-use form.     

Approximation Algorithms for Quickest Spanning Tree Problems

Let $G=(V,E)$ be an undirected multigraph with a special vertex ${\it root} \in V$, and where each edge $e \in E$ is endowed with a length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$ that connects $u$ and $v$, the {\it transmission time} of $P$ is defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 / c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$ path in $T$. The {\sc quickest radius spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is minimized. In this paper we present a 2-approximation algorithm for this problem, and show that unless $P =NP$, there is no approximation algorithm with a performance guarantee of $2 - \epsilon$ for any $\epsilon >0$. The {\sc quickest diameter spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V} t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation to this problem, and prove that unless $P=NP$ there is no approximation algorithm with a performance guarantee of ${3 \over 2}-\epsilon$ for any $\epsilon >0$.     

Optimization in terms of interval uncertainty: The determinization method

The current approaches to the optimization of systems under uncertainty are considered. An exact formulation of the problem of the conditional optimization of the target function parameters and limitations under interval uncertainty is given. A determinization method allowed us to solve the problem by reducing it to two completely determined ones of conditional optimization of the same type is stated and proved.     

A linear-encoding model explains the variability of the target morphology in regeneration

A fundamental assumption of today''s molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This ‘inverse problem’ is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering.     

The measurement problem of detecting gravitational waves from binary pulsars

A new method for processing the output signal from a gravitational wave direction finder in the measurement problem of detecting and identifying gravitational waves from binary relativistic astrophysical objects is discussed and studied.     

Study of postgrowth processing in the fabrication of quantum-cascade lasers

The special postgrowth processing of structures for quantum-cascade lasers is studied. The processing includes regrowth with a high-resistivity material (indium phosphide) with a carrier concentration of n ≈ 5 × 10¹⁰ cm^?3, photolithography with various wet chemical etchants, and the fabrication of special contacts providing enhanced heat removal. The use of modified postgrowth processing provides necessary parameters satisfying requirements for high-quality devices.