On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach

This research presents bending responses of FG-GPLRC plates based upon higher order shear deformation theory (HSDT) for various sets of boundary conditions. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the differential quadrature method (DQM). Afterward, a parametric study is done to present the effects of three kinds of FG patterns, weight fraction of the GPLs, radius ratio, and thickness to inner radius ratio on the bending characteristics of the FG-GPLRC disk. Numerical results reveal that in the initial value of the \(Zt/h\), using more GPLs for reinforcing the structure provides an increase in the normal stresses but this matter is inverse for the higher value of the \(Zt/h\). The results show that considering the smaller radius ratio is a reason for boosting the shear stresses of the structure for each \(Zt/h\). Another consequence is that for the negative value of \(Zt/h\), it is true that by increasing \(h/{R}_{i}\) , the normal stresses increases but if there is positive value for \(Zt/h\), the radial and circumferential stresses fall down by having an increase in the \(h/{R}_{i}\).

     

Efficient monitoring of hyperproperties using prefix trees

Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other and are thus not monitorable by tools that consider computations in isolation. We present the monitoring approach implemented in the latest version of \(\text {RVHyper}\), a runtime verification tool for hyperproperties. The input to the tool are specifications given in the temporal logic \(\text {HyperLTL}\), which extends linear-time temporal logic (LTL) with trace quantifiers and trace variables. \(\text {RVHyper}\) processes execution traces sequentially until a violation of the specification is detected. In this case, a counterexample, in the form of a set of traces, is returned. \(\text {RVHyper}\) employs a range of optimizations: a preprocessing analysis of the specification and a procedure that minimizes the traces that need to be stored during the monitoring process. In this article, we introduce a novel trace storage technique that arranges the traces in a tree-like structure to exploit partially equal traces. We evaluate \(\text {RVHyper}\) on existing benchmarks on secure information flow control, error correcting codes, and symmetry in hardware designs. As an example application outside of security, we show how \(\text {RVHyper}\) can be used to detect spurious dependencies in hardware designs.

     

Bounds on Threshold Probabilities for Coloring Properties of Random Hypergraphs

We study the threshold probability for the property of existence of a special-form \(r\)?-?coloring for a random \(k\)?-?uniform hypergraph in the \(H(n,k,p)\) binomial model. A parametric set of \(j\)?-?chromatic numbers of a random hypergraph is considered. A coloring of hypergraph vertices is said to be \(j\)?-?proper if every edge in it contains no more than \(j\) vertices of each color. We analyze the question of finding the sharp threshold probability of existence of a \(j\)?-?proper \(r\)?-?coloring for \(H(n,k,p)\). Using the second moment method, we obtain rather tight bounds for this probability provided that \(k\) and \(j\) are large as compared to \(r\).

     

Numerical solution of a phase field model for polycrystallization processes in binary mixtures

We consider the numerical solution of a phase field model for polycrystallization in the solidification of binary mixtures in a domain \( \varOmega \subset \mathbb {R}^2\). The model is based on a free energy in terms of three order parameters: the local orientation \(\varTheta \) of the crystals, the local crystallinity \(\phi \), and the concentration c of one of the components of the binary mixture. The equations of motion are given by an initial-boundary value problem for a coupled system of partial differential equations consisting of a regularized second order total variation flow in \( \varTheta \), an \(L^2\) gradient flow in \(\phi \), and a \(W^{1,2}(\varOmega )^*\) gradient flow in c. Based on an implicit discretization in time by the backward Euler scheme, we suggest a splitting method such that the three semidiscretized equations can be solved separately and prove existence of a solution. As far as the discretization in space is concerned, the fourth order Cahn–Hilliard type equation in c is taken care of by a \(\hbox {C}^0\) Interior Penalty Discontinuous Galerkin approximation which has the advantage that the same finite element space can be used as well for the spatial discretization of the equations in \( \varTheta \) and \( \phi \). The fully discretized equations represent parameter dependent nonlinear algebraic systems with the discrete time as a parameter. They are solved by a predictor corrector continuation strategy featuring an adaptive choice of the time-step. Numerical results illustrate the performance of the suggested numerical method.

     

Numerical simulations based on shifted second-order difference/finite element algorithms for the time fractional Maxwell’s system

In this article, mixed element algorithms with second-order time convergence results for the two-dimensional time fractional Maxwell’s equations in the Cole–Cole dispersive medium are developed. Fully discrete mixed element systems with shifted parameters \(\theta\) at time \(t=t_{n-\theta }\), which are constructed by combining the generalized BDF2-\(\theta\) schemes in temporal direction and a mixed element method in space direction, are formulated. For the two-dimensional case of the fractional Maxwell’s system, the algorithm implementation process based on the rectangular subdivision is shown in detail. Finally, two numerical examples are provided to confirm the validity of our method and to analyze the influence of parameters \(\alpha\), \(\theta\) for numerical solutions.

     

Large deflection electro-mechanical analysis of composite structures bonded with macro-fiber composite actuators considering thermal loads

In this paper, static analysis of laminated composite plates and shells bonded with macro-fiber composite (MFC) actuators under thermo-electro-mechanical loads is considered. Most earlier studies in the literature focused on the effects of MFC actuation power and fiber orientations on shape deformation of composite plates/shells subjected to electrical voltage only. Also most of the earlier studies on MFC-\(\hbox {d}_{33}\) bonded smart structures in literature are performed by commercial softwares like Ansys or Abaqus using the thermal strain equivalent approach to model the piezomechanical coupling. Here, our earlier developed geometrically nonlinear plate and shell finite elements considering finite rotation theory are extended for MFC actuator-bonded composite structures taking into account additionally the response to temperature gradients. An improved Reissner–Mindlin hypothesis is considered to derive the variational formulation, in which a parabolic assumption of transverse shear strains across the thickness is assumed. MFC actuators dominated by the \(\hbox {d}_{33}\) effect (MFC-\(\hbox {d}_{33}\)) with arbitrary fiber orientations are considered. The numerical model is validated with composite beams and plates by comparing the results of simulations with experimental investigations existing in the literature. An angle-ply composite shell structure is studied in detail concerning geometrically nonlinear analysis of bending and twisting deformations under different MFC-\(\hbox {d}_{33}\) fiber orientations under electric loading. Shape control of thermally induced deformations of composite plates and shells is performed using bonded MFC-\(\hbox {d}_{33}\) actuators and the significance of the present geometrically nonlinear model is highlighted.

     

Adaptive finite-time congestion controller design of TCP/AQM systems based on neural network and funnel control

This work investigates an adaptive finite-time congestion control problem of transmission control protocol/active queue management. By means of the funnel control, neural networks and sliding mode control, a new AQM algorithm is proposed to ensure that the tracking error \(e_{1}\left( t\right) \) converges to the prescribed boundary in finite time and the transient and steady-state performances of \(e_{1}\left( t\right) \) can be satisfied. The stability analysis is given to prove that all the signals of the closed-loop system are finite-time bounded. Finally, a comparison example is considered to demonstrate the feasibility and superiority of the presented scheme.

     

On topological systems

We establish the reflectivity of the subcategories of \(T_{0}\) and sober topological systems in the category \(\mathbf {TopSys}\) of topological systems. We also introduce a Sierpinski object in the category \(\mathbf {TopSys}\) and point out its connection with \(T_{0}\) and sober topological systems and also with injective \(T_{0}\)-topological systems.     

The representations and computations of generalized inverses $$A^{(1)}_{T,S}$$, $$A^{(1,2)}_{T,S}$$AT,S(1,2) and the group inverse

In this paper, we derive novel representations of generalized inverses \(A^{(1)}_{T,S}\) and \(A^{(1,2)}_{T,S}\), which are much simpler than those introduced in Ben-Israel and Greville (Generalized inverses: theory and applications. Springer, New York, 2003). When \(A^{(1,2)}_{T,S}\) is applied to matrices of index one, a simple representation for the group inverse \(A_{g}\) is derived. Based on these representations, we derive various algorithms for computing \(A^{(1)}_{T,S}\), \(A^{(1,2)}_{T,S}\) and \(A_{g}\), respectively. Moreover, our methods can be achieved through Gauss–Jordan elimination and complexity analysis indicates that our method for computing the group inverse \(A_{g}\) is more efficient than the other existing methods in the literature for a large class of problems in the computational complexity sense. Finally, numerical experiments show that our method for the group inverse \(A_{g}\) has highest accuracy among all the existing methods in the literature and also has the lowest cost of CPU time when applied to symmetric matrices or matrices with high rank or small size matrices with low rank in practice.     

Dusty flow with different water based nanoparticles along a paraboloid revolution: thermal analysis

The thermal analysis on hydromagnetic two-dimensional flow of dusty nano fluid along an upper horizontal surface of paraboloid revolution have been scrutinized. The governing flow are derived under the assumptions of Boussinesq’s boundary layer approximation theory. The effects of Cattaneo-Christov heat flux, variable thermal conductivity, joule heating and viscous dissipation are incorporated in the energy equation. The governing PDE’s for the flow and energy transfer for both the phases are transformed into ODE’S by employing the suitable similarity transformations. The final dimensionless governing coupled ordinary differential equations are resolved with the aid of bvp5c procedure in computational Matlab software. The effects of dimensionless governing controlled flow parameters on velocity, micropolar velocity, and temperature profiles for both the phases are reported and discussed elaborately through plots and tables. The emerging three nanoparticles namely gold, silver and platinum (\(Au,Ag\) and \(Pt\)) are considered throughout graphical analysis along with \(H_{2} O\) is used as a base liquid. It is revealed that the flow velocity declined for strengthen of the applied magneticfield. It is worthy note that the larger values of thermal relaxation parameter \(\gamma\) declines the fluid temperature for both phases. Also, the rate of heat transfer is an increasing function to the escalating values of variable thermal conductivity \(\varepsilon\), while it is reverse trend for the thermal relaxation parameter \(\gamma\). The observations exhibit the prominent features in the field of an advanced bio-medical and thermal engineering.

     

New q-ary quantum MDS codes with distances bigger than $$\frac{ q}{2}$$

The construction of quantum MDS codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474–1484, 2015) for known constructions. However, there have been constructed only a few q-ary quantum MDS \([[n,n-2d+2,d]]_q\) codes with minimum distances \(d>\frac{q}{2}\) for sparse lengths \(n>q+1\). In the case \(n=\frac{q^2-1}{m}\) where \(m|q+1\) or \(m|q-1\) there are complete results. In the case \(n=\frac{q^2-1}{m}\) while \(m|q^2-1\) is neither a factor of \(q-1\) nor \(q+1\), no q-ary quantum MDS code with \(d> \frac{q}{2}\) has been constructed. In this paper we propose a direct approach to construct Hermitian self-orthogonal codes over \(\mathbf{F}_{q^2}\). Then we give some new q-ary quantum codes in this case. Moreover many new q-ary quantum MDS codes with lengths of the form \(\frac{w(q^2-1)}{u}\) and minimum distances \(d > \frac{q}{2}\) are presented.     

Exploring Dynamic Impact of Foreign Direct Investment on China’s CO$$_{}$$ Emissions Using Markov-Switching Vector Error Correction Model

The impact of foreign direct investment (FDI) on China’s CO\(_{2}\) emissions is an important index to evaluate the effect of foreign investment policy. This paper uses the monthly data of CO\(_{2}\) emissions and FDI from January 1997 to December 2013 to analyze the regime states, switching probability and regime correlation between FDI and CO\(_{2}\) emissions with the help of nonlinear Markov-switching vector error correction model (MS-VECM), The results indicate that the influence of FDI on CO\(_{2}\) emissions shows the two-regime dynamic characteristics, FDI has played a stimulating role in promoting China’s CO\(_{2}\) emissions during the period from January 1997 to October 2003, while played an inhibiting role during the period from November 2003 to December 2013. The duration of the inhibiting effect of FDI on CO\(_{2}\) emissions is longer, and the frequency is higher than that of the stimulating effect. Therefore, the overall influence of FDI on CO\(_{2}\) emissions during the period from January 1997 to December 2013 is inhibitive, which means FDI has contributed to CO\(_{2}\) emissions reduction. The innovation points of this study are mainly reflected in the following two aspects: first, nonlinear MS-VECM is introduced to dynamically study the relationship between FDI and CO\(_{2}\) emissions in contrast to prior studies that simply use static analysis method; second, the effect of China’s foreign investment policies on CO\(_{2}\) emissions is evaluated in each period according to the empirical results of MS-VECM.     

Two-Level Penalty Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics Equations

This work is concerned with the study of two-level penalty finite element method for the 2D/3D stationary incompressible magnetohydrodynamics equations. The new method is an interesting combination of the Newton iteration and two-level penalty finite element algorithm with two different finite element pairs \(P_{1}b\)-\(P_{1}\)-\(P_{1}b\) and \(P_{1}\)-\(P_{0}\)-\(P_{1}\). Moreover, the rigorous analysis of stability and error estimate for the proposed method are given. Numerical results verify the theoretical results and show the applicability and effectiveness of the presented scheme.     

Delay-discretization-based sliding mode $$H_{\infty }$$ load frequency control scheme considering actuator saturation of wind-integrated power system

This paper investigates the combined effect of actuator saturation and time-delay on load frequency control (LFC) of a wind-integrated power system (WIPS). Actuator saturation is represented in two different approaches such as polytopic and sector bounding. Delay-discretization-based sliding mode \(H_{\infty }\) control approach is proposed to design a novel LFC scheme. The proposed control scheme requires present as well as delayed states information as input to the controller. This requirement of control scheme is fulfilled by adopting a finite known delay. This finite known delay used in controller design is discretized into delay intervals. Lyapunov–Krasovskii functional is defined for each delay interval, and \(H_{\infty }\) stabilization criteria for the closed loop WIPS are derived in linear matrix inequality framework using Wirtinger-based inequality. The proposed control scheme is tested by considering a numerical example of two-area WIPS.

     

The categories L-\mathbf{Top}_{0} and L-\mathbf{Sob} as epireflective hulls

We show that the category \(L\) - \(\mathbf{Top}_{0}\) of \(T_{0}\) - \(L\) -topological spaces is the epireflective hull of Sierpinski \(L\) -topological space in the category \(L\) - \(\mathbf{Top}\) of \(L\) -topological spaces and the category \(L\) - \(\mathbf{Sob}\) of sober \(L\) -topological spaces is the epireflective hull of Sierpinski \(L\) -topological space in the category \(L\) - \(\mathbf{Top}_{0}\) .     

Parameterized complexity of three edge contraction problems with degree constraints

For any graph class \(\mathcal{H}\) , the \(\mathcal{H}\) -Contraction problem takes as input a graph \(G\) and an integer \(k\) , and asks whether there exists a graph \(H\in \mathcal{H}\) such that \(G\) can be modified into \(H\) using at most \(k\) edge contractions. We study the parameterized complexity of \(\mathcal{H}\) -Contraction for three different classes \(\mathcal{H}\) : the class \(\mathcal{H}_{\le d}\) of graphs with maximum degree at most  \(d\) , the class \(\mathcal{H}_{=d}\) of \(d\) -regular graphs, and the class of \(d\) -degenerate graphs. We completely classify the parameterized complexity of all three problems with respect to the parameters \(k\) , \(d\) , and \(d+k\) . Moreover, we show that \(\mathcal{H}\) -Contraction admits an \(O(k)\) vertex kernel on connected graphs when \(\mathcal{H}\in \{\mathcal{H}_{\le 2},\mathcal{H}_{=2}\}\) , while the problem is \(\mathsf{W}[2]\) -hard when \(\mathcal{H}\) is the class of \(2\) -degenerate graphs and hence is expected not to admit a kernel at all. In particular, our results imply that \(\mathcal{H}\) -Contraction admits a linear vertex kernel when \(\mathcal{H}\) is the class of cycles.     

Gauge Neural Network with Z(2) Synaptic Variables: Phase Structure and Simulation of Learning and Recalling Patterns

We study the Z(2) gauge-invariant neural network which is defined on a partially connected random network and involves Z(2) neuron variables \(S_i\) (\(=\pm \)1) and Z(2) synaptic connection (gauge) variables \(J_{ij}\) (\(=\pm \)1). Its energy consists of the Hopfield term \(-c_1S_iJ_{ij}S_j\), double Hopfield term \(-c_2 S_iJ_{ij}J_{jk} S_k\), and the reverberation (triple Hopfield) term \(-c_3 J_{ij}J_{jk}J_{ki}\) of synaptic self interactions. For the case \(c_2=0\), its phase diagram in the \(c_3-c_1\) plane has been studied both for the symmetric couplings \(J_{ij}=J_{ji}\) and asymmetric couplings (\(J_{ij}\) and \(J_{ji}\) are independent); it consists of the Higgs, Coulomb and confinement phases, each of which is characterized by the ability of learning and/or recalling patterns. In this paper, we consider the phase diagram for the case of nonvanishing \(c_2\), and examine its effect. We find that the \(c_2\) term enlarges the region of Higgs phase and generates a new second-order transition. We also simulate the dynamical process of learning patterns of \(S_i\) and recalling them and measure the performance directly by overlaps of \(S_i\). We discuss the difference in performance for the cases of Z(2) variables and real variables for synaptic connections.     

Shrinking one-way cellular automata

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata (\(\text{OCA}\)) with the additional property that during a computation any cell of the \(\text{OCA}\) has the ability to dissolve itself, so-called shrinking one-way cellular automata (\(\text{SOCA}\)). It turns out that real-time \(\text{SOCA}\) are more powerful than real-time \(\text{OCA}\), since they can accept certain linear-time \(\text{OCA}\) languages. On the other hand, linear-time \(\text{OCA}\) are more powerful than real-time \(\text{SOCA}\), which is witnessed even by a unary language. Additionally, a construction is provided that enables real-time \(\text{SOCA}\) to accept the reversal of real-time iterative array languages. Finally, restricted real-time \(\text{SOCA}\) are investigated. We distinguish two limitations for the dissolving of cells. One restriction is to bound the total number of cells that are allowed to dissolve by some function. In this case, an infinite strict hierarchy of language classes is obtained. The second restriction is inspired by an approach to limit the amount of nondeterminism in \(\text{OCA}\). Compared with the first restriction, the total number of cells that may dissolve is still unbounded, but the number of time steps at which a cell may dissolve is bounded. The possibility to dissolve is allowed only in the first k time steps, where \(k\ge 0\) is some constant. For this mode of operation an infinite, tight, and strict hierarchy of language classes is obtained as well.     

Improved constructions for quantum maximum distance separable codes

In this work, we further improve the distance of the quantum maximum distance separable (MDS) codes of length \(n=\frac{q^2+1}{10}\). This yields new families of quantum MDS codes. We also construct a family of new quantum MDS codes with parameters \([[\frac{q^2-1}{3}, \frac{q^2-1}{3}-2d+2, d]]_{q}\), where \(q=2^m\), \(2\le d\le \frac{q-1}{3}\) if \(3\mid (q+2)\), and \(2\le d\le \frac{2q-1}{3}\) if \(3\mid (q+1)\). Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.     

Combined analytical and numerical approach for auxetic FG-CNTRC plate subjected to a sudden load

In the current work, the dynamic behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate with negative Poisson’s ratio (NPR) is investigated by combining higher-order shear deformation theory and large deflection theory. First, explicit solutions are proposed to predict the effective Poisson’s ratio (EPR) of the laminates. Taking carbon nanotube-reinforced composite (CNTRC) as an example, the maximum NPR is obtained for \(\left( { \pm \theta } \right)_{{3{\text{T}}}}\) laminate as well. Results show that the EPR (\(v_{13}^{\text{e}}\),\(v_{23}^{\text{e}}\)) can range from a positive value of 0.311 to a negative value of 0.63. For the dynamic response problem, the asymptotic solutions with a two-step perturbation approach are derived for FG-CNTRC plates to capture the relationship between the center deflection and time. Several key factors such as functionally graded distribution, variations in the elastic foundation, and thermal stress produced by changing the temperature field are considered in the subsequent analysis. Numerical simulations are carried out to examine the corresponding dynamic behavior of FG-CNTRC plates when these factors are taken into account.