Linear Superposition Technique Research Articles

The positive multi-complexiton solution to a generalized Kadomtsev–Petviashvili equation

Recently, Lin et al. (Appl. Math. Lett. 78 (2018) 112–117) established the resonant multiple-wave solution of a generalized Kadomtsev–Petviashvili (gKP) equation with applications in applied sciences using the linear superposition technique. In the present paper, according to the results obtained by Lin et al. and adopting a systematic method established by Zhou and Manukure, the positive multi-complexiton solution to the generalized Kadomtsev–Petviashvili equation is constructed for the first time. Several simulations in three dimensions are conducted formally in order to examine the dynamic behavior of positive multi-complexiton solutions, particularly the positive single-, double-, and triple-complexion waves. The current research outcomes definitely will enrich studies related to the gKP equation and its exact solutions.

A New Stress Intensity Factor Solution Based on the Response Surface Method for Nozzle Corner Cracks in Nuclear Reactor for Thermal Energy Generation

As considered carbon-free, the use of nuclear energy for thermal energy generation may expand in the future, with the guarantee of safe operation of the nuclear reactor. In a nuclear reactor pressure vessel (RPV), the nozzle area is an important part of the safe operation. It bears internal pressure, axial force, and overall moment, and at the same time bears higher stress than the rest of the vessel. To assess the integrity of the nozzle structure with a crack under combined load, an accurate solution of stress intensity factors (SIF) along the crack front is necessary. To obtain the SIF, this paper proposes a solution method that uses the stress on the crack surface and the response surface method to fit the stress under the framework of the linear superposition technique. This method is the first choice to determine a series of influence coefficients under unit pressure load. Then, one can estimate the SIFs by superposition method for an arbitrary stress distribution resulted from combined loads. The proposed solution is verified for a typical RPV with cracks under internal pressure, axial force, and global bending moment. The results reveal that the proposed solution is in good agreement with the existing solutions under internal pressure. Therefore, it can be obtained that this solution can be effectively used for the structural integrity assessment of RPV with nozzle corner cracks.

Integration of thixotropy into Giesekus model for characterization of human blood

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, yield stress, and thixotropy. Using a recently developed linear superposition technique to account for the effects of thixotropy with the Giesekus model and recently collected human blood rheological data from a strain-controlled rheometer, we perform parametric and statistical analysis of the parameter values of 5 donors. The work is validated with the incorporation of a recent thixotropic framework to model elastic and viscoelastic contributions from the microstructure. The elastic and viscoelastic stress contributions from the microstructure are then linearly superimposed with the viscoelastic backbone solution for stress given by the classic Giesekus rheological model. Demonstrated here are a parametric and statistical analysis and a comparison of the ability of the new enhanced thixotropic Giesekus model to predict large amplitude oscillatory shear and uni-directional large amplitude oscillatory shear flow. In addition, there is a new methodology to model the normal forces of blood. We compare this approach to other recently developed enhanced thixotropic Oldroyd-8 inspired models.

Optimal control design for reducing vertical acceleration of a motor yacht form

Ship motions and their adverse effects have always been studied with the aim of reducing motions and accelerations using whatsoever plausible ways during both the ship design process and operating lifetime. In the present work, a simulation study is carried out by taking into consideration the passengers in several locations of the selected motor yacht in an intermediate sea state with Hs = 1 m. Irregular head wave scenario at Fn = 0.25 is investigated and a controller design is implemented to ensure that the calculated RMS vertical acceleration values are decreased to tolerated levels in terms of motion sickness index. First, wave loads are obtained in the time domain by using strip theory, linear superposition technique, and the most common realization technique. Then, using a linear two-degree-of-freedom mathematical model, in which pitch and heave motions are considered together with the direct solution of convolution integrals, the uncontrolled motions and accelerations are obtained. Then, the linear matrix inequalities based on robust static output feedback controller are designed to mitigate the vertical acceleration of the ship. Finally, the results obtained with the robust static output feedback control design are presented in numerical simulation studies to demonstrate the effectiveness of the proposed control approach.

A millimeter wave linear superposition oscillator in 0.18 μm CMOS technology

This paper presents a millimeter wave (mm-wave) oscillator that generates signal at 36.56 GHz. The mm-wave oscillator is realized in a UMC 0.18 μm CMOS process. The linear superposition (LS) technique breaks through the limit of cut-off frequency (fT), and realizes a much higher oscillation than fT. Measurement results show that the LS oscillator produces a calibrated −37.17 dBm output power when biased at 1.8 V; the output power of fundamental signal is −10.85 dBm after calibration. The measured phase noise at 1 MHz frequency offset is −112.54 dBc/Hz at the frequency of 9.14 GHz. This circuit can be properly applied to mm-wave communication systems with advantages of low cost and high integration density.

Boundary integral equations for 2D elasticity and its application in discrete dislocation dynamics simulation in finite body: 1. General theory

A unified approach, originating from Cauchy integral theorem, is presented to derive boundary integral equations for two dimensional elasticity problems. Several sets of boundary integral equations are derived and their relations are revealed. Explicit expressions for materials with different symmetry planes are listed. Special attention is given to the formulation that is based on the tractions and the tangential derivatives of displacements along solid boundary, since its integral kernels have the weakest singularities. The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary, without involving the linear superposition technique that was often used in the literature. Its application in simulating discrete dislocation motion in a finite solid body is discussed.

Circuit Implementations and Comparison betweenDifferent Multiplication Factors in Terahertz FrequencyGeneration in 90nm Process Using Linear Superposition

In this paper, the Linear Superposition technique for Terahertz frequency generation in CMOS circuits has been reviewed. The CMOS circuits are designed in 90nm process and oscillator parameters are designed to have a fundamental oscillation frequency of 91 GHz. Circuit designs for different values of multiplying factor N are demonstrated and their Pspice simulation results are presented and compared. In these simulations, oscillation of up to 910 GHz (for N=10) was observed. signal in simulation in 90nm process. The underlying mechanism and design techniques of the circuits are explained in detail, and the simulation results are presented and compared for different values of N. The paper organization is as follows: Section II gives a review of the Linear Superposition method. Section III presents the analysis of the circuit for N=2 for explanation of the underlying principle of the circuit. Section IV describes the circuits for N=4, 6, 8 and 10 and their design techniques. The Simulation results are presented and compared in Section V. Finally, Section VI concludes the paper.

Terahertz CMOS Frequency Generator Using Linear Superposition Technique

A low Terahertz (324 GHz) frequency generator is realized in 90 nm CMOS by linearly superimposing quadruple (N=4) phase shifted fundamental signals at one fourth of the output frequency (81 GHz). The developed technique minimizes the fundamental, second and third order harmonics without extra filtering and results in a high fundamental-to-4 th harmonic signal conversion ratio of 0.17 or -15.4 dB. The demonstrated prototype produces a calibrated -46 dBm output power when biased at 1 V and 12 mA with 4 GHz tuning range and extrapolated phase noise of -91 dBc/Hz at 10 MHz frequency offset. The linear superposition (LS) technique can be generalized for all even number cases (N=2k, where k=1,2,3,4,...,n) with different tradeoffs in output power and frequency. As CMOS continues to scale, we anticipate the LS N=4 VCO to generate signals beyond 2 Terahertz by using 22 nm CMOS and produce output power up to -1.5 dBm with 1.7% power added efficiency with an LS VCO + Class-B Power Amplifier cascaded circuit architecture.

An Investigation of Added Resistance of Ships in Oblique Seas

Two approaches have been applied for numerical calculations of total added resistance both in regular and irregular long crested waves for Series 60 ships, parent form. In the first approach, total added resistance in regular waves has been determined by adding separately Maruo’s method for ship motion to that of Fujii-Takahashi’s method for wave reflection. In the second approach, Maru-Ishi’s method for ship motion has been added to that of Fuji-Takhashi’s method for wave reflection. Computed results have been compared with experimental ones in regular waves and other investigator in irregular waves. Average added resistance in a seaway is obtained from the analytically obtained mean response curve and the ISSC (International Ship and Offshore Structures Congress) spectrum applying linear superposition technique. Effects of speed, wave direction and block coefficients on added resistance have been examined and the percentage added resistance with respect to calm water resistance in different sea states h...

Substrate conduction mechanisms in convectively cooled simulated electronic packages

An analytical model is developed for the conduction from a heated surface element to a conductive substrate or board. The interaction from neighboring components on the board is modeled by modifying the upper board surface temperature. A linear superposition technique is used to demonstrate that the base solution for an isolated component may be used to predict board-level behavior by modification of the driving temperature difference for board conduction. By comparison of the model with data for an array of 1.27-cm cubical elements on a mildly conducting substrate, it is shown that the use of the measured element's adiabatic temperature as a descriptor of the board temperature allows successful correlation of both single element and surrounded element conduction heat transfer with two geometric parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An application of the time-domain boundary integral equation method to dynamic crack propagation

An application of the time-domain boundary integral equation method (TBIEM) to the case of rapidly moving cracks in a continuum is presented. The major objective of this paper is to explore the potential of the TBIEM in solving problems in dynamic fracture where inertia effects cannot be ignored. In earlier investigations, the method proved to be accurate and efficient for stationary cracks under dynamic loading conditions. A survey of the literature indicates no attempt at applying this method to any dynamically moving crack problems. A linear superposition technique is applied to derive the solution for the case of moving cracks from that of a stationary crack under dynamic loading. Comparison of the numerical results with the exact solution for the case of a semi-infinite crack subjected to full and partial loading on the crack face shows good agreement. It is concluded that the present numerical scheme is a viable method for determining the dynamic stress intensity factors for running cracks.

AN ALGORITHM FOR THE OPTIMAL SYNTHESIS OF COMPLEX FUNCTION GENERATORS

This article presents an effective algorithm for the optimum synthesis of complex function generators. Bagci's linear superposition technique is applied to obtain feasible initial estimates. In the optimum synthesis, the sum of squares of the structural errors at every design point is used as the objective function, subject to the constraints or the ratios of link lengths and the constraints of closure. Results are obtained by the constrained flexible polyhedron method. This algorithm can not only carry out the optimum synthesis effectively but also can get rid of the problems of branch defects and degeneracy.

Diffraction Theory and Statistical Methods To Predict Wave-Induced Motions and Loads for Large Structures

This paper presents the results of computations of wave loads on fixed antifloating structures using three-dimensional, sink-source techniques (diffraction theory). Theoretical calculations are compared with model experiments. Statistical methods are discussed also. Introduction Basic contributions to the use of three-dimensional diffraction theory are the studies of Lebreton and Cormault and Garrison and Seetharama Rao. Since their presentations, this method increasingly has become the predominant technique for handling wave-induced loads on large offshore structures of arbitrary form. However, strip theories based on two-dimensional (diffraction) solutions have been applied in ship design to determine responses in regular waves for some time. The linear superposition technique proposed by St. Denis and Pierson normally is used to determine the responses in irregular seas. Different computer programs have been developed on the basis of the method proposed by Lebreton and Cormault. This paper presents the applications of a computer program and information gained from experimental program and information gained from experimental results. Computations of short-term responses in irregular seas using different wave-spectrum formulations are included also. This procedure has not been prominent in the design of large offshore structures yet, although it long has been used widely in ship design. Theoretical Formulation A review of the basic equations used in the diffraction theory program is presented in the following section. The Equations of Motions The motions of a floating structure are derived from the condition of dynamic equilibrium between excitation and restoring and the damping and inertial reactions of the system. Assuming that the system is harmonic, the six coupled linear differential equations of motions may be written as 6 -iwt (mjl + mjl) nl + Wjl nl + Cjl Nl = Fje. l=1 .................................(1) Here, mj is the component of the generalized mass matrix (j=l = 1,2, . . . 6) and mjl and Wjl are the added-mass and damping coefficients, respectively. The restoring coefficients Cjl and the complex amplitude of the exciting forces and moments are Fj. The real part should be used in all expressions where e-iwt is part should be used in all expressions where e-iwt is involved. The wave encounter frequency that is the same as the response frequency is denoted as w. Displacements are represented by n. Dots are used to indicate time derivatives. A right-handed coordinate system (x, y, z) fixed with respect to the mean position of the structure with an origin in the plane of the free undisturbed surface is presented. The coordinate z points up vertically through the center of gravity and the coordinate x points in the direction of backward motion. It is assumed that the structure is symmetric about the x-z plane and the center of gravity is located in (O, O, Zc). JPT P. 549

Optimum synthesis of planar function generators by the linear partition of the dyadic loop equations

Introduction of optimum design techniques at the early stages of engineering programs for the timely transfer of engineering technology to industrial applications demands optimum design techniques in which satisfactory solutions can be reached by varying only a few parameters of a system without involving time consuming iterations. This article presents such a method of optimum synthesis of planar function generators, where the dimensions of an optimum mechanism are determined by minimizing the error in Freudenstein's input-output displacement equation of the mechanism at N design positions, where N is not limited by the number of unknowns of the system. Design equations are formed by partitioning Freudenstein's displacement equation into dyadic loop equations using the linear superposition technique, and they are linear in terms of the unknowns of the system. Hence, the solution requires no iteration. Equations for the optimum synthesis of the plane four-bar and slider-crank mechanisms are developed with three, four, and five unknown dimensions, which are also used for the optimum synthesis of multiloop mechanisms having series connected four-bar and slider-crank loops.

Optimum Synthesis of Plane Mechanisms for the Generation of Paths and Rigid-Body Positions via the Linear Superposition Technique

A method of optimum synthesis of plane mechanisms for the generation of paths and rigid-body positions is presented. The method is developed for the four-bar plane mechanism with six and eight unknown dimensions. Dimensions of the optimum mechanism are determined by minimizing the error in the loop-closure equations for N design points on the path, along with the loop-closure equation of the linkage, where N is not limited by the number of the unknown dimensions of the system. Design equations are linearized by the method of linear superposition. Solution of design equations requires no iterations, and it leads to a series of optimum mechanisms of different efficiency of approximation. Numerical examples are given.

Computer Algorithms and Detector Electronics for the Transmission X-Ray Tomography

This paper is addressed to the problem associated with transmission tomography and its implications in solving large numbers of simultaneous equations and associated parameters, such as multimillion weighting factors. Mathematical approaches to this problem in several directions are briefly reviewed and a technique (linear superposition technique with compensation) developed for this purpose, along with results obtained with this method is presented. Another important aspect of the multiple scanning tomography is counting statistics which requires the count rate be in the order of 5 MHz or more for the pulse counting to have statistical accuracy of 0.5% or better. Several alternative detectors besides conventional Sodium Iodine (NaI(Tl)) detector, namely, plastic scintillator (with enhanced photoelectric absorbtion by, for instance, tin loading) and various semiconductor detectors, such as CdTe and possible HgI2 are under investigation. Plastic scintillators will naturally be a suitable candidate owing to their fast light decay characteristics. A tin loaded plastic scintillator (HE 140 type) is under investigation and some of the preliminary results are reported. With the semiconductor detectors, the preliminary charge collection time observations and calculations indicate that these new exotic detectors (CdTe and HgI2) can be applicable to the high rate operations primarily by virtue of their short charge collection times and moderately good energy resolutions.

Predicting Long Term Trends of Deck Wetness for Ships in Ocean Waves

A method of predicting the short term probability of deck wetness and the long term probability of “wet-deck navigation” is presented, along with results of its application to cargo ships operating on the North Atlantic.Relative bow motions have been evaluated theoretically for geometrically similar ships of various sizes at different headings to regular and irregular waves, based upon the linear strip theory and the linear superposition technique. According to those results, the relationship between the short term probability of deck wetness related to bow freeboard and the significant wave height of irregular sea has been determined in correlation to average wave period, heading angle and ship speed. Then, the long term probabilities of “wet-deck navigation”, where the short term probability of deck wetness will be larger than 1/10, are predicted for different seasons and for various wind forces by the aid of long term wave statistics on the North Atlantic.The following trends of deck wetness related to bow freeboard are concluded from the predicted results : (a) The probability of deck wetness is large in head and bow seas, and small in following, quartering and beam seas.(b) The probability of deck wetness decreases with decrease of ship speed, but the influence of ship speed is rather small in higher speeds beyond 10 knots.(c) A large sized ship has small probability of deck wetness.(d) A full ship has small probability of deck wetness.(e) The long term probability of “wet-deck navigation” is large in winter and small in summer on the North Atlantic.(f) The long term probability of “wet-deck navigation” increases with increase of wind force on the North Atlantic, but this trend is not so remarkable in extremely heavy weather.