Rectangular Systems Research Articles

Analytical Solving a Nonlinear Model of the Glow Discharge

A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.

Flexible Krylov Methods for Edge Enhancement in Imaging.

Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-smooth regularization terms (e.g., total variation). Such regularization methods can be treated as iteratively reweighted least squares problems (IRLS), which are usually solved by the repeated application of a Krylov projection method. This approach gives rise to an inner–outer iterative scheme where the outer iterations update the weights and the inner iterations solve a least squares problem with fixed weights. Recently, flexible or generalized Krylov solvers, which avoid inner–outer iterations by incorporating iteration-dependent weights within a single approximation subspace for the solution, have been devised to efficiently handle IRLS problems. Indeed, substantial computational savings are generally possible by avoiding the repeated application of a traditional Krylov solver. This paper aims to extend the available flexible Krylov algorithms in order to handle a variety of edge-enhancing regularization terms, with computationally convenient adaptive regularization parameter choice. In order to tackle both square and rectangular linear systems, flexible Krylov methods based on the so-called flexible Golub–Kahan decomposition are considered. Some theoretical results are presented (including a convergence proof) and numerical comparisons with other edge-enhancing solvers show that the new methods compute solutions of similar or better quality, with increased speedup.

Power Allocation for Reliable SIC Detection of Rectangular QAM-based NOMA Systems

This paper considers the power allocation for non-orthogonal multiple access (NOMA) users to enable using the successive interference cancellation (SIC) while providing reliable error performance. The derived closed-form expressions are applicable for arbitrary number of NOMA users each of which has a square or rectangular quadrature amplitude modulation (QAM) constellation with arbitrary order. The obtained numerical results show that power assignment process at the transmitter for the superposition process and at the receiver for the SIC process should be performed meticulously because the power difference between the weakest and strongest users can be tremendous when the number of users or the modulation orders increase. Moreover, the derived expressions can be used to reduce the computational complexity that is required to obtain the optimal power coefficients using brute force methods by significantly reducing the search space.

Transient thermal behavior of a segmented thermoelectric cooler with variable cross‐sectional areas

In this work, a simulation model based on finite element analysis for a one-dimensional p-type segmented semiconductor element with different cross-sectional areas is analyzed to predict transient thermal behavior for thermoelectric coolers (TECs). The proposed model considers all thermoelectric effects, including the Peltier effect, Thomson effect, Joule heating, and Fourier's heat conduction. The supercooling occurs when a pulse current higher than the steady-state optimum current is applied to a TEC. Dynamic characteristics, such as minimum cold side temperature and holding time of transient state, which arise in transient supercooling are very important to be considered for the design and operation of TECs. In this study, we present a new approach of transient performance based on leg geometry shape, considering variable cross-sectional areas, as well as individual element lengths of two different thermoelectric materials using a segmentation model proposed. A variety of model designs are analyzed, considering rectangular, trapezoidal, and inverse trapezoidal legs, where also optimum pulse current is found as a function of the element lengths. It is demonstrated that an improvement of 4.75% in the cooling is possible when using trapezoidal legs compared with conventional rectangular systems. Our presented model is mainly a new alternative in characterizing Peltier supercooling as a function of both pulse current ratio as well as the leg shape.

A Review on Thermal Design of Liquid Droplet Radiator System

Liquid Droplet Radiator (LDR) system is regarded as a quite promising waste heat rejection system for aerospace engineering. A comprehensive review on the state-of-the-art of LDR system was carried out. The thermal design considerations of crucial components such as working fluid, droplet generator and collector, intermediate heat exchanger, circulating pump and return pipe were reviewed. The state-of-the-art of existing mathematical models of radiation and evaporation characteristics of droplet layer from literatures were summarized. Furthermore, thermal designs of three LDR systems were completed. The weight and required planform area between the rectangular and triangular LDR systems were respectively compared and the evaporation models for calculating the mass loss were evaluated. Based on the review, some prospective studies of LDR system were put forward in this paper.

On convergence of two-stage iterative scheme

Climent and Perea [Journal of Computational and Applied Mathematics 58:43–48, 2003; MR2013603] proposed first the convergence theory of two-stage iterative scheme for solving real rectangular linear systems. In this article, we revisit the same theory. The first main result provides some sufficient conditions which guarantee that the induced splitting from a two-stage iterative scheme is a proper weak regular splitting. We then establish a few comparison results. Out of these, many are even new in nonsingular matrix setting. Further, we study the monotone convergence theory of the two-stage iterative method. Besides these, we also prove the uniqueness of a proper splitting of a rectangular matrix under certain assumptions.

Extensions of the Augmented Block Cimmino Method to the Solution of Full Rank Rectangular Systems

For the solution of large sparse unsymmetric systems, Duff et al. [SIAM J. Sci. Comput., 37 (2015), pp. A1248--A1269] proposed an approach based on the block Cimmino iterations [Numer. Math., 35 (1...

Geophysical Investigations of the Bronze Age Andreevskoye Settlement in the Southern Trans-Urals (Russia)

The settlements and cemeteries of the Sintashta – type (21st–18th century BC) are concentrated in the southern Trans-Urals steppe. The earliest stage of investigations was related to the decoding of aerial photos that allowed specialists to discover and identify the majority of the settlements. This report presents the results of a geophysical investigation at the Andreevskoye settlement, where we conducted micro-magnetic and ground penetrating radar (GPR) surveys. Magnetic studies have provided new information on the structure of the fortifications and the number and location of houses in the settlements during their occupancy, as well as on the many wells discovered inside the houses. Drawing on our data, a new plan of the settlement was produced, more accurate than the one prepared solely from interpretations of aerial photographs. The settlement consists of multiple layers and is characterized by a complex configuration formed from three rectangular systems of defensive structures. We obtained GPR deep sections along three profiles, indicating the ditches and dwellings of the ancient settlement under sediments and the ruins of walls. Based on these data, we conclude that the depth from the modern surface of the earth to the occupation layer in the dwellings of the ancient settlement is approximately 50–70 cm. Our results provide archaeologists with reliable data that are necessary for the selection of excavation sites.

Dependences of local density of state on temperature, size, and shape in two-dimensional nano-structured superconductors

In this paper, we investigate a local density of state (LDOS) in a two-dimensional nano-structured superconductor. We solve the Bogoliubov-de Gennes equations self-consistently with the two-dimensional finite element method. In the nano-structured superconductor, the LDOS as a function of energy has many discrete peaks. Discretization of the LDOS comes from discretization of energy levels due to the quantum confinement effect in the nano-structured system. When temperature increases, a width of a peak in the LDOS is spread to a large energy range and neighbor peaks are overlapped. On the other hand, for the fixed temperature, the behavior of the LDOS is different between nano-scaled rectangular and square systems. In the nano-scaled rectangular system, when only a length of a long side increases, a contribution of the quantum confinement effect from the long side is suppressed, while the contribution from a length of a short side remains large. Then, some peaks are left in the LDOS even when the length of the long side is very large. These peaks form a periodic structure and can be regarded as gaps in a multi gap structure due to the quantum confinement effect. On the other hand, energy levels in the square system tend to arrange equally. Then, in the square system, peaks in the LDOS which exist in the rectangular system are small. Also, the period between peaks in the LDOS in the square system is smaller than that in the rectangular system.

Observers for rectangular descriptor systems with output nonlinearities: application to secure communications and microcontroller implementation

This work considers full and reduced-order observer design for rectangular descriptor systems with application to secure communications. The output of the system is assumed to have a nonlinear term coupled with the linear part, a case that is often overlooked in the literature. The observer design is feasible under some algebraic conditions and the feasibility of a linear matrix inequality. The results are showcased through the application of secure communications, for the safe transmission and estimation of an information signal and also an encrypted image. Also, a microcontroller implementation of the master system is performed, which is the first step towards a full realisation of the design.

Closed Forms of General Solutions for Rectangular Systems of Coupled Generalized Sylvester Matrix Differential Equations

We investigate a rectangular system of coupled generalized Sylvester matrix differential equations in both nonhomogeneous and homogeneous cases. In order to obtain a closed form of its general solution, we transform it to an equivalent vector differential equation. This is done by using the vector operator and the Kronecker product. An explicit form of its general solution is given in terms of matrix series concerning Mittag-Leffler functions, exponentials, and hyperbolic functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases.

Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs—Application to secure communications

SummaryThis work considers the problem of observer design for rectangular descriptor systems with nonlinearities satisfying incremental quadratic constraints. The observer design is feasible under the satisfaction of a linear matrix inequality and some algebraic relations in the system matrices. The special case of nonlinearities in the output is also considered. Finally, the developed approach is applied to the problem of secure communications and illustrated through numerical examples.

Investigations on the dependence of the stability threshold on different operating procedures in a single-phase rectangular natural circulation loop

During the past years, several studies were focused on the instability of single-phase rectangular natural circulation systems. However, experimental identification of instability threshold and categorization of instability regimes is of prime interest in many industrial applications which have been addressed by very few researchers that too limited to lower diameter loops only. Hence, in the present study, a larger diameter rectangular loop with horizontal heater horizontal cooler (HHHC) configuration has been designed to generate single phase natural circulation data on the steady state and stability behavior. Effect of different operating procedures (i.e., start-up from rest, power raising from stable steady state, and power reduction from an unstable state) on stability behavior are studied. Most of the oscillatory regimes are identified and noticed that the operating procedure can influence the instability threshold. The instability threshold was found to increase with the lowering of the coolant temperature and increasing its flow rate. The operating procedures i.e., power raising from stable steady state and start-up from rest gave the maximum and minimum values of the stability threshold respectively. As opposed to this, the minimum instability threshold in smaller diameter loops was reported for the operating procedure with power reduction from an unstable state. The experimental results confirm the occurrence of the hysteresis phenomenon. Due to the larger diameter and lower Lt/D ratio of the loop, all the oscillatory behaviors were aperiodic in nature in contrast to the observations in smaller diameter loops.

Symmetry exploitation to reduce impedance evaluations in grounding grids

One main concern on wideband evaluation of grounding systems is the high computational burden related to the determination of the impedance matrices. Traditionally, one has to divide any given conductor in a large number of segments which leads to a rather time consuming procedure. However, there are a number of geometrical symmetries that if exploited can significantly reduce the overall computational time. This work aims at investigating the adequacy of using some existing symmetries to reduce computer burden in the assessment of a wideband grounding system in models based on the Method of Moments. An algorithmic approach is proposed to extend the symmetry exploitation to arbitrarily oriented uniform rectangular grounding systems. Several topologies are used to assess the performance of the proposed approach. According to results, the proposed methodology can be more than 12 times faster than the traditional approach without loss of accuracy because it is not a numerical approximation.

Subduction Dynamics and Mantle Pressure: 1. An Analytical Framework Relating Subduction Geometry, Plate Motion, and Asthenospheric Pressure

AbstractRecent work suggests that slab dip may be controlled by differences in dynamic pressure above and below the slab at mid‐asthenospheric depth, motivating exploration of how plate and slab motion are linked to dynamic pressure in the asthenosphere. This paper, the first of two companion papers, presents an analytical method for determining dynamic pressure and velocity in a thin asthenospheric channel, with linear viscosity, consistent with prescribed plate and slab kinematics. Slabs are explicitly incorporated as vertical barriers to asthenospheric flow. Dynamic pressure is expressed as sums of functions with two functional forms, Pedge and Pwall; the former generates discontinuities in velocity (but not pressure) at non‐slab boundaries, and the latter generates discontinuities in pressure (but not velocity) at boundaries with slabs. Application to simple rectangular plate systems demonstrates that asthenospheric velocities within about one trench length of slabs are insensitive to processes on the opposing side of the slab, that dynamic pressure scales linearly with trench length for a given plate aspect ratio and scales approximately linearly with the shortest plate dimension. Although dynamic pressure is quasisymmetrical across convergent plate boundaries that lack slabs, the presence of slabs creates discontinuity and asymmetry in dynamic pressure across subduction zones. When flux of asthenosphere into the lower mantle occurs adjacent to subducting slabs, dynamic pressure is decreased on the side of the slab where down‐flux occurs. This analytical method, applied to systems with multiple arbitrarily shaped plate boundaries, yields excellent results as benchmarked against 3‐D numerical solutions.

The steepest descent of gradient-based iterative method for solving rectangular linear systems with an application to Poisson\u2019s equation

We introduce an effective iterative method for solving rectangular linear systems, based on gradients along with the steepest descent optimization. We show that the proposed method is applicable with any initial vectors as long as the coefficient matrix is of full column rank. Convergence analysis produces error estimates and the asymptotic convergence rate of the algorithm, which is governed by the term sqrt {1-kappa^{-2}}, where κ is the condition number of the coefficient matrix. Moreover, we apply the proposed method to a sparse linear system arising from a discretization of the one-dimensional Poisson equation. Numerical simulations illustrate the capability and effectiveness of the proposed method in comparison to the well-known and recent methods.

On the multi-scale vibroacoustic behavior of multi-layer rectangular core topology systems

The present work deals with multi-layer rectangular core topology systems built up by stacking layers made of different rectangular core geometries. Multi-layer systems have been intensively studied in terms of mechanical performances whereas their vibroacoustic behavior, acoustic efficiency and design is however still an open issue. Several design parameters should be considered to fully understand the dynamic and acoustic behaviour of such structures. Therefore, this paper focuses on controlling the transition frequency and the Sound Transmission Loss (STL) by modifying geometrical parameters of the unit cell, while keeping the mass constant. Infinite panels and real wavenumbers will be considered in the study. The Wave Finite Element Method (WFEM) is used to obtain the targeted indicators. The proposed designs give the opportunity to shift the transition frequency and to control the flexural waves propagating in the structure. Besides, the STL is highly improved in the full frequency range of interest compared to a standard sandwich panel made of a single core.

Computational evaluation of mass filter acceptance and transmittance influenced by developing fields: An application of the plane method to investigate prefilter efficacy for rectangular wave operated mass filters.

The acceptance of quadrupole mass filters is improved when the alternating current (AC) and direct current (DC) fields are developed separately. Physically, this is achieved when a short RF only quadrupole (prefilter) is situated directly ahead of the mass filter. The acceptance gained by a system operating with a prefilter can be observed as an increase in sensitivity over conventional operation. Frequency dynamic duty cycle based rectangular waveform driven (rectangular wave) mass filters, a recent development, currently do not operate with prefilters. Little is known about the influence of duty cycle changes on the acceptance of rectangular wave mass filters. The sensitivity gain seen by conventional systems operating with prefilters indicates that the sensitivity of duty cycle based rectangular wave systems should increase comparably. The objective of this work was to determine prefilter efficacy for nonspecific rectangular wave mass filter systems. In this work, the plane method of acceptance was used to model the change to the acceptance and transmittance of sine and rectangular waveform driven mass filters under different modes of field development. Both systems indicated a fourfold increase in sensitivity when the mass filtering DC or duty cycle was delayed.

On the rectangular fuzzy complex linear systems

In this paper, we focus on generalized fuzzy complex numbers and provide several examples of membership functions and graphical representations of these numbers. Then, a specific type of fuzzy complex linear systems, called the rectangular fuzzy complex linear system, is considered and its algebraic and general solutions are defined. Finally an approach based on restricting the general solution is presented to solve a rectangular fuzzy complex linear system. It is illustrated that the proposed method gives a unique algebraic solution to a rectangular fuzzy complex linear system if it exists. To show the ability and efficiency of the method and for more illustration, three numerical examples including a real application in electrical engineering are modeled and solved.

Stability analysis and numerical simulation of a composite laminated piezoelectric rectangular plate system

This paper investigates the stability behavior in three-degree-freedom composite laminated piezoelectric rectangular plate system based on the Routh-Hurwitz criterion and the normal form theory. Firstly, the stability behavior of the composite laminated piezoelectric rectangular plate is determined by applying the Routh-Hurwitz criterion. Then, the normal forms of the composite laminated piezoelectric rectangular plate systems for the case of one non-semi-simple double zero and two pairs of pure imaginary eigenvalues are obtained by using the normal form theory. Finally, numerical simulations are carried out to illustrate the main results.