Approximate Controllability of Fractional Semilinear Stochastic System of Order <Emphasis Type="Italic">α</Emphasis>∈ (1,2]

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in L _p spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.     

Turbulent convective heat transfer of methane at supercritical pressure in a helical coiled tube

The heat transfer of methane at supercritical pressure in a helically coiled tube was numerically investigated using the Reynolds Stress Model under constant wall temperature. The effects of mass flux (G), inlet pressure (P_in) and buoyancy force on the heat transfer behaviors were discussed in detail. Results show that the light fluid with higher temperature appears near the inner wall of the helically coiled tube. When the bulk temperature is less than or approach to the pseudocritical temperature (T _pc ), the combined effects of buoyancy force and centrifugal force make heavy fluid with lower temperature appear near the outer-right of the helically coiled tube. Beyond the T _pc , the heavy fluid with lower temperature moves from the outer-right region to the outer region owing to the centrifugal force. The buoyancy force caused by density variation, which can be characterized by Gr/Re² and Gr/Re^2.7, enhances the heat transfer coefficient (h) when the bulk temperature is less than or near the T _pc , and the h experiences oscillation due to the buoyancy force. The oscillation is reduced progressively with the increase of G. Moreover, h reaches its peak value near the T _pc . Higher G could improve the heat transfer performance in the whole temperature range. The peak value of h depends on P_in. A new correlation was proposed for methane at supercritical pressure convective heat transfer in the helical tube, which shows a good agreement with the present simulated results.     

Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients

We investigate Gevrey order and summability properties of formal power series solutions of some classes of inhomogeneous linear partial differential equations with variable coefficients and analytic initial conditions. In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient k, in a given direction.     

Second-Order Viability Problems with Perturbation in Hilbert Spaces

In this paper, we study the existence of viable solutions to the differential inclusion

$ \ddot{x}(t) \in f\left( {t,x(t),\dot{x}(t)} \right) + F\left( {x(t),\dot{x}(t)} \right), $

where f is a Carathéodory single-valued map and F is an upper semi-continuous multifunction with compact values contained in the Clarke subdifferential ? _c V of an uniformly regular function V.

     

Adjoint Orbits of <Emphasis Type="Italic">sl</Emphasis>(2, ℝ) on Real Simple Lie Algebras and Controllability

This paper shows that for any Lie group G whose Lie algebra L is the split real form of a complex simple Lie algebra, and for any arbitrary root α, there exists a Cartan decomposition of L, related to α, which characterizes some controllability properties by using the adjoint orbits of sl(2, ?). For a class of invariant control systems evolving on G, it is proved that the necessary full rank condition for controllability is also sufficient.     

Existence of Solutions and Approximate Controllability of Fractional Nonlocal Neutral Impulsive Stochastic Differential Equations of Order 1 &lt; <Emphasis Type="Italic">q</Emphasis> &lt; 2 with Infinite Delay and Poisson Jumps

In this paper, we study the existence of mild solutions and the approximate controllability of nonlinear fractional nonlocal neutral impulsive stochastic differential equations of order 1 < q < 2 with infinite delay and Poisson jumps in which the initial value belong to the abstract phase space C _h . The existence of mild solutions is derived with the help of Sadovskii’s fixed point theorem. The approximate controllability of the nonlinear fractional nonlocal neutral impulsive stochastic differential systems of order 1 < q < 2 with infinite delay and Poisson jumps is discussed under the assumption that the corresponding linear system is approximately controllable. Moreover, the approximate controllability of the above control system is established by using Lebesgue dominated convergence theorem. An example is provided to illustrate the theory.     

Influence of gamma radiation on spectral photosensitivity of (Si<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript> (ZnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solution

Increase of the photosensitivity of the pSi-n(Si₂)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.01) structure exposed to gamma radiation with photon energy E _ph ≥ 2.3 eV has been demonstrated. It is shown that irradiation with dose up to 10⁴ rad raises and radiation with dose up to 10⁵ rad reduces the forward current of the pSi-n(Si₂)_{1 ? x} (ZnSe) _x structure.     

Cascade Linearization of Invariant Control Systems

Let Pfaffian system ω define an intrinsically nonlinear control system on manifold M that is invariant under the free, regular action of a Lie group G. The problem of identifying and constructing static feedback linearizable G-quotients of ω was solved in De Doná et al. (2016). Building on these results, the present paper proves that the trajectories of ω can often be expressed as the composition of the trajectories of a static feedback linearizable quotient control system, ω/G, on quotient manifold M/G, and those of a separate control system, γ ^G , evolving on a principal G-bundle over a jet space. Furthermore, we point out that ω may not only have a static feedback linearizable quotient, ω/G but additionally, γ ^G itself may possess a static feedback linearizable reduction as well. This enables one to express the trajectories of an intrinsically nonlinear control system as the composition of the trajectories of static feedback linearizable control systems, thereby providing a geometric criterion for the explicit integrability of intrinsically nonlinear systems. Moreover, special integrability properties arise when G is solvable. Examples are presented in which the above phenomena are explicitly demonstrated. An important aspect of the examples is that they gather evidence for the conjecture that our sufficient conditions for explicit integrability are also necessary.     

On High Dimensional Schrödinger Equation with Quasi-Periodic Potentials

In this paper, we consider the high dimensional Schrödinger equation \( -\frac {d^{2}y}{dt^{2}} + u(t)y= Ey, y\in \mathbb {R}^{n}, \) where u(t) is a real analytic quasi-periodic symmetric matrix, \(E= \text {diag}({\lambda _{1}^{2}}, \ldots , {\lambda _{n}^{2}})\) is a diagonal matrix with λ _j >0,j=1,…,n, being regarded as parameters, and prove that if the basic frequencies of u satisfy a Bruno-Rüssmann’s non-resonant condition, then for most of sufficiently large λ _j ,j=1,…,n, there exist n pairs of conjugate quasi-periodic solutions.     

Analysis of turbulence and surface growth models on the estimation of soot level in ethylene non-premixed flames

Soot prediction in a combustion system has become a subject of attention, as many factors influence its accuracy. An accurate temperature prediction will likely yield better soot predictions, since the inception, growth and destruction of the soot are affected by the temperature. This paper reported the study on the influences of turbulence closure and surface growth models on the prediction of soot levels in turbulent flames. The results demonstrated that a substantial distinction was observed in terms of temperature predictions derived using the k-ε and the Reynolds stress models, for the two ethylene flames studied here amongst the four types of surface growth rate model investigated, the assumption of the soot surface growth rate proportional to the particle number density, but independent on the surface area of soot particles, f(A_s) = ρN_s, yields in closest agreement with the radial data. Without any adjustment to the constants in the surface growth term, other approaches where the surface growth directly proportional to the surface area and square root of surface area, f(A_s) = A_s and f(A_s) = √A_s, result in an under-prediction of soot volume fraction. These results suggest that predictions of soot volume fraction are sensitive to the modelling of surface growth.     

Fabrication and investigation of ultravialet Au-Zn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Cd<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>S-Mo-structures

For the first time fabricated and investigated the photovoltaic characteristics of Au-Zn _x Cd_1–x S-Mofilm structural injection photo detectors sensitive to narrow the ultraviolet region of the electromagnetic spectrum, based on polycrystalline Zn _x Cd_1–x S layers. It was found by adjusting the flow of ZnS and CdS coming to the surface Mo substrate can control the shape of the spectral sensitivity of the Au-Zn _x Cd_1–x S-Mo-film structural injection photo detectors. The results will allow to optimize the structure of photo detectors and solar cells based on polycrystalline thin film solar cells.     

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number 40≤ Re ≤200 and various rotation rate θ_i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method(FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow.The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re increases,the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution forθ_iθ_(crit), It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.     

On Symmetries in Time Optimal Control,Sub-Riemannian Geometries,and the <Emphasis Type="Italic">K</Emphasis>−<Emphasis Type="Italic">P</Emphasis> Problem

The goal of this paper is to describe a method to solve a class of time optimal control problems which are equivalent to finding the sub-Riemannian minimizing geodesics on a manifold M. In particular, we assume that the manifold M is acted upon by a group G which is a symmetry group for the dynamics. The action of G on M is proper but not necessarily free. As a consequence, the orbit space M/G is not necessarily a manifold but it presents the more general structure of a stratified space. The main ingredients of the method are a reduction of the problem to the orbit space M/G and an analysis of the reachable sets on this space. We give general results relating the stratified structure of the orbit space, and its decomposition into orbit types, with the optimal synthesis. We consider in more detail the case of the so-called K?P problem where the manifold M is itself a Lie group and the group G is determined by a Cartan decomposition of M. In this case, the geodesics can be explicitly calculated and are analytic. As an illustration, we apply our method and results to the complete optimal synthesis on S O(3).     

Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses

The objective of this paper is to establish the sufficient condition for the controllability of a control problem represented by second-order nonlinear differential equation with non-instantaneous impulses in a Hilbert space X. The results are obtained using the strongly continuous cosine family of linear operators and Banach fixed point method. Also, we study the controllability of the nonlocal as well as integro-differential systems. Finally, a few examples are provided to illustrate the applications of the obtained abstract results.     

Natural heat accumulation in large enclosures of premises with an insulation passive solar heating system

This article provides the results of design studies intended to determine the specific amount of heat accumulated in the inner layers of vast enclosures used in premises with an insulation passive solar heating system (Q _acc) by the temperature-wave method. As shown by the calculation data, the value of Q _acc depends significantly on the ratio of the F _te surface area of the translucent enclosure of the considered premise to the F _fl surface area of its floor slabs and the amplitude of air motion in the heated premise. According to the calculated data, Q _acc, at the end of the second decade of March, is 169.0 kJ/m² at F _te/F _fl = 0.30–0.40 whereas the coefficient of natural heat accumulation in the inner layers of the given vast enclosure is ≈0.12.     

Approximate and Near Weak Invariance for Nonautonomous Differential Inclusions

Let X be a real Banach space and I a nonempty interval. Let \(K:I\rightsquigarrow X\) be a multi-function with the graph \(\mathcal {K} \). We give here a characterization for \(\mathcal {K} \) to be approximate/near weakly invariant with respect to the differential inclusion \(x^{\prime }(t)\in F(t, x(t))\) by means of an appropriate tangency concept and Lipschitz conditions on F. The tangency concept introduced in this paper extends in a natural way the quasi-tangency concept introduced by Cârj? et al. (Trans Amer Math Soc. [2009];361:343–90) (see also Cârj? et al. ([2007])). Viability, invariance and applications. Amsterdam: Elsevier Science B V) in the case when F is independent of t. As an application, we give some results concerning the set of solutions for the differential inclusion \(x^{\prime }(t)\in F(t,x(t))\).     

Influence of composition and heat treatment in CdCl<Subscript>2</Subscript> solution on intrinsic point defects in CdTe films

CdTe films of different compositions were grown by the chemical molecular-beam deposition method. The activation energy and the nature of deep levels in relation with the composition of films based on the temperature dependence of electroconductivity are defined, and the influence on these levels of heat treatment process in CdCl₂ solution has been studied. Deep levels with the following activation energies are defined: E_v +0.31 eV; E_v + 0.42 ± 0.03 eV; E_c–0.44 ± 0.01 eV; E_c–0.28 eV; E_v + 0.24 ± 0.01 eV.     

Small Time Asymptotics on the Diagonal for Hörmander’s Type Hypoelliptic Operators

We compute the small time asymptotics of the fundamental solution of Hörmander’s type hypoelliptic operators with drift, on the diagonal at a point x ₀. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x ₀, then so is also the original control problem, and in this case we show that the fundamental solution blows up as \(\phantom {\dot {i}\!}t^{-\mathcal {N}/2}\), where \(\phantom {\dot {i}\!}\mathcal {N}\) is a number determined by the Lie algebra at x ₀ of the fields, that define the hypoelliptic operator.     

When a Minimal Map Is Totally Transitive on a <Emphasis Type="Italic">G</Emphasis>-Space

In this paper, we introduce the notion of G-regular periodic decomposition (GRPD) for maps on G-spaces and investigate its relation with G-transitivity. It is shown that if a pseudoequivariant, G-transitive map on a G-space has a GRPD of some length n, then its nth iterate is not G-transitive. On the other hand, if a pseudoequivariant, G-transitive map on a G-space has a non-G-transitive nth iterate, then it admits a GRPD of length p for some prime p dividing n. Using the notion of GRPD, it is obtained that a pseudoequivariant, G-minimal map is totally G-transitive on a connected G-space.     

General Expansiveness for Diffeomorphisms from the Robust and Generic Properties

Let f:M → M be a diffeomorphism on a closed smooth d(d ≥ 2)-dimensional manifold. For each \(n\in \mathbb N\), if f belongs to C ¹-interior of the set of the n-expansive diffeomorphisms, then f satisfies quasi-Anosov. For C ¹-generic f, if f is n-expansive then f satisfies both Axiom A and the no-cycle condition.