An extended continuum model accounting for the driver's timid and aggressive attributions

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Ge, Hongxia; Wang, Jufeng

2017-04-01

Considering the driver's timid and aggressive behaviors simultaneously, a new continuum model is put forwarded in this paper. By applying the linear stability theory, we presented the analysis of new model's linear stability. Through nonlinear analysis, the KdV-Burgers equation is derived to describe density wave near the neutral stability line. Numerical results verify that aggressive driving is better than timid act because the aggressive driver will adjust his speed timely according to the leading car's speed. The key improvement of this new model is that the timid driving deteriorates traffic stability while the aggressive driving will enhance traffic stability. The relationship of energy consumption between the aggressive and timid driving is also studied. Numerical results show that aggressive driver behavior can not only suppress the traffic congestion but also reduce the energy consumption.

Interpreting Popov criteria in Lure´ systems with complex scaling stability analysis

NASA Astrophysics Data System (ADS)

Zhou, J.

2018-06-01

The paper presents a novel frequency-domain interpretation of Popov criteria for absolute stability in Lure´ systems by means of what we call complex scaling stability analysis. The complex scaling technique is developed for exponential/asymptotic stability in LTI feedback systems, which dispenses open-loop poles distribution, contour/locus orientation and prior frequency sweeping. Exploiting the technique for alternatively revealing positive realness of transfer functions, re-interpreting Popov criteria is explicated. More specifically, the suggested frequency-domain stability conditions are conformable both in scalar and multivariable cases, and can be implemented either graphically with locus plotting or numerically without; in particular, the latter is suitable as a design tool with auxiliary parameter freedom. The interpretation also reveals further frequency-domain facts about Lure´ systems. Numerical examples are included to illustrate the main results.

The stagnation-point flow towards a shrinking sheet with homogeneous - heterogeneous reactions effects: A stability analysis

NASA Astrophysics Data System (ADS)

Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah

2017-01-01

A numerical study is performed to evaluate the problem of stagnation - point flow towards a shrinking sheet with homogeneous - heterogeneous reaction effects. By using non-similar transformation, the governing equations be able to reduced to an ordinary differential equation. Then, results of the equations can be obtained numerically by shooting method with maple implementation. Based on the numerical results obtained, the velocity ratio parameter λ< 0, the dual solutions do exist. Then, the stability analysis is carried out to determine which solution is more stable between both of the solutions by bvp4c solver in Matlab.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

An extended continuum model considering optimal velocity change with memory and numerical tests

NASA Astrophysics Data System (ADS)

Qingtao, Zhai; Hongxia, Ge; Rongjun, Cheng

2018-01-01

In this paper, an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory. The new model's stability condition and KdV-Burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis, respectively. Numerical simulation is carried out to study the extended continuum model, which explores how optimal velocity changes with memory affected velocity, density and energy consumption. Numerical results show that when considering the effects of optimal velocity changes with memory, the traffic jams can be suppressed efficiently. Both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently. Furthermore, numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information, which increases the stability of traffic flow on road, and so it improve the traffic flow stability and minimize cars' energy consumptions.

Comparison between numerical and analytical results on the required rf current for stabilizing neoclassical tearing modes

NASA Astrophysics Data System (ADS)

Wang, Xiaojing; Yu, Qingquan; Zhang, Xiaodong; Zhang, Yang; Zhu, Sizheng; Wang, Xiaoguang; Wu, Bin

2018-04-01

Numerical studies on the stabilization of neoclassical tearing modes (NTMs) by electron cyclotron current drive (ECCD) have been carried out based on reduced MHD equations, focusing on the amount of the required driven current for mode stabilization and the comparison with analytical results. The dependence of the minimum driven current required for NTM stabilization on some parameters, including the bootstrap current density, radial width of the driven current, radial deviation of the driven current from the resonant surface, and the island width when applying ECCD, are studied. By fitting the numerical results, simple expressions for these dependences are obtained. Analysis based on the modified Rutherford equation (MRE) has also been carried out, and the corresponding results have the same trend as numerical ones, while a quantitative difference between them exists. This difference becomes smaller when the applied radio frequency (rf) current is smaller.

Langley Stability and Transition Analysis Code (LASTRAC) Version 1.2 User Manual

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2004-01-01

LASTRAC is a general-purposed, physics-based transition prediction code released by NASA for Laminar Flow Control studies and transition research. The design and development of the LASTRAC code is aimed at providing an engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. It was written from scratch based on the state-of-the-art numerical methods for stability analysis and modern software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory or linear parabolized stability equations method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. This document describes the governing equations, numerical methods, code development, detailed description of input/output parameters, and case studies for the current release of LASTRAC.

Effect of current vehicle’s interruption on traffic stability in cooperative car-following theory

NASA Astrophysics Data System (ADS)

Zhang, Geng; Liu, Hui

2017-12-01

To reveal the impact of the current vehicle’s interruption information on traffic flow, a new car-following model with consideration of the current vehicle’s interruption is proposed and the influence of the current vehicle’s interruption on traffic stability is investigated through theoretical analysis and numerical simulation. By linear analysis, the linear stability condition of the new model is obtained and the negative influence of the current vehicle’s interruption on traffic stability is shown in the headway-sensitivity space. Through nonlinear analysis, the modified Korteweg-de Vries (mKdV) equation of the new model near the critical point is derived and it can be used to describe the propagating behavior of the traffic density wave. Finally, numerical simulation confirms the analytical results, which shows that the current vehicle’s interruption information can destabilize traffic flow and should be considered in real traffic.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature

NASA Technical Reports Server (NTRS)

Yoo, Paul

2013-01-01

Investigation of sonic boom has been one of the major areas of study in aeronautics due to the benefits a low-boom aircraft has in both civilian and military applications. This work conducts a numerical analysis of the effects of streamwise lift distribution on the shock coalescence characteristics. A simple wing-canard-stabilator body model is used in the numerical simulation. The streamwise lift distribution is varied by fixing the canard at a deflection angle while trimming the aircraft with the wing and the stabilator at the desired lift coefficient. The lift and the pitching moment coefficients are computed using the Missile DATCOM v. 707. The flow field around the wing-canard- stabilator body model is resolved using the OVERFLOW-2 flow solver. Overset/ chimera grid topology is used to simplify the grid generation of various configurations representing different streamwise lift distributions. The numerical simulations are performed without viscosity unless it is required for numerical stability. All configurations are simulated at Mach 1.4, angle-of-attack of 1.50, lift coefficient of 0.05, and pitching moment coefficient of approximately 0. Four streamwise lift distribution configurations were tested.

Developments in Cylindrical Shell Stability Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.; Starnes, James H., Jr.

1998-01-01

Today high-performance computing systems and new analytical and numerical techniques enable engineers to explore the use of advanced materials for shell design. This paper reviews some of the historical developments of shell buckling analysis and design. The paper concludes by identifying key research directions for reliable and robust methods development in shell stability analysis and design.

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

NASA Astrophysics Data System (ADS)

Dai, Xiao-Lin

2014-04-01

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional (2D) systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

NASA Astrophysics Data System (ADS)

Ma, Zhisai; Liu, Li; Zhou, Sida; Naets, Frank; Heylen, Ward; Desmet, Wim

2017-03-01

The problem of linear time-varying(LTV) system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the "frozen-time" assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stability-preserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system's stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam experimental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides a new way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

Numerical simulations and linear stability analysis of a boundary layer developed on wavy surfaces

NASA Astrophysics Data System (ADS)

Siconolfi, Lorenzo; Camarri, Simone; Fransson, Jens H. M.

2015-11-01

The development of passive methods leading to a laminar to turbulent transition delay in a boundary layer (BL) is a topic of great interest both for applications and academic research. In literature it has been shown that a proper and stable spanwise velocity modulation can reduce the growth rate of Tollmien-Schlichting (TS) waves and delay transition. In this study, we investigate numerically the possibility of obtaining a stabilizing effect of the TS waves through the use of a spanwise sinusoidal modulation of a flat plate. This type of control has been already successfully investigated experimentally. An extensive set of direct numerical simulations is carried out to study the evolution of a BL flow developed on wavy surfaces with different geometric characteristics, and the results will be presented here. Moreover, since this configuration is characterized by a slowly-varying flow field in streamwise direction, a local stability analysis is applied to define the neutral stability curves for the BL flow controlled by this type of wall modifications. These results give the possibility of investigating this control strategy and understanding the effect of the free parameters on the stabilization mechanism.

Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves

NASA Astrophysics Data System (ADS)

Barker, Blake; Jung, Soyeun; Zumbrun, Kevin

2018-03-01

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.

Characteristics pertaining to a stiffness cross-coupled Jeffcott model

NASA Technical Reports Server (NTRS)

Spanyer, K. L.

1985-01-01

Rotordynamic studies of complex systems utilizing multiple degree-of-freedom analysis have been performed to understand response, loads, and stability. In order to understand the fundamental nature of rotordynamic response, the Jeffcott rotor model has received wide attention. The purpose of this paper is to provide a generic rotordynamic analysis of a stiffness cross-coupled Jeffcott rotor model to illustrate characteristics of a second order stiffness-coupled linear system. The particular characteristics investigated were forced response, force vector diagrams, response orbits, and stability. Numerical results were achieved through a fourth order Runge-Kutta method for solving differential equations and the Routh Hurwitz stability criterion. The numerical results were verified to an exact mathematical solution for the steady state response.

Stability analysis of unsteady ablation fronts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-08-01

The linear stability analysis of unsteady ablation fronts, is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

Stability analysis of unsteady ablation fronts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-11-08

The linear stability analysis of unsteady ablation fronts is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

Stability analysis of cylinders with circular cutouts

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Brogan, F. A.; Marlowe, M. B.

1973-01-01

The stability of axially compressed cylinders with circular cutouts is analyzed numerically. An extension of the finite-difference method is used which removes the requirement that displacement components be defined in the directions of the grid lines. The results of this nonlinear analysis are found to be in good agreement with earlier experimental results.

Nonlinear analysis of an improved continuum model considering headway change with memory

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Wang, Jufeng; Ge, Hongxia; Li, Zhipeng

2018-01-01

Considering the effect of headway changes with memory, an improved continuum model of traffic flow is proposed in this paper. By means of linear stability theory, the new model’s linear stability with the effect of headway changes with memory is obtained. Through nonlinear analysis, the KdV-Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the improved traffic flow model, which explores how the headway changes with memory affected each car’s velocity, density and energy consumption. Numerical results show that when considering the effects of headway changes with memory, the traffic jams can be suppressed efficiently. Furthermore, research results demonstrate that the effect of headway changes with memory can avoid the disadvantage of historical information, which will improve the stability of traffic flow and minimize car energy consumption.

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

An extended macro model accounting for acceleration changes with memory and numerical tests

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Ge, Hongxia; Sun, Fengxin; Wang, Jufeng

2018-09-01

Considering effect of acceleration changes with memory, an improved continuum model of traffic flow is proposed in this paper. By applying the linear stability theory, we derived the new model's linear stability condition. Through nonlinear analysis, the KdV-Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the extended traffic flow model, which explores how acceleration changes with memory affected each car's velocity, density and fuel consumption and exhaust emissions. Numerical results demonstrate that acceleration changes with memory have significant negative effect on dynamic characteristic of traffic flow. Furthermore, research results verify that the effect of acceleration changes with memory will deteriorate the stability of traffic flow and increase cars' total fuel consumptions and emissions during the whole evolution of small perturbation.

Spherical gyroscopic moment stabilizer for attitude control of microsatellites

NASA Astrophysics Data System (ADS)

Keshtkar, Sajjad; Moreno, Jaime A.; Kojima, Hirohisa; Uchiyama, Kenji; Nohmi, Masahiro; Takaya, Keisuke

2018-02-01

This paper presents a new and improved concept of recently proposed two-degrees of freedom spherical stabilizer for triaxial orientation of microsatellites. The analytical analysis of the advantages of the proposed mechanism over the existing inertial attitude control devices are introduced. The extended equations of motion of the stabilizing satellite including the spherical gyroscope, for control law design and numerical simulations, are studied in detail. A new control algorithm based on continuous high-order sliding mode algorithms, for managing the torque produced by the stabilizer and therefore the attitude control of the satellite in the presence of perturbations/uncertainties, is presented. Some numerical simulations are carried out to prove the performance of the proposed mechanism and control laws.

Guidelines for Computing Longitudinal Dynamic Stability Characteristics of a Subsonic Transport

NASA Technical Reports Server (NTRS)

Thompson, Joseph R.; Frank, Neal T.; Murphy, Patrick C.

2010-01-01

A systematic study is presented to guide the selection of a numerical solution strategy for URANS computation of a subsonic transport configuration undergoing simulated forced oscillation about its pitch axis. Forced oscillation is central to the prevalent wind tunnel methodology for quantifying aircraft dynamic stability derivatives from force and moment coefficients, which is the ultimate goal for the computational simulations. Extensive computations are performed that lead in key insights of the critical numerical parameters affecting solution convergence. A preliminary linear harmonic analysis is included to demonstrate the potential of extracting dynamic stability derivatives from computational solutions.

Design of Rock Slope Reinforcement: An Himalayan Case Study

NASA Astrophysics Data System (ADS)

Tiwari, Gaurav; Latha, Gali Madhavi

2016-06-01

The stability analysis of the two abutment slopes of a railway bridge proposed at about 359 m above the ground level, crossing a river and connecting two hill faces in the Himalayas, India, is presented. The bridge is located in a zone of high seismic activity. The rock slopes are composed of a heavily jointed rock mass and the spacing, dip and dip direction of joint sets are varying at different locations. Geological mapping was carried out to characterize all discontinuities present along the slopes. Laboratory and field investigations were conducted to assess the geotechnical properties of the intact rock, rock mass and joint infill. Stability analyses of these rock slopes were carried out using numerical programmes. Loads from the foundations resting on the slopes and seismic accelerations estimated from site-specific ground response analysis were considered. The proposed slope profile with several berms between successive foundations was simulated in the numerical model. An equivalent continuum approach with Hoek and Brown failure criterion was initially used in a finite element model to assess the global stability of the slope abutments. In the second stage, finite element analysis of rock slopes with all joint sets with their orientations, spacing and properties explicitly incorporated into the numerical model was taken up using continuum with joints approach. It was observed that the continuum with joints approach was able to capture the local failures in some of the slope sections, which were verified using wedge failure analysis and stereographic projections. Based on the slope deformations and failure patterns observed from the numerical analyses, rock anchors were designed to achieve the target factors of safety against failure while keeping the deformations within the permissible limits. Detailed design of rock anchors and comparison of the stability of slopes with and without reinforcement are presented.

A note on the effects of viscosity on the stability of a trailing-line vortex

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Khorrami, Mehdi R.

1992-01-01

The linear stability of the Batchelor (1964) vortex is examined with emphasis on new viscous modes recently found numerically by Khorrami (1991). Unlike the previously reported inviscid modes of instability, these modes are destabilized by viscosity and exhibit small growth rates at large Reynolds numbers. The analysis presented here uses a combination of asymptotic and numerical techniques. The results confirm the existence of the additional modes of instability due to viscosity.

The use of the modified Cholesky decomposition in divergence and classification calculations

NASA Technical Reports Server (NTRS)

Van Rooy, D. L.; Lynn, M. S.; Snyder, C. H.

1973-01-01

This report analyzes the use of the modified Cholesky decomposition technique as applied to the feature selection and classification algorithms used in the analysis of remote sensing data (e.g., as in LARSYS). This technique is approximately 30% faster in classification and a factor of 2-3 faster in divergence, as compared with LARSYS. Also numerical stability and accuracy are slightly improved. Other methods necessary to deal with numerical stability problems are briefly discussed.

Stability of mixing layers

NASA Technical Reports Server (NTRS)

Tam, Christopher; Krothapalli, A

1993-01-01

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Stability analysis of magnetized neutron stars - a semi-analytic approach

NASA Astrophysics Data System (ADS)

Herbrik, Marlene; Kokkotas, Kostas D.

2017-04-01

We implement a semi-analytic approach for stability analysis, addressing the ongoing uncertainty about stability and structure of neutron star magnetic fields. Applying the energy variational principle, a model system is displaced from its equilibrium state. The related energy density variation is set up analytically, whereas its volume integration is carried out numerically. This facilitates the consideration of more realistic neutron star characteristics within the model compared to analytical treatments. At the same time, our method retains the possibility to yield general information about neutron star magnetic field and composition structures that are likely to be stable. In contrast to numerical studies, classes of parametrized systems can be studied at once, finally constraining realistic configurations for interior neutron star magnetic fields. We apply the stability analysis scheme on polytropic and non-barotropic neutron stars with toroidal, poloidal and mixed fields testing their stability in a Newtonian framework. Furthermore, we provide the analytical scheme for dropping the Cowling approximation in an axisymmetric system and investigate its impact. Our results confirm the instability of simple magnetized neutron star models as well as a stabilization tendency in the case of mixed fields and stratification. These findings agree with analytical studies whose spectrum of model systems we extend by lifting former simplifications.

Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Käppeli, Roger

2017-05-01

In this paper we focus on the numerical solution of the induction equation using Runge-Kutta Discontinuous Galerkin (RKDG)-like schemes that are globally divergence-free. The induction equation plays a role in numerical MHD and other systems like it. It ensures that the magnetic field evolves in a divergence-free fashion; and that same property is shared by the numerical schemes presented here. The algorithms presented here are based on a novel DG-like method as it applies to the magnetic field components in the faces of a mesh. (I.e., this is not a conventional DG algorithm for conservation laws.) The other two novel building blocks of the method include divergence-free reconstruction of the magnetic field and multidimensional Riemann solvers; both of which have been developed in recent years by the first author. Since the method is linear, a von Neumann stability analysis is carried out in two-dimensions to understand its stability properties. The von Neumann stability analysis that we develop in this paper relies on transcribing from a modal to a nodal DG formulation in order to develop discrete evolutionary equations for the nodal values. These are then coupled to a suitable Runge-Kutta timestepping strategy so that one can analyze the stability of the entire scheme which is suitably high order in space and time. We show that our scheme permits CFL numbers that are comparable to those of traditional RKDG schemes. We also analyze the wave propagation characteristics of the method and show that with increasing order of accuracy the wave propagation becomes more isotropic and free of dissipation for a larger range of long wavelength modes. This makes a strong case for investing in higher order methods. We also use the von Neumann stability analysis to show that the divergence-free reconstruction and multidimensional Riemann solvers are essential algorithmic ingredients of a globally divergence-free RKDG-like scheme. Numerical accuracy analyses of the RKDG-like schemes are presented and compared with the accuracy of PNPM schemes. It is found that PNPM retrieve much of the accuracy of the RKDG-like schemes while permitting a larger CFL number.

On the numerical treatment of nonlinear source terms in reaction-convection equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

DOE PAGES

Jiang, Nan; Tran, Hoang A.

2015-04-01

In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which u(n+1) + u(n-1) equivalent to 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

Stability of numerical integration techniques for transient rotor dynamics

NASA Technical Reports Server (NTRS)

Kascak, A. F.

1977-01-01

A finite element model of a rotor bearing system was analyzed to determine the stability limits of the forward, backward, and centered Euler; Runge-Kutta; Milne; and Adams numerical integration techniques. The analysis concludes that the highest frequency mode determines the maximum time step for a stable solution. Thus, the number of mass elements should be minimized. Increasing the damping can sometimes cause numerical instability. For a uniform shaft, with 10 mass elements, operating at approximately the first critical speed, the maximum time step for the Runge-Kutta, Milne, and Adams methods is that which corresponds to approximately 1 degree of shaft movement. This is independent of rotor dimensions.

Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow

NASA Astrophysics Data System (ADS)

Barker, Blake

2014-10-01

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV-KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar-Nepomnyashchy and Johnson-Noble-Rodrigues-Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.

Analysis of Time Filters in Multistep Methods

NASA Astrophysics Data System (ADS)

Hurl, Nicholas

Geophysical ow simulations have evolved sophisticated implicit-explicit time stepping methods (based on fast-slow wave splittings) followed by time filters to control any unstable models that result. Time filters are modular and parallel. Their effect on stability of the overall process has been tested in numerous simulations, but never analyzed. Stability is proven herein for the Crank-Nicolson Leapfrog (CNLF) method with the Robert-Asselin (RA) time filter and for the Crank-Nicolson Leapfrog method with the Robert-Asselin-Williams (RAW) time filter for systems by energy methods. We derive an equivalent multistep method for CNLF+RA and CNLF+RAW and stability regions are obtained. The time step restriction for energy stability of CNLF+RA is smaller than CNLF and CNLF+RAW time step restriction is even smaller. Numerical tests find that RA and RAW add numerical dissipation. This thesis also shows that all modes of the Crank-Nicolson Leap Frog (CNLF) method are asymptotically stable under the standard timestep condition.

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Part 2: Stability

NASA Technical Reports Server (NTRS)

Tanveer, Saleh

1989-01-01

The analysis is extended to determine the linear stability of a bubble in a Hele-Shaw cell analytically. Only the solution branch corresponding to largest possible bubble velocity U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Improved result on stability analysis of discrete stochastic neural networks with time delay

NASA Astrophysics Data System (ADS)

Wu, Zhengguang; Su, Hongye; Chu, Jian; Zhou, Wuneng

2009-04-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

NASA Astrophysics Data System (ADS)

Gangadhar, Nalwala Rohitbabu; Balasubramanian, Periyasamy

2010-10-01

In this paper, we present the stability analysis of delay differential equations which arise as a result of transportation lag in the CSTR-mechanical separator recycle system. A first order irreversible elementary reaction is considered to model the system and is governed by the delay differential equations. The DDE-BIFTOOL software package is used to analyze the stability of the delay system. The present analysis reveals that the system exhibits delay independent stability for isothermal operation of the CSTR. In the absence of delay, the system is dynamically unstable for non-isothermal operation of the CSTR, and as a result of delay, the system exhibits delay dependent stability.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

PubMed Central

2012-01-01

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis. PMID:22655859

Classical linear-control analysis applied to business-cycle dynamics and stability

NASA Technical Reports Server (NTRS)

Wingrove, R. C.

1983-01-01

Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.

Influence of foam on the stability characteristics of immiscible flow in porous media

NASA Astrophysics Data System (ADS)

van der Meer, J. M.; Farajzadeh, R.; Rossen, W. R.; Jansen, J. D.

2018-01-01

Accurate field-scale simulations of foam enhanced oil recovery are challenging, due to the sharp transition between gas and foam. Hence, unpredictable numerical and physical behavior is often observed, casting doubt on the validity of the simulation results. In this paper, a thorough stability analysis of the foam model is presented to validate the simulation results. We study the effect of a strongly non-monotonous total mobility function arising from foam models on the stability characteristics of the flow. To this end, we apply the linear stability analysis to nearly discontinuous relative permeability functions and compare the results with those of highly accurate numerical simulations. In addition, we present a qualitative analysis of the effect of different reservoir and fluid properties on the foam fingering behavior. In particular, we consider the effect of heterogeneity of the reservoir, injection rates, and foam quality. Relative permeability functions play an important role in the onset of fingering behavior of the injected fluid. Hence, we can deduce that stability properties are highly dependent on the non-linearity of the foam transition. The foam-water interface is governed by a very small total mobility ratio, implying a stable front. The transition between gas and foam, however, exhibits a huge total mobility ratio, leading to instabilities in the form of viscous fingering. This implies that there is an unstable pattern behind the front. We deduce that instabilities are able to grow behind the front but are later absorbed by the expanding wave. Moreover, the stability analysis, validated by numerical simulations, provides valuable insights about the important scales and wavelengths of the foam model. In this way, we remove the ambiguity regarding the effect of grid resolution on the convergence of the solutions. This insight forms an essential step toward the design of a suitable computational solver that captures all the appropriate scales, while retaining computational efficiency.

Stability analysis of the Euler discretization for SIR epidemic model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suryanto, Agus

2014-06-19

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaosmore » phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.« less

Numerical linear analysis of the effects of diamagnetic and shear flow on ballooning modes

NASA Astrophysics Data System (ADS)

Yanqing, HUANG; Tianyang, XIA; Bin, GUI

2018-04-01

The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvature-driving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition, through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.

Tangential acceleration feedback control of friction induced vibration

NASA Astrophysics Data System (ADS)

Nath, Jyayasi; Chatterjee, S.

2016-09-01

Tangential control action is studied on a phenomenological mass-on-belt model exhibiting friction-induced self-excited vibration attributed to the low-velocity drooping characteristics of friction which is also known as Stribeck effect. The friction phenomenon is modelled by the exponential model. Linear stability analysis is carried out near the equilibrium point and local stability boundary is delineated in the plane of control parameters. The system is observed to undergo a Hopf bifurcation as the eigenvalues determined from the linear stability analysis are found to cross the imaginary axis transversally from RHS s-plane to LHS s-plane or vice-versa as one varies the control parameters, namely non-dimensional belt velocity and the control gain. A nonlinear stability analysis by the method of Averaging reveals the subcritical nature of the Hopf bifurcation. Thus, a global stability boundary is constructed so that any choice of control parameters from the globally stable region leads to a stable equilibrium. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO validate these analytically obtained results. Pole crossover design is implemented to optimize the filter parameters with an independent choice of belt velocity and control gain. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.

A dynamic analysis of the motion of a low-wing general aviation aircraft about its calculated equilibrium flat spin mode

NASA Technical Reports Server (NTRS)

Tischler, M. B.; Barlow, J. B.

1980-01-01

The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.

Stope Stability Assessment and Effect of Horizontal to Vertical Stress Ratio on the Yielding and Relaxation Zones Around Underground Open Stopes Using Empirical and Finite Element Methods

NASA Astrophysics Data System (ADS)

Sepehri, Mohammadali; Apel, Derek; Liu, Wei

2017-09-01

Predicting the stability of open stopes can be a challenging task for underground mine engineers. For decades, the stability graph method has been used as the first step of open stope design around the world. However, there are some shortcomings with this method. For instance, the stability graph method does not account for the relaxation zones around the stopes. Another limitation of the stability graph is that this method cannot to be used to evaluate the stability of the stopes with high walls made of backfill materials. However, there are several analytical and numerical methods that can be used to overcome these limitations. In this study, both empirical and numerical methods have been used to assess the stability of an open stope located between mine levels N9225 and N9250 at Diavik diamond underground mine. It was shown that the numerical methods can be used as complementary methods along with other analytical and empirical methods to assess the stability of open stopes. A three dimensional elastoplastic finite element model was constructed using Abaqus software. In this paper a sensitivity analysis was performed to investigate the impact of the stress ratio "k" on the extent of the yielding and relaxation zones around the hangingwall and footwall of the understudy stope.

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

A numerical study of variable density flow and mixing in porous media

NASA Astrophysics Data System (ADS)

Fan, Yin; Kahawita, René

1994-10-01

A numerical study of a negatively buoyant plume intruding into a neutrally stratified porous medium has been undertaken using finite different methods. Of particular interest has been to ascertain whether the experimentally observed gravitational instabilities that form along the lower edge of the plume are reproduced in the numerical model. The model has been found to faithfully reproduce the mean flow as well as the gravitational instabilities in the intruding plume. A linear stability analysis has confirmed the fact that the negatively buoyant plume is in fact gravitationally unstable and that the stability depends on two parameters: a concentration Rayleigh number and a characteristic length scale which is dependent on the transverse dispersivity.

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Research study on stabilization and control: Modern sampled data control theory

NASA Technical Reports Server (NTRS)

Kuo, B. C.; Singh, G.; Yackel, R. A.

1973-01-01

A numerical analysis of spacecraft stability parameters was conducted. The analysis is based on a digital approximation by point by point state comparison. The technique used is that of approximating a continuous data system by a sampled data model by comparison of the states of the two systems. Application of the method to the digital redesign of the simplified one axis dynamics of the Skylab is presented.

Stability analysis and application of a mathematical cholera model.

PubMed

Liao, Shu; Wang, Jin

2011-07-01

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

A multi-scale Q1/P0 approach to langrangian shock hydrodynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shashkov, Mikhail; Love, Edward; Scovazzi, Guglielmo

A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the form of a pressure correction. With respect to currently implemented hourglass control approaches, the novelty of the method resides in its residual-based character. The stabilizing residual has a definite physical meaning, since it embeds a discrete form of the Clausius-Duhem inequality. Effectively, the proposed stabilization samples and acts to counter the production of entropy due to numerical instabilities. The proposed techniquemore » is applicable to materials with no shear strength, for which there exists a caloric equation of state. The stabilization operator is incorporated into a mid-point, predictor/multi-corrector time integration algorithm, which conserves mass, momentum and total energy. Encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method.« less

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Stabilization of a spatially uniform steady state in two systems exhibiting Turing patterns

NASA Astrophysics Data System (ADS)

Konishi, Keiji; Hara, Naoyuki

2018-05-01

This paper deals with the stabilization of a spatially uniform steady state in two coupled one-dimensional reaction-diffusion systems with Turing instability. This stabilization corresponds to amplitude death that occurs in a coupled system with Turing instability. Stability analysis of the steady state shows that stabilization does not occur if the two reaction-diffusion systems are identical. We derive a sufficient condition for the steady state to be stable for any length of system and any boundary conditions. Our analytical results are supported with numerical examples.

Stability analysis and wave dynamics of an extended hybrid traffic flow model

NASA Astrophysics Data System (ADS)

Wang, Yu-Qing; Zhou, Chao-Fan; Li, Wei-Kang; Yan, Bo-Wen; Jia, Bin; Wang, Ji-Xin

2018-02-01

The stability analysis and wave dynamic properties of an extended hybrid traffic flow model, WZY model, are intensively studied in this paper. The linear stable condition obtained by the linear stability analysis is presented. Besides, by means of analyzing Korteweg-de Vries equation, we present soliton waves in the metastable region. Moreover, the multiscale perturbation technique is applied to derive the traveling wave solution of the model. Furthermore, by means of performing Darboux transformation, the first-order and second-order doubly-periodic solutions and rational solutions are presented. It can be found that analytical solutions match well with numerical simulations.

Thermal Noise Limit in Frequency Stabilization of Lasers with Rigid Cavities

NASA Technical Reports Server (NTRS)

Numata, Kenji; Kemery, Amy; Camp, Jordan

2005-01-01

We evaluated thermal noise (Brownian motion) in a rigid reference cavity Used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with the direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency-reference cavity of order 1 Hz/rtHz at 10mHz at room temperature. This level coincides with the world-highest level stabilization results.

Influence of the Roof Movement Control Method on the Stability of Remnant

NASA Astrophysics Data System (ADS)

Adach-Pawelus, Karolina

2017-12-01

In the underground mines, there are geological and mining situations that necessitate leaving behind remnants in the mining field. Remnants, in the form of small, irregular parcels, are usually separated in the case of: significant problems with maintaining roof stability, high rockburst hazard, the occurrence of complex geological conditions and for random reasons (ore remnants), as well as for economic reasons (undisturbed rock remnants). Remnants left in the mining field become sites of high stress values concentration and may affect the rock in their vicinity. The values of stress inside the remnant and its vicinity, as well as the stability of the remnant, largely depend on the roof movement control method used in the mining field. The article presents the results of the numerical analysis of the influence of roof movement control method on remnant stability and the geomechanical situation in the mining field. The numerical analysis was conducted for the geological and mining conditions characteristic of Polish underground copper mines owned by KGHM Polska Miedz S.A. Numerical simulations were performed in a plane strain state by means of Phase 2 v. 8.0 software, based on the finite element method. The behaviour of remnant and rock mass in its vicinity was simulated in the subsequent steps of the room and pillar mining system for three types of roof movement control method: roof deflection, dry backfill and hydraulic backfill. The parameters of the rock mass accepted for numerical modelling were calculated by means of RocLab software on the basis of the Hoek-Brown classification. The Mohr-Coulomb strength criterion was applied.

a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms

NASA Astrophysics Data System (ADS)

Beale, D. G.; Lee, S. W.

1996-05-01

A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].

Acceleration of convergence of vector sequences

NASA Technical Reports Server (NTRS)

Sidi, A.; Ford, W. F.; Smith, D. A.

1983-01-01

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

NASA Astrophysics Data System (ADS)

Kim, Min Chan

2014-11-01

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

Bifurcation analysis of parametrically excited bipolar disorder model

NASA Astrophysics Data System (ADS)

Nana, Laurent

2009-02-01

Bipolar II disorder is characterized by alternating hypomanic and major depressive episode. We model the periodic mood variations of a bipolar II patient with a negatively damped harmonic oscillator. The medications administrated to the patient are modeled via a forcing function that is capable of stabilizing the mood variations and of varying their amplitude. We analyze analytically, using perturbation method, the amplitude and stability of limit cycles and check this analysis with numerical simulations.

Numerical analysis of stiffened shells of revolution. Volume 1: Theory manual for STARS-2S, 2B, 2V digital computer programs

NASA Technical Reports Server (NTRS)

Svalbonas, V.

1973-01-01

The theoretical analysis background for the STARS-2 (shell theory automated for rotational structures) program is presented. The theory involved in the axisymmetric nonlinear and unsymmetric linear static analyses, and the stability and vibrations (including critical rotation speed) analyses involving axisymmetric prestress are discussed. The theory for nonlinear static, stability, and vibrations analyses, involving shells with unsymmetric loadings are included.

Numerical equilibrium analysis for structured consumer resource models.

PubMed

de Roos, A M; Diekmann, O; Getto, P; Kirkilionis, M A

2010-02-01

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for "Daphnia consuming algae" models in C-code. The results obtained by way of this implementation are shown in the form of graphs.

An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems

NASA Technical Reports Server (NTRS)

Farhat, C.; Park, K. C.; Dubois-Pelerin, Y.

1991-01-01

An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay

NASA Astrophysics Data System (ADS)

Pal, Nikhil; Samanta, Sudip; Biswas, Santanu; Alquran, Marwan; Al-Khaled, Kamel; Chattopadhyay, Joydev

In the present paper, we study the effect of gestation delay on a tri-trophic food chain model with Holling type-II functional response. The essential mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. Considering time-delay as the bifurcation parameter, the Hopf-bifurcation analysis is carried out around the coexisting equilibrium. The direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and center manifold theorem. We observe that if the magnitude of the delay is increased, the system loses stability and shows limit cycle oscillations through Hopf-bifurcation. The system also shows the chaotic dynamics via period-doubling bifurcation for further enhancement of time-delay. Our analytical findings are illustrated through numerical simulations.

Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.

PubMed

Cao, Jinde; Xiao, Min

2007-03-01

Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.

Analysis of vortex shedding by 2-D numerical simulation for a solid rocket motor and calculations of the nonstationary thrust

NASA Astrophysics Data System (ADS)

Lupoglazoff, N.; Vuillot, F.

Periodic vortex shedding (VS) has been studied by 2-D numerical simulation for the C1 test case in the framework of the ASSM program concerning the stability of the Ariane-5 P230 solid rocket motor. The Flandro method is found to be unsuitable for the type of configuration considered here. The acoustic frequency of VS is a function of the configuration. Calculations of nonstationary thrust indicate that there is no direct relationship between the pressure oscillation amplitudes and the thrust. Secondary injection is found to have a stabilizing effect.

Stability analysis for stochastic BAM nonlinear neural network with delays

NASA Astrophysics Data System (ADS)

Lv, Z. W.; Shu, H. S.; Wei, G. L.

2008-02-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.

An extended car-following model to describe connected traffic dynamics under cyberattacks

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Yu, Guizhen; Wu, Xinkai; Qin, Hongmao; Wang, Yunpeng

2018-04-01

In this paper, the impacts of the potential cyberattacks on vehicles are modeled through an extended car-following model. To better understand the mechanism of traffic disturbance under cyberattacks, the linear and nonlinear stability analysis are conducted respectively. Particularly, linear stability analysis is performed to obtain different neutral stability conditions with various parameters; and nonlinear stability analysis is carried out by using reductive perturbation method to derive the soliton solution of the modified Korteweg de Vries equation (mKdV) near the critical point, which is used to draw coexisting stability lines. Furthermore, by applying linear and nonlinear stability analysis, traffic flow state can be divided into three states, i.e., stable, metastable and unstable states which are useful to describe shockwave dynamics and driving behaviors under cyberattacks. The theoretical results show that the proposed car-following model is capable of successfully describing the car-following behavior of connected vehicles with cyberattacks. Finally, numerical simulation using real values has confirmed the validity of theoretical analysis. The results further demonstrate our model can be used to help avoid collisions and relieve traffic congestion with cybersecurity threats.

TH-AB-BRA-09: Stability Analysis of a Novel Dose Calculation Algorithm for MRI Guided Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zelyak, O; Fallone, B; Cross Cancer Institute, Edmonton, AB

2016-06-15

Purpose: To determine the iterative deterministic solution stability of the Linear Boltzmann Transport Equation (LBTE) in the presence of magnetic fields. Methods: The LBTE with magnetic fields under investigation is derived using a discrete ordinates approach. The stability analysis is performed using analytical and numerical methods. Analytically, the spectral Fourier analysis is used to obtain the convergence rate of the source iteration procedures based on finding the largest eigenvalue of the iterative operator. This eigenvalue is a function of relevant physical parameters, such as magnetic field strength and material properties, and provides essential information about the domain of applicability requiredmore » for clinically optimal parameter selection and maximum speed of convergence. The analytical results are reinforced by numerical simulations performed using the same discrete ordinates method in angle, and a discontinuous finite element spatial approach. Results: The spectral radius for the source iteration technique of the time independent transport equation with isotropic and anisotropic scattering centers inside infinite 3D medium is equal to the ratio of differential and total cross sections. The result is confirmed numerically by solving LBTE and is in full agreement with previously published results. The addition of magnetic field reveals that the convergence becomes dependent on the strength of magnetic field, the energy group discretization, and the order of anisotropic expansion. Conclusion: The source iteration technique for solving the LBTE with magnetic fields with the discrete ordinates method leads to divergent solutions in the limiting cases of small energy discretizations and high magnetic field strengths. Future investigations into non-stationary Krylov subspace techniques as an iterative solver will be performed as this has been shown to produce greater stability than source iteration. Furthermore, a stability analysis of a discontinuous finite element space-angle approach (which has been shown to provide the greatest stability) will also be investigated. Dr. B Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization)« less

A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.

2018-03-01

Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

Stability of the iterative solutions of integral equations as one phase freezing criterion.

PubMed

Fantoni, R; Pastore, G

2003-10-01

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the standard iterative solution of hypernetted chain and Percus-Yevick integral equations for the one-dimensional (1D) hard rods fluid shows the same behavior observed in 3D systems. Since no phase transition is allowed in such 1D system, our analysis shows that the proposed one phase criterion, at least in this case, fails. We argue that the observed proximity between the numerical and the structural instability in 3D originates from the enhanced structure present in the fluid but, in view of the arbitrary dependence on the iteration scheme, it seems uneasy to relate the numerical stability analysis to a robust one-phase criterion for predicting a thermodynamic phase transition.

influx_s: increasing numerical stability and precision for metabolic flux analysis in isotope labelling experiments.

PubMed

Sokol, Serguei; Millard, Pierre; Portais, Jean-Charles

2012-03-01

The problem of stationary metabolic flux analysis based on isotope labelling experiments first appeared in the early 1950s and was basically solved in early 2000s. Several algorithms and software packages are available for this problem. However, the generic stochastic algorithms (simulated annealing or evolution algorithms) currently used in these software require a lot of time to achieve acceptable precision. For deterministic algorithms, a common drawback is the lack of convergence stability for ill-conditioned systems or when started from a random point. In this article, we present a new deterministic algorithm with significantly increased numerical stability and accuracy of flux estimation compared with commonly used algorithms. It requires relatively short CPU time (from several seconds to several minutes with a standard PC architecture) to estimate fluxes in the central carbon metabolism network of Escherichia coli. The software package influx_s implementing this algorithm is distributed under an OpenSource licence at http://metasys.insa-toulouse.fr/software/influx/. Supplementary data are available at Bioinformatics online.

Direct numerical simulation of axisymmetric laminar low-density jets

NASA Astrophysics Data System (ADS)

Gomez Lendinez, Daniel; Coenen, Wilfried; Sevilla, Alejandro

2017-11-01

The stability of submerged laminar axisymmetric low-density jets has been investigated experimentally (Kyle & Sreenivasan 1993, Hallberg & Strykowski 2006) and with linear analysis (Jendoubi & Strykowski 1994, Coenen & Sevilla 2012, Coenen et al. 2017). These jets become globally unstable when the Reynolds number is larger than a certain critical value which depends on the density ratio and on the velocity profile at the injector outlet. In this work, Direct Numerical Simulations using FreeFEM + + (Hecht 2012) with P1 elements for pressure and P2 for velocity and density are performed to complement the above mentioned studies. Density and velocity fields are analyzed at long time showing the unforced space-time evolution of nonlinear disturbances propagating along the jet. Using the Stuart-Landau model to fit the numerical results for the self-excited oscillations we have computed a neutral stability curve that shows good agreement with experiments and stability theory. Thanks to Spanish MINECO under projects DPI2014-59292-C3-1-P and DPI2015-71901-REDT for financial support.

Investigation of flow-induced numerical instability in a mixed semi-implicit, implicit leapfrog time discretization

NASA Astrophysics Data System (ADS)

King, Jacob; Kruger, Scott

2017-10-01

Flow can impact the stability and nonlinear evolution of range of instabilities (e.g. RWMs, NTMs, sawteeth, locked modes, PBMs, and high-k turbulence) and thus robust numerical algorithms for simulations with flow are essential. Recent simulations of DIII-D QH-mode [King et al., Phys. Plasmas and Nucl. Fus. 2017] with flow have been restricted to smaller time-step sizes than corresponding computations without flow. These computations use a mixed semi-implicit, implicit leapfrog time discretization as implemented in the NIMROD code [Sovinec et al., JCP 2004]. While prior analysis has shown that this algorithm is unconditionally stable with respect to the effect of large flows on the MHD waves in slab geometry [Sovinec et al., JCP 2010], our present Von Neumann stability analysis shows that a flow-induced numerical instability may arise when ad-hoc cylindrical curvature is included. Computations with the NIMROD code in cylindrical geometry with rigid rotation and without free-energy drive from current or pressure gradients qualitatively confirm this analysis. We explore potential methods to circumvent this flow-induced numerical instability such as using a semi-Lagrangian formulation instead of time-centered implicit advection and/or modification to the semi-implicit operator. This work is supported by the DOE Office of Science (Office of Fusion Energy Sciences).

The influence of continuous historical velocity difference information on micro-cooperative driving stability

NASA Astrophysics Data System (ADS)

Yang, Liang-Yi; Sun, Di-Hua; Zhao, Min; Cheng, Sen-Lin; Zhang, Geng; Liu, Hui

2018-03-01

In this paper, a new micro-cooperative driving car-following model is proposed to investigate the effect of continuous historical velocity difference information on traffic stability. The linear stability criterion of the new model is derived with linear stability theory and the results show that the unstable region in the headway-sensitivity space will be shrunk by taking the continuous historical velocity difference information into account. Through nonlinear analysis, the mKdV equation is derived to describe the traffic evolution behavior of the new model near the critical point. Via numerical simulations, the theoretical analysis results are verified and the results indicate that the continuous historical velocity difference information can enhance the stability of traffic flow in the micro-cooperative driving process.

Evaluating the Effect of Rainfall Infiltration on the Slope Stability of T16 tower of Taipei Mao-kong Gondola by Numerical Methods

NASA Astrophysics Data System (ADS)

RUNG, J.

2013-12-01

In this study, a series of rainfall-stability analyses were performed to simulate the failure mechanism and the function of remediation works of the down slope of T-16 tower pier, Mao-Kong gondola (or T-16 Slope) at the hillside of Taipei City using two-dimensional finite element method. The failure mechanism of T-16 Slope was simulated using the rainfall hyetograph of Jang-Mi typhoon in 2008 based on the field investigation data, monitoring data, soil/rock mechanical testing data and detail design plots of remediation works. Eventually, the numerical procedures and various input parameters in the analysis were verified by comparing the numerical results with the field observations. In addition, 48 hrs design rainfalls corresponding to 5, 10, 25 and 50 years return periods were prepared using the 20 years rainfall data of Mu-Zha rainfall observation station, Central Weather Bureau for the rainfall-stability analyses of T-16 Slope to inspect the effect of the compound stabilization works on the overall stability of the slope. At T-16 Slope, without considering the longitudinal and transverse drainages on the ground surface, there totally 4 types of stabilization works were installed to stabilize the slope. From the slope top to the slope toe, the stabilization works of T-16 Slope consists of RC-retaining wall with micro-pile foundation at the up-segment, earth anchor at the up-middle-segment, soil nailing at the middle-segment and retaining pile at the down-segment of the slope. The effect of each individual stabilization work on the slope stability under rainfall condition was examined and evaluated by raising field groundwater level.

Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

NASA Astrophysics Data System (ADS)

Zhang, Lingling; Huang, Jianhua; Huang, Lihong; Zhang, Zhizhou

This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ1 and τ2. Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.

Lagrangian analysis of multiscale particulate flows with the particle finite element method

NASA Astrophysics Data System (ADS)

Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy

2014-05-01

We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils

NASA Astrophysics Data System (ADS)

Soranzo, Enrico; Wu, Wei

2013-04-01

Excavation of shallow tunnels with the New Austrian Tunnelling Method (NATM) requires proper assessing of the tunnel face stability, to enable an open-face excavation, and the estimation of the correspondent surface settlements. Soils in a partially saturated condition exhibit a higher cohesion than in a fully saturated state, which can be taken into account when assessing the stability of the tunnel face. For the assessment of the face support pressure, different methods are used in engineering practice, varying from simple empirical and analytical formulations to advanced finite element analysis. Such procedures can be modified to account for the unsaturated state of soils. In this study a method is presented to incorporate the effect of partial saturation in the numerical analysis. The results are then compared with a simple analytical formulation derived from parametric studies. As to the numerical analysis, the variation of cohesion and of Young's modulus with saturation can be considered when the water table lies below the tunnel in a soil exhibiting a certain capillary rise, so that the tunnel is driven in a partially saturated layer. The linear elastic model with Mohr-Coulomb failure criterion can be extended to partially saturated states and calibrated with triaxial tests on unsaturated. In order to model both positive and negative pore water pressure (suction), Bishop's effective stress is incorporated into Mohr-Coulomb's failure criterion. The effective stress parameter in Bishop's formulation is related to the degree of saturation as suggested by Fredlund. If a linear suction distribution is assumed, the degree of saturation can be calculated from the Soil Water Characteristic Curve (SWCC). Expressions exist that relate the Young's modulus of unsaturated soils to the net mean stress and the matric suction. The results of the numerical computation can be compared to Vermeer & Ruse's closed-form formula that expresses the limit support pressure of the tunnel face. The expression is derived from parametric studies and predicts stability of the tunnel face when negative values are returned, suggesting that open-face tunnelling can be performed. The formula can be modified to account for the variation of cohesion along the tunnel face. The results obtained from both the numerical analysis and the analytical formulation are well in agreement and show that the stability of the tunnel face can greatly benefit from the enhanced cohesion of partially saturated soils.

The three-dimensional wake of a cylinder undergoing a combination of translational and rotational oscillation in a quiescent fluid

NASA Astrophysics Data System (ADS)

Nazarinia, M.; Lo Jacono, D.; Thompson, M. C.; Sheridan, J.

2009-06-01

Previous two-dimensional numerical studies have shown that a circular cylinder undergoing both oscillatory rotational and translational motions can generate thrust so that it will actually self-propel through a stationary fluid. Although a cylinder undergoing a single oscillation has been thoroughly studied, the combination of the two oscillations has not received much attention until now. The current research reported here extends the numerical study of Blackburn et al. [Phys. Fluids 11, L4 (1999)] both experimentally and numerically, recording detailed vorticity fields in the wake and using these to elucidate the underlying physics, examining the three-dimensional wake development experimentally, and determining the three-dimensional stability of the wake through Floquet stability analysis. Experiments conducted in the laboratory are presented for a given parameter range, confirming the early results from Blackburn et al. [Phys. Fluids 11, L4 (1999)]. In particular, we confirm the thrust generation ability of a circular cylinder undergoing combined oscillatory motions. Importantly, we also find that the wake undergoes three-dimensional transition at low Reynolds numbers (Re≃100) to an instability mode with a wavelength of about two cylinder diameters. The stability analysis indicates that the base flow is also unstable to another mode at slightly higher Reynolds numbers, broadly analogous to the three-dimensional wake transition mode for a circular cylinder, despite the distinct differences in wake/mode topology. The stability of these flows was confirmed by experimental measurements.

Lyapunov stability analysis for the generalized Kapitza pendulum

NASA Astrophysics Data System (ADS)

Druzhinina, O. V.; Sevastianov, L. A.; Vasilyev, S. A.; Vasilyeva, D. G.

2017-12-01

In this work generalization of Kapitza pendulum whose suspension point moves in the vertical and horizontal planes is made. Lyapunov stability analysis of the motion for this pendulum subjected to excitation of periodic driving forces and stochastic driving forces that act in the vertical and horizontal planes has been studied. The numerical study of the random motion for generalized Kapitza pendulum under stochastic driving forces has made. It is shown the existence of stable quasi-periodic motion for this pendulum.

Asymptotic behavior of modulated Taylor-Couette flows with a crystalline inner cylinder

NASA Technical Reports Server (NTRS)

Braun, R. J.; Mcfadden, G. B.; Murray, B. T.; Coriell, S. R.; Glicksman, M. E.; Selleck, M. E.

1993-01-01

The linear stability of a modulated Taylor-Couette system when the inner cylindrical boundary consists of a crystalline solid-liquid interface is considered. Both experimentally and in numerical calculations it is found that the two-phase system is significantly less stable than the analogous rigid-walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two-phase system is considerably simpler than that of the rigid-walled system, despite the complications introduced by the presence of the crystal-melt interface.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition.

PubMed

Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang

2017-10-01

This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

An extended lattice model accounting for traffic jerk

NASA Astrophysics Data System (ADS)

Redhu, Poonam; Siwach, Vikash

2018-02-01

In this paper, a flux difference lattice hydrodynamics model is extended by considering the traffic jerk effect which comes due to vehicular motion of non-motor automobiles. The effect of traffic jerk has been examined through linear stability analysis and shown that it can significantly enlarge the unstable region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear stability analysis. The theoretical findings have been verified using numerical simulation which confirms that the jerk parameter plays an important role in stabilizing the traffic jam efficiently in sensing the flux difference of leading sites.

Stability analysis of neural networks with time-varying delay: Enhanced stability criteria and conservatism comparisons

NASA Astrophysics Data System (ADS)

Lin, Wen-Juan; He, Yong; Zhang, Chuan-Ke; Wu, Min

2018-01-01

This paper is concerned with the stability analysis of neural networks with a time-varying delay. To assess system stability accurately, the conservatism reduction of stability criteria has attracted many efforts, among which estimating integral terms as exact as possible is a key issue. At first, this paper develops a new relaxed integral inequality to reduce the estimation gap of popular Wirtinger-based inequality (WBI). Then, for showing the advantages of the proposed inequality over several existing inequalities that also improve the WBI, four stability criteria are derived through different inequalities and the same Lyapunov-Krasovskii functional (LKF), and the conservatism comparison of them is analyzed theoretically. Moreover, an improved criterion is established by combining the proposed inequality and an augmented LKF with delay-product-type terms. Finally, several numerical examples are used to demonstrate the advantages of the proposed method.

Bifurcations and chaos in a parametrically damped two-well Duffing oscillator subjected to symmetric periodic pulses.

PubMed

Chacón, R; Martínez García-Hoz, A

1999-06-01

We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically.

Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1980-01-01

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

An embedded formula of the Chebyshev collocation method for stiff problems

NASA Astrophysics Data System (ADS)

Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu

2017-12-01

In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wollaber, Allan B., E-mail: wollaber@lanl.go; Larsen, Edward W., E-mail: edlarsen@umich.ed

2011-02-20

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, wemore » also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.« less

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

NASA Astrophysics Data System (ADS)

Wollaber, Allan B.; Larsen, Edward W.

2011-02-01

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ⩽ 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.

Thermal Noise Limit in Frequency Stabilization of Lasers with Rigid Cavities

NASA Technical Reports Server (NTRS)

Numata, Kenji; Kemery, Amy; Camp, Jordan

2004-01-01

We evaluated thermal noise (Brownian motion) in a rigid reference cavity used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with t.he direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency- reference cavity of order 1 Hz/square root Hz(0.01 Hz/square root Hz) at 10 mHz (100 Hz) at room temperature. This level coincides with the world-highest level stabilization results.

A case study of multi-seam coal mine entry stability analysis with strength reduction method

PubMed Central

Tulu, Ihsan Berk; Esterhuizen, Gabriel S; Klemetti, Ted; Murphy, Michael M.; Sumner, James; Sloan, Michael

2017-01-01

In this paper, the advantage of using numerical models with the strength reduction method (SRM) to evaluate entry stability in complex multiple-seam conditions is demonstrated. A coal mine under variable topography from the Central Appalachian region is used as a case study. At this mine, unexpected roof conditions were encountered during development below previously mined panels. Stress mapping and observation of ground conditions were used to quantify the success of entry support systems in three room-and-pillar panels. Numerical model analyses were initially conducted to estimate the stresses induced by the multiple-seam mining at the locations of the affected entries. The SRM was used to quantify the stability factor of the supported roof of the entries at selected locations. The SRM-calculated stability factors were compared with observations made during the site visits, and the results demonstrate that the SRM adequately identifies the unexpected roof conditions in this complex case. It is concluded that the SRM can be used to effectively evaluate the likely success of roof supports and the stability condition of entries in coal mines. PMID:28239503

A case study of multi-seam coal mine entry stability analysis with strength reduction method.

PubMed

Tulu, Ihsan Berk; Esterhuizen, Gabriel S; Klemetti, Ted; Murphy, Michael M; Sumner, James; Sloan, Michael

2016-03-01

In this paper, the advantage of using numerical models with the strength reduction method (SRM) to evaluate entry stability in complex multiple-seam conditions is demonstrated. A coal mine under variable topography from the Central Appalachian region is used as a case study. At this mine, unexpected roof conditions were encountered during development below previously mined panels. Stress mapping and observation of ground conditions were used to quantify the success of entry support systems in three room-and-pillar panels. Numerical model analyses were initially conducted to estimate the stresses induced by the multiple-seam mining at the locations of the affected entries. The SRM was used to quantify the stability factor of the supported roof of the entries at selected locations. The SRM-calculated stability factors were compared with observations made during the site visits, and the results demonstrate that the SRM adequately identifies the unexpected roof conditions in this complex case. It is concluded that the SRM can be used to effectively evaluate the likely success of roof supports and the stability condition of entries in coal mines.

Numerical Stability and Control Analysis Towards Falling-Leaf Prediction Capabilities of Splitflow for Two Generic High-Performance Aircraft Models

NASA Technical Reports Server (NTRS)

Charlton, Eric F.

1998-01-01

Aerodynamic analysis are performed using the Lockheed-Martin Tactical Aircraft Systems (LMTAS) Splitflow computational fluid dynamics code to investigate the computational prediction capabilities for vortex-dominated flow fields of two different tailless aircraft models at large angles of attack and sideslip. These computations are performed with the goal of providing useful stability and control data to designers of high performance aircraft. Appropriate metrics for accuracy, time, and ease of use are determined in consultations with both the LMTAS Advanced Design and Stability and Control groups. Results are obtained and compared to wind-tunnel data for all six components of forces and moments. Moment data is combined to form a "falling leaf" stability analysis. Finally, a handful of viscous simulations were also performed to further investigate nonlinearities and possible viscous effects in the differences between the accumulated inviscid computational and experimental data.

Investigating Strategies to Increase Persistence and Success Rates among Anatomy & Physiology Students: A Case Study at Austin Community College District

NASA Astrophysics Data System (ADS)

Vedartham, Padmaja B.

Snap-through buckling provides an intricate force-displacement relationship for study. With the possibility for multiple limit points and pitchfork bifurcations and large regions of instability, experimental validation of numerical analysis can become difficult. This requires stabilization of unstable static equilibria, for which limited prior research exists. For all but the simplest cases, more than one actuator is needed, increasing the complexity of the experiment to the point of intractability without a control system. In this thesis, the necessary conditions for stabilization of a buckled beam with pinned boundaries under transverse loading were determined. By combining various nonlinear solution methods, a control system was created that could stabilize any branch of the force-displacement response. Experimental traversal of an unstable branch are presented along with other unstable static equilibrium configurations. The control system had numerical limitations, losing convergence near singular points. The groundwork for experimental stabilization was validated and demonstrated.

Theoretical prediction of the energy stability of graphene nanoblisters

NASA Astrophysics Data System (ADS)

Glukhova, O. E.; Slepchenkov, M. M.; Barkov, P. V.

2018-04-01

The paper presents the results of a theoretical prediction of the energy stability of graphene nanoblisters with various geometrical parameters. As a criterion for the evaluation of the stability of investigated carbon objects we propose to consider the value of local stress of the nanoblister atomic grid. Numerical evaluation of stresses experienced by atoms of the graphene blister framework was carried out by means of an original method for calculation of local stresses that is based on energy approach. Atomistic models of graphene nanoblisters corresponding to the natural experiment data were built for the first time in this work. New physical regularities of the influence of topology on the thermodynamic stability of nanoblisters were established as a result of the analysis of the numerical experiment data. We built the distribution of local stresses for graphene blister structures, whose atomic grid contains a variety of structural defects. We have shown how the concentration and location of defects affect the picture of the distribution of the maximum stresses experienced by the atoms of the nanoblisters.

Complete synchronization of the global coupled dynamical network induced by Poisson noises.

PubMed

Guo, Qing; Wan, Fangyi

2017-01-01

The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.

Study on the Influence of Elevation of Tailing Dam on Stability

NASA Astrophysics Data System (ADS)

Wan, Shuai; Wang, Kun; Kong, Songtao; Zhao, Runan; Lan, Ying; Zhang, Run

2017-12-01

This paper takes Yunnan as the object of a tailing, by theoretical analysis and numerical calculation method of the effect of seismic load effect of elevation on the stability of the tailing, to analyse the stability of two point driven safety factor and liquefaction area. The Bishop method is adopted to simplify the calculation of dynamic safety factor and liquefaction area analysis using comparison method of shear stress to analyse liquefaction, so we obtained the influence of elevation on the stability of the tailing. Under the earthquake, with the elevation increased, the safety coefficient of dam body decreases, shallow tailing are susceptible to liquefy. Liquefaction area mainly concentrated in the bank below the water surface, to improve the scientific basis for the design and safety management of the tailing.

Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

NASA Astrophysics Data System (ADS)

Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

2016-08-01

Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

Stability and bifurcation analysis of three-species predator-prey model with non-monotonic delayed predator response

NASA Astrophysics Data System (ADS)

Balilo, Aldrin T.; Collera, Juancho A.

2018-03-01

In this paper, we consider delayed three-species predator-prey model with non-monotonic functional response where two predator populations feed on a single prey population. Response function in both predator populations includes a time delay which represents the gestation period of the predator populations. We call a positive equlibrium solution of the form E*S=(x*,y*,y*) as a symmetric equilibrium. The goal of this paper is to determine the effect of the difference in gestation periods of predator populations to the local dynamics of symmetric equilibria. Our results include conditions on the existence of equilibrium solutions, and stability and bifurcations of symmetric equilibria as the gestation periods of predator populations are varied. A numerical bifurcation analysis tool is also used to illustrate our results. Stability switch occurs at a Hopf bifurcation. Moreover, a branch of stable periodic solutions, obtained using numerical continuation, emerges from the Hopf bifurcation. This shows that the predator population with longer gestation period oscillates higher than the predator population with shorter gestation period.

Instability risk analysis and risk assessment system establishment of underground storage caverns in bedded salt rock

NASA Astrophysics Data System (ADS)

Jing, Wenjun; Zhao, Yan

2018-02-01

Stability is an important part of geotechnical engineering research. The operating experiences of underground storage caverns in salt rock all around the world show that the stability of the caverns is the key problem of safe operation. Currently, the combination of theoretical analysis and numerical simulation are the mainly adopts method of reserve stability analysis. This paper introduces the concept of risk into the stability analysis of underground geotechnical structure, and studies the instability of underground storage cavern in salt rock from the perspective of risk analysis. Firstly, the definition and classification of cavern instability risk is proposed, and the damage mechanism is analyzed from the mechanical angle. Then the main stability evaluating indicators of cavern instability risk are proposed, and an evaluation method of cavern instability risk is put forward. Finally, the established cavern instability risk assessment system is applied to the analysis and prediction of cavern instability risk after 30 years of operation in a proposed storage cavern group in the Huai’an salt mine. This research can provide a useful theoretical base for the safe operation and management of underground storage caverns in salt rock.

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.; Tang, Harry (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

An Entropy-Based Approach to Nonlinear Stability

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Huygens' inspired multi-pendulum setups: Experiments and stability analysis

NASA Astrophysics Data System (ADS)

Hoogeboom, F. N.; Pogromsky, A. Y.; Nijmeijer, H.

2016-11-01

This paper examines synchronization of a set of metronomes placed on a lightweight foam platform. Two configurations of the set of metronomes are considered: a row setup containing one-dimensional coupling and a cross setup containing two-dimensional coupling. Depending on the configuration and coupling between the metronomes, i.e., the platform parameters, in- and/or anti-phase synchronized behavior is observed in the experiments. To explain this behavior, mathematical models of a metronome and experimental setups have been derived and used in a local stability analysis. It is numerically and experimentally demonstrated that varying the coupling parameters for both configurations has a significant influence on the stability of the synchronized solutions.

The Absolute Stability Analysis in Fuzzy Control Systems with Parametric Uncertainties and Reference Inputs

NASA Astrophysics Data System (ADS)

Wu, Bing-Fei; Ma, Li-Shan; Perng, Jau-Woei

This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed in the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur'e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Finally, the comparisons are also given to show the effectiveness of the analysis method.

A rumor transmission model with incubation in social networks

NASA Astrophysics Data System (ADS)

Jia, Jianwen; Wu, Wenjiang

2018-02-01

In this paper, we propose a rumor transmission model with incubation period and constant recruitment in social networks. By carrying out an analysis of the model, we study the stability of rumor-free equilibrium and come to the local stable condition of the rumor equilibrium. We use the geometric approach for ordinary differential equations for showing the global stability of the rumor equilibrium. And when ℜ0 = 1, the new model occurs a transcritical bifurcation. Furthermore, numerical simulations are used to support the analysis. At last, some conclusions are presented.

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

Formal Solutions for Polarized Radiative Transfer. III. Stiffness and Instability

NASA Astrophysics Data System (ADS)

Janett, Gioele; Paganini, Alberto

2018-04-01

Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge–Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented.

Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles

NASA Astrophysics Data System (ADS)

Kaur, Ramanpreet; Sharma, Sapna

2018-06-01

Basic lattice model is extended to study the heterogeneous traffic by considering the optimal current difference effect on a unidirectional single lane highway. Heterogeneous traffic consisting of low- and high-sensitivity vehicles is modeled and their impact on stability of mixed traffic flow has been examined through linear stability analysis. The stability of flow is investigated in five distinct regions of the neutral stability diagram corresponding to the amount of higher sensitivity vehicles present on road. In order to investigate the propagating behavior of density waves non linear analysis is performed and near the critical point, the kink antikink soliton is obtained by driving mKdV equation. The effect of fraction parameter corresponding to high sensitivity vehicles is investigated and the results indicates that the stability rise up due to the fraction parameter. The theoretical findings are verified via direct numerical simulation.

Nonlinear density wave investigation for an extended car-following model considering driver’s memory and jerk

NASA Astrophysics Data System (ADS)

Jin, Zhizhan; Li, Zhipeng; Cheng, Rongjun; Ge, Hongxia

2018-01-01

Based on the two velocity difference model (TVDM), an extended car-following model is developed to investigate the effect of driver’s memory and jerk on traffic flow in this paper. By using linear stability analysis, the stability conditions are derived. And through nonlinear analysis, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are obtained, respectively. The mKdV equation is constructed to describe the traffic behavior near the critical point. The evolution of traffic congestion and the corresponding energy consumption are discussed. Numerical simulations show that the improved model is found not only to enhance the stability of traffic flow, but also to depress the energy consumption, which are consistent with the theoretical analysis.

Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model.

PubMed

Cairoli, Andrea; Piovani, Duccio; Jensen, Henrik Jeldtoft

2014-12-31

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.

Stability analysis of fractional-order Hopfield neural networks with time delays.

PubMed

Wang, Hu; Yu, Yongguang; Wen, Guoguang

2014-07-01

This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analysis of aggregate pier systems for stabilization of subgrade settlement.

DOT National Transportation Integrated Search

2014-12-01

Every year, ODOT undertakes numerous pavement patching/resurfacing projects to repair pavement : distress and structural failure due to soft and/or organic soils constituting the subgrade. Other than the : temporary solution of patching/resurfacing, ...

Gravitational modulation of thermosolutal convection during directional solidification

NASA Astrophysics Data System (ADS)

Murray, B. T.; Coriell, S. R.; McFadden, G. B.; Wheeler, A. A.; Saunders, B. V.

1993-03-01

During directional solidification of a binary alloy at constant velocity, thermosolutal convection may occur due to the temperature and solute gradients associated with the solidification process. For vertical growth in an ideal furnace (lacking horizontal gradients) a quiescent state is possible. The effect of a time-periodic vertical gravitational acceleration (or equivalently vibration) on the onset of thermosolutal convection is calculated based on linear stability using Floquet theory. Numerical calculations for the onset of instability have been carried out for a semiconductor alloy with Schmidt number of 10 and Prandtl number of 0.1 with primary emphasis on large modulation frequencies in a microgravity environment for which the background gravitational acceleration is negligible. The numerical results demonstrate that there is a significant difference in stability depending on whether a heavier or lighter solute is rejected. For large modulation frequencies, the stability behavior can be described by either the method of averaging or an asymptotic resonant mode analysis.

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Survivability of Deterministic Dynamical Systems

PubMed Central

Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen

2016-01-01

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures. PMID:27405955

Robust stability of fractional order polynomials with complicated uncertainty structure

PubMed Central

Şenol, Bilal; Pekař, Libor

2017-01-01

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. PMID:28662173

Delay-slope-dependent stability results of recurrent neural networks.

PubMed

Li, Tao; Zheng, Wei Xing; Lin, Chong

2011-12-01

By using the fact that the neuron activation functions are sector bounded and nondecreasing, this brief presents a new method, named the delay-slope-dependent method, for stability analysis of a class of recurrent neural networks with time-varying delays. This method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed Lyapunov-Krasovskii functional. Then some improved delay-dependent stability criteria with less computational burden and conservatism are obtained. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.

From LIDAR Scanning to 3d FEM Analysis for Complex Surface and Underground Excavations

NASA Astrophysics Data System (ADS)

Chun, K.; Kemeny, J.

2017-12-01

Light detection and ranging (LIDAR) has been a prevalent remote-sensing technology applied in the geological fields due to its high precision and ease to use. One of the major applications is to use the detailed geometrical information of underground structures as a basis for the generation of three-dimensional numerical model that can be used in FEM analysis. To date, however, straightforward techniques in reconstructing numerical model from the scanned data of underground structures have not been well established or tested. In this paper, we propose a comprehensive approach integrating from LIDAR scanning to finite element numerical analysis, specifically converting LIDAR 3D point clouds of object containing complex surface geometry into finite element model. This methodology has been applied to the Kartchner Caverns in Arizona for the stability analysis. Numerical simulations were performed using the finite element code ABAQUS. The results indicate that the highlights of our technologies obtained from LIDAR is effective and provide reference for other similar engineering project in practice.

A Leap-Frog Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations in Metamaterials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, J., Waters, J. W., Machorro, E. A.

2012-06-01

Numerical simulation of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. In this paper, we propose a leap-frog discontinuous Galerkin method to solve the time-dependent Maxwell’s equations in metamaterials. Conditional stability and error estimates are proved for the scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

A priori stability results for PFC

NASA Astrophysics Data System (ADS)

Rossiter, J. A.

2017-02-01

Despite its popularity in industry and obvious efficacy, predictive functional control has few rigorous a priori stability results in the literature. In many cases, common sense and intuition with some trial and error are the main design tools. This paper seeks to tackle that gap by providing some analysis of the control law and showing what forms of stability assurances can be given and how these depend on the user choices of coincidence horizon and desired closed-loop pole. The conditions are separated into necessary, but not sufficient conditions for stability and, conversely, sufficient but not necessary conditions. Numerical examples demonstrate the efficacy of these conditions and the ease of use.

Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Sabari, S.; Murali, R.

2018-05-01

We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.

Mean-field velocity difference model considering the average effect of multi-vehicle interaction

NASA Astrophysics Data System (ADS)

Guo, Yan; Xue, Yu; Shi, Yin; Wei, Fang-ping; Lü, Liang-zhong; He, Hong-di

2018-06-01

In this paper, a mean-field velocity difference model(MFVD) is proposed to describe the average effect of multi-vehicle interactions on the whole road. By stability analysis, the stability condition of traffic system is obtained. Comparison with stability of full velocity-difference (FVD) model and the completeness of MFVD model are discussed. The mKdV equation is derived from MFVD model through nonlinear analysis to reveal the traffic jams in the form of the kink-antikink density wave. Then the numerical simulation is performed and the results illustrate that the average effect of multi-vehicle interactions plays an important role in effectively suppressing traffic jam. The increase strength of the mean-field velocity difference in MFVD model can rapidly reduce traffic jam and enhance the stability of traffic system.

Modeling and analysis to quantify MSE wall behavior and performance.

DOT National Transportation Integrated Search

2009-08-01

To better understand potential sources of adverse performance of mechanically stabilized earth (MSE) walls, a suite of analytical models was studied using the computer program FLAC, a numerical modeling computer program widely used in geotechnical en...

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear

NASA Astrophysics Data System (ADS)

Panday, Pijush; Pal, Nikhil; Samanta, Sudip; Chattopadhyay, Joydev

In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

NASA Technical Reports Server (NTRS)

Lallemand, Pierre; Luo, Li-Shi

2000-01-01

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Numerical simulation and stability analysis of solutocapillary effect in ultrathin films

NASA Astrophysics Data System (ADS)

Gordeeva, V. Yu.; Lyushnin, A. V.

2017-04-01

Polar fluids, like water or polydimethylsiloxane, are widely used in technical and medical applications. Capillary effects arising from surface tension gradients can be significant in thin liquid films. The present paper is dedicated to investigation of capillary flow due to a surfactant added to a polar liquid under conditions when intermolecular forces and disjoining pressure play an important role. Evolution equations are formulated for a film profile and the surfactant concentration. Stability analysis shows that the Marangoni effect destabilizes the film, and oscillatory modes appear at slow evaporation rates. We find that the film has four stability modes of at slow evaporation: monotonic stable, monotonic unstable, oscillatory stable, and oscillatory unstable, depending on the wave number of disturbances.

Finite-time stability of neutral-type neural networks with random time-varying delays

NASA Astrophysics Data System (ADS)

Ali, M. Syed; Saravanan, S.; Zhu, Quanxin

2017-11-01

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov-Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.

Power System Transient Stability Improvement by the Interline Power Flow Controller (IPFC)

NASA Astrophysics Data System (ADS)

Zhang, Jun; Yokoyama, Akihiko

This paper presents a study on the power system transient stability improvement by means of interline power flow controller (IPFC). The power injection model of IPFC in transient analysis is proposed and can be easily incorporated into existing power systems. Based on the energy function analysis, the operation of IPFC should guarantee that the time derivative of the global energy of the system is not greater than zero in order to damp the electromechanical oscillations. Accordingly, control laws of IPFC are proposed for its application to the single-machine infinite-bus (SMIB) system and the multimachine systems, respectively. Numerical simulations on the corresponding model power systems are presented to demonstrate their effectiveness in improving power system transient stability.

The structure of non-hierarchical triple system stability regions

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.; Rubinov, A. V.

2009-08-01

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

The stability of stratified spatially periodic shear flows at low Péclet number

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garaud, Pascale, E-mail: pgaraud@ucsc.edu; Gallet, Basile; Bischoff, Tobias

2015-08-15

This work addresses the question of the stability of stratified, spatially periodic shear flows at low Péclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of “low-Péclet-number equations” proposed by Lignières [“The small-Péclet-number approximation in stellar radiative zones,” Astron. Astrophys. 348, 933–939 (1999)]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire’s theorem to the low-Péclet-number equations, which shows that the first unstable mode is always two-dimensional. Wemore » then perform an energy stability analysis of the low-Péclet-number equations and prove that for a given value of the Reynolds number, above a critical strength of the stratification, any smooth periodic shear flow is stable to perturbations of arbitrary amplitude. In that parameter regime, the flow can only be laminar and turbulent mixing does not take place. Finding that the conditions for linear and energy stability are different, we thus identify a region in parameter space where finite-amplitude instabilities could exist. Using direct numerical simulations, we indeed find that the system is subject to such finite-amplitude instabilities. We determine numerically how far into the linearly stable region of parameter space turbulence can be sustained.« less

Three-dimensional analysis of tokamaks and stellarators

PubMed Central

Garabedian, Paul R.

2008-01-01

The NSTAB equilibrium and stability code and the TRAN Monte Carlo transport code furnish a simple but effective numerical simulation of essential features of present tokamak and stellarator experiments. When the mesh size is comparable to the island width, an accurate radial difference scheme in conservation form captures magnetic islands successfully despite a nested surface hypothesis imposed by the mathematics. Three-dimensional asymmetries in bifurcated numerical solutions of the axially symmetric tokamak problem are relevant to the observation of unstable neoclassical tearing modes and edge localized modes in experiments. Islands in compact stellarators with quasiaxial symmetry are easier to control, so these configurations will become good candidates for magnetic fusion if difficulties with safety and stability are encountered in the International Thermonuclear Experimental Reactor (ITER) project. PMID:18768807

Direct numerical simulations of mack-mode damping on porous coated cones

NASA Astrophysics Data System (ADS)

Lüdeke, H.; Wartemann, V.

2013-06-01

The flow field over a 3 degree blunt cone is investigated with respect to a hypersonic stability analysis of the boundary-layer flow at Mach 6 with porous as well as smooth walls by comparing local direct numerical simulations (DNS) and linear stability theory (LST) data. The original boundary-layer profile is generated by a finite volume solver, using shock capturing techniques to generate an axisymmetric flow field. Local boundary-layer profiles are extracted from this flow field and hypersonic Mack-modes are superimposed for cone-walls with and without a porous surface used as a passive transition-reduction device. Special care is taken of curvature effects of the wall on the mode development over smooth and porous walls.

Influence of a white noise at channel inlet on the parallel and wavy convective instabilities of Poiseuille-Rayleigh-Bénard flows

NASA Astrophysics Data System (ADS)

Nicolas, Xavier; Zoueidi, Noussaiba; Xin, Shihe

2012-08-01

The present paper concerns Poiseuille-Rayleigh-Bénard mixed convection flows in horizontal rectangular air-filled channels of large spanwise aspect ratio (W/H ≥ 10) and it focuses on the primary and secondary thermoconvective instabilities made of steady longitudinal and unsteady wavy rolls for 100 ≤ Re ≤ 200, 3000 < Ra < 15 000, Pr = 0.7, and W/H = 10. Time linear stability analysis of longitudinal rolls and 3D nonlinear numerical simulations using a specially tailored finite difference code is performed for this purpose. A bibliographical review, linear stability analysis and 3D numerical simulations allow establishing the full stability diagram for Re ≤ 300 and Ra ≤ 20 000. The linear stability analysis indicates that the critical Rayleigh number Ra≈*(Re) of the neutral curve between longitudinal and wavy rolls for W/H = 10 is increased at least by a factor of 1.5 in comparison with infinite W/H. The numerical study shows that the usual definitions of growth lengths for longitudinal rolls are inappropriate and it explains the discrepancies observed on wall Nusselt numbers in the literature between experimental and numerical results for the fully developed longitudinal rolls: Nusselt number decreasing at Ra > 8000 is due to spanwise oscillations of thermoconvective rolls that favor a bulk temperature homogenization. Because they are a convective instability, wavy rolls and their space and time development are studied numerically by maintaining at channel inlet, a permanent random excitation: it is designed to cover all the modes and allows detecting the wavy roll modes that are naturally amplified by the flow and those that are damped. Wavy roll patterns are characterized with respect to its three control parameters: Re, the relative distance ɛ to the critical Rayleigh number Ra≈*, and the excitation magnitude Aexc. The growth length of the wavy rolls is shown to correlate with ɛ-0.72 and Log(Aexc). The frequency, wave number, and phase velocity of the most amplified mode, the wall averaged Nusselt number and the spanwise displacements of the wavy rolls are independent of Aexc in the fully developed zone, but depend a lot on ɛ for ɛ < 2 and nearly stabilize for ɛ > 2 (i.e., Ra > 3Ra≈*). Correlation laws as a function of Re, ɛ, and Aexc are proposed for most of the exploited quantities. Numerical simulations performed are in a good agreement with experimental results on the wavy rolls obtained by Pabiou et al. ["Wavy secondary instability of longitudinal rolls in Rayleigh-Bénard-Poiseuille flows," J. Fluid Mech. 542, 175 (2005), 10.1017/S0022112005006154]. Finally, wavy roll characteristics are shown to be potentially interesting to better homogenize the vapor depositions in the horizontal rectangular chemical vapor deposition reactors used to make thin coatings on heated substrates from gaseous components.

Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

Floquet stability analysis of the longitudinal dynamics of two hovering model insects

PubMed Central

Wu, Jiang Hao; Sun, Mao

2012-01-01

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed. PMID:22491980

Temporal model of an optically pumped co-doped solid state laser

NASA Technical Reports Server (NTRS)

Wangler, T. G.; Swetits, J. J.; Buoncristiani, A. M.

1993-01-01

Currently, research is being conducted on the optical properties of materials associated with the development of solid state lasers in the two micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are attained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.

Spatial solitons and stability in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with fourth-order diffraction and parity-time-symmetric potentials

NASA Astrophysics Data System (ADS)

Tiofack, C. G. L.; Ndzana, F., II; Mohamadou, A.; Kofane, T. C.

2018-03-01

We investigate the existence and stability of solitons in parity-time (PT )-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT -breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.

Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach

NASA Astrophysics Data System (ADS)

Ngoduy, D.

2013-10-01

This paper proposes a macroscopic model to describe the operations of cooperative adaptive cruise control (CACC) traffic flow, which is an extension of adaptive cruise control (ACC) traffic flow. In CACC traffic flow a vehicle can exchange information with many preceding vehicles through wireless communication. Due to such communication the CACC vehicle can follow its leader at a closer distance than the ACC vehicle. The stability diagrams are constructed from the developed model based on the linear and nonlinear stability method for a certain model parameter set. It is found analytically that CACC vehicles enhance the stabilization of traffic flow with respect to both small and large perturbations compared to ACC vehicles. Numerical simulation is carried out to support our analytical findings. Based on the nonlinear stability analysis, we will show analytically and numerically that the CACC system better improves the dynamic equilibrium capacity over the ACC system. We have argued that in parallel to microscopic models for CACC traffic flow, the newly developed macroscopic will provide a complete insight into the dynamics of intelligent traffic flow.

Numerical Study of Buoyancy and Different Diffusion Effects on the Structure and Dynamics of Triple Flames

NASA Technical Reports Server (NTRS)

Chen, Jyh-Yuan; Echekki, Tarek

2001-01-01

Numerical simulations of 2-D triple flames under gravity force have been implemented to identify the effects of gravity on triple flame structure and propagation properties and to understand the mechanisms of instabilities resulting from both heat release and buoyancy effects. A wide range of gravity conditions, heat release, and mixing widths for a scalar mixing layer are computed for downward-propagating (in the same direction with the gravity vector) and upward-propagating (in the opposite direction of the gravity vector) triple flames. Results of numerical simulations show that gravity strongly affects the triple flame speed through its contribution to the overall flow field. A simple analytical model for the triple flame speed, which accounts for both buoyancy and heat release, is developed. Comparisons of the proposed model with the numerical results for a wide range of gravity, heat release and mixing width conditions, yield very good agreement. The analysis shows that under neutral diffusion, downward propagation reduces the triple flame speed, while upward propagation enhances it. For the former condition, a critical Froude number may be evaluated, which corresponds to a vanishing triple flame speed. Downward-propagating triple flames at relatively strong gravity effects have exhibited instabilities. These instabilities are generated without any artificial forcing of the flow. Instead disturbances are initiated by minute round-off errors in the numerical simulations, and subsequently amplified by instabilities. A linear stability analysis on mean profiles of stable triple flame configurations have been performed to identify the most amplified frequency in spatially developed flows. The eigenfunction equations obtained from the linearized disturbance equations are solved using the shooting method. The linear stability analysis yields reasonably good agreements with the observed frequencies of the unstable triple flames. The frequencies and amplitudes of disturbances increase with the magnitude of the gravity vector. Moreover, disturbances appear to be most amplified just downstream of the premixed branches. The effects of mixing width and differential diffusion are investigated and their roles on the flame stability are studied.

Pitching stability analysis of half-rotating wing air vehicle

NASA Astrophysics Data System (ADS)

Wang, Xiaoyi; Wu, Yang; Li, Qian; Li, Congmin; Qiu, Zhizhen

2017-06-01

Half-Rotating Wing (HRW) is a new power wing which had been developed by our work team using rotating-type flapping instead of oscillating-type flapping. Half-Rotating Wing Air Vehicle (HRWAV) is similar as Bionic Flapping Wing Air Vehicle (BFWAV). It is necessary to guarantee pitching stability of HRWAV to maintain flight stability. The working principle of HRW was firstly introduced in this paper. The rule of motion indicated that the fuselage of HRWAV without empennage would overturn forward as it generated increased pitching movement. Therefore, the empennage was added on the tail of HRWAV to balance the additional moment generated by aerodynamic force during flight. The stability analysis further shows that empennage could weaken rapidly the pitching disturbance on HRWAV and a new balance of fuselage could be achieved in a short time. Case study using numerical analysis verified correctness and validity of research results mentioned above, which could provide theoretical guidance to design and control HRWAV.

Topics in Modeling of Cochlear Dynamics: Computation, Response and Stability Analysis

NASA Astrophysics Data System (ADS)

Filo, Maurice G.

This thesis touches upon several topics in cochlear modeling. Throughout the literature, mathematical models of the cochlea vary according to the degree of biological realism to be incorporated. This thesis casts the cochlear model as a continuous space-time dynamical system using operator language. This framework encompasses a wider class of cochlear models and makes the dynamics more transparent and easier to analyze before applying any numerical method to discretize space. In fact, several numerical methods are investigated to study the computational efficiency of the finite dimensional realizations in space. Furthermore, we study the effects of the active gain perturbations on the stability of the linearized dynamics. The stability analysis is used to explain possible mechanisms underlying spontaneous otoacoustic emissions and tinnitus. Dynamic Mode Decomposition (DMD) is introduced as a useful tool to analyze the response of nonlinear cochlear models. Cochlear response features are illustrated using DMD which has the advantage of explicitly revealing the spatial modes of vibrations occurring in the Basilar Membrane (BM). Finally, we address the dynamic estimation problem of BM vibrations using Extended Kalman Filters (EKF). Due to the limitations of noninvasive sensing schemes, such algorithms are inevitable to estimate the dynamic behavior of a living cochlea.

A Stability Analysis for a Hydrodynamic Three-Wave Journal Bearing

NASA Technical Reports Server (NTRS)

Ene, Nicoleta M.; Dimofte, Florin; Keith, Theo G., Jr.

2007-01-01

The influence of the wave amplitude and oil supply pressure on the dynamic behavior of a hydrodynamic three-wave journal bearing is presented. Both, a transient and a small perturbation technique, were used to predict the threshold to fractional frequency whirl (FFW). In addition, the behavior of the rotor after FFW appeared was determined from the transient analysis. The turbulent effects were also included in the computations. Bearings having a diameter of 30 mm, a length of 27.5 mm, and a clearance of 35 microns were analyzed. Numerical results were compared to experimental results obtained at the NASA GRC. Numerical and experimental results showed that the above-mentioned wave bearing with a wave amplitude ratio of 0.305 operates stably at rotational speeds up to 60,000 rpm, regardless of the oil supply pressure. For smaller wave amplitude ratios, a threshold of stability was found. It was observed that the threshold of stability for lower wave amplitude strongly depends on the oil supply pressure and on the wave amplitude. When the FFW occurs, the journal center maintains its trajectory inside the bearing clearance and therefore the rotor can be run safely without damaging the bearing surfaces.

Stability analysis of rimming flow inside a horizontally rotating cylinder in the presence of an insoluble surfactant

NASA Astrophysics Data System (ADS)

Kumawat, Tara Chand; Tiwari, Naveen

2017-12-01

Two-dimensional base state solutions for rimming flows and their stability analysis to small axial perturbations are analyzed numerically. A thin liquid film which is uniformly covered with an insoluble surfactant flows inside a counterclockwise rotating horizontal cylinder. In the present work, a mathematical model is obtained which consists of coupled thin film thickness and surfactant concentration evolution equations. The governing equations are obtained by simplifying the momentum and species transport equations using the thin-film approximation. The model equations include the effect of gravity, viscosity, capillarity, inertia, and Marangoni stress. The concentration gradients generated due to flow result in the surface tension gradient that generates the Marangoni stress near the interface region. The oscillations in the flow due to inertia are damped out by the Marangoni stress. It is observed that the Marangoni stress has stabilizing effect, whereas inertia and surface tension enhance the instability growth rate. In the presence of low diffusion of the surfactant or large value of the Péclet number, the Marangoni stress becomes more effective. The analytically obtained eigenvalues match well with the numerically computed eigenvalues in the absence of gravity.

The effect of a shear boundary layer on the stability of a capillary jet

NASA Astrophysics Data System (ADS)

Ganan-Calvo, Alfonso; Montanero, Jose M.; Herrada, Miguel A.

2014-11-01

The generic stabilization effect of a shear boundary layer over the free surface of a capillary jet is here studied from analytical (asymptotic), numerical and experimental approaches. In first place, we show the consistency of the proposed asymptotic analysis by a linear stability (numerical) analysis of the Navier-Stokes equations for a finite boundary layer thickness. We show how the convective-to-absolute instability transition departs drastically from the flat velocity profile case as the axial coordinate becomes closer to the origin of the boundary layer development. For large enough axial distances from that origin, Rayleigh's dispersion relation is recovered. A collection of experimental observations is analyzed from the perspective provided by these results. We propose a systematic framework to the dynamics of capillary jets issued from a nozzle, either by direct injection into a quiescent atmosphere or in a co-flow (e.g. gas flow-focused jets), which exhibit peculiarities now definitely attributable in first order to the formation of shear boundary layers. Partial support from the Ministry of Economy and Competitiveness, Junta de Extremadura, and Junta de Andalucia (Spain) through Grant Nos. DPI2010-21103, GR10047, P08-TEP-04128, and TEP-7465, respectively, is gratefully acknowledged.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Numerical study of signal propagation in corrugated coaxial cables

DOE PAGES

Li, Jichun; Machorro, Eric A.; Shields, Sidney

2017-01-01

Our article focuses on high-fidelity modeling of signal propagation in corrugated coaxial cables. Taking advantage of the axisymmetry, the authors reduce the 3-D problem to a 2-D problem by solving time-dependent Maxwell's equations in cylindrical coordinates.They then develop a nodal discontinuous Galerkin method for solving their model equations. We prove stability and error analysis for the semi-discrete scheme. We we present our numerical results, we demonstrate that our algorithm not only converges as our theoretical analysis predicts, but it is also very effective in solving a variety of signal propagation problems in practical corrugated coaxial cables.

The Three-Dimensional (3D) Numerical Stability Analysis of Hyttemalmen Open-Pit

NASA Astrophysics Data System (ADS)

Cała, Marek; Kowalski, Michał; Stopkowicz, Agnieszka

2014-10-01

The purpose of this paper was to perform the 3D numerical calculations allowing slope stability analysis of Hyttemalmen open pit (location Kirkenes, Finnmark Province, Norway). After a ramp rock slide, which took place in December 2010, as well as some other small-scale rock slope stability problems, it proved necessary to perform a serious stability analyses. The Hyttemalmen open pit was designed with a depth up to 100 m, a bench height of 24 m and a ramp width of 10 m. The rock formation in the iron mining district of Kirkenes is called the Bjornevaten Group. This is the most structurally complicated area connected with tectonic process such as folding, faults and metamorphosis. The Bjornevaten Group is a volcano-sedimentary sequence. Rock slope stability depends on the mechanical properties of the rock, hydro-geological conditions, slope topography, joint set systems and seismic activity. However, rock slope stability is mainly connected with joint sets. Joints, or general discontinuities, are regarded as weak planes within rock which have strength reducing consequences with regard to rock strength. Discontinuities within the rock mass lead to very low tensile strength. Several simulations were performed utilising the RocLab (2007) software to estimate the gneiss cohesion for slopes of different height. The RocLab code is dedicated to estimate rock mass strength using the Hoek-Brown failure criterion. Utilising both the GSI index and the Hoek-Brown strength criterion the equivalent Mohr-Coulomb parameters (cohesion and angle of internal friction) can be calculated. The results of 3D numerical calculations (with FLA3D code) show that it is necessary to redesign the slope-bench system in the Hyttemalmen open pit. Changing slope inclination for lower stages is recommended. The minimum factor of safety should be equal 1.3. At the final planned stage of excavation, the factor of safety drops to 1.06 with failure surface ranging through all of the slopes. In the case of a slope angle 70° for lower stages, FS = 1.26, which is not enough to provide slope stability. Another series of calculations were therefore performed taking water table lowering into consideration, which increases the global safety factor. It was finally evaluated, that for a water table level of 72 m the factor of safety equals 1.3, which is enough to assure global open-pit stability.

Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.

2015-03-01

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.; Pop, Ioan

2018-06-01

The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

Dynamic stability analysis of fractional order leaky integrator echo state neural networks

NASA Astrophysics Data System (ADS)

Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.

2017-06-01

The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.

Stability Limits and Dynamics of Nonaxisymmetric Liquid Bridges

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.

1998-01-01

Theoretical and experimental investigation of the stability of nonaxisymmetric and nonaxisymmetric bridges contained between equal and unequal radii disks as a function of Bond and Weber number with emphasis on the transition from unstable axisymmetric to stable nonaxisymmetric shapes. Numerical analysis of the stability of nonaxisymmetric bridges for various orientations of the gravity vector for equal and unequal disks. Experimental and theoretical investigation of large (nonaxisymmetric) oscillations and breaking of liquid bridges. This project involves both experimental and theoretical work. Static and dynamic experiments are conducted in a Plateau tank which makes a range of static Bond numbers accessible.

LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

NASA Astrophysics Data System (ADS)

Zhang, Hai; Ye, Renyu; Liu, Song; Cao, Jinde; Alsaedi, Ahmad; Li, Xiaodi

2018-02-01

This paper is concerned with the asymptotic stability of the Riemann-Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results.

Stability and bifurcation analysis for the Kaldor-Kalecki model with a discrete delay and a distributed delay

NASA Astrophysics Data System (ADS)

Yu, Jinchen; Peng, Mingshu

2016-10-01

In this paper, a Kaldor-Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.

Effect of antibodies on pathogen dynamics with delays and two routes of infection

NASA Astrophysics Data System (ADS)

Elaiw, A. M.; Almatrafi, A. A.; Hobiny, A. D.

2018-06-01

We study the global stability of pathogen dynamics models with saturated pathogen-susceptible and infected-susceptible incidence. The models incorporate antibody immune response and three types of discrete or distributed time delays. We first show that the solutions of the model are nonnegative and ultimately bounded. We determine two threshold parameters, the basic reproduction number and antibody response activation number. We establish the existence and stability of the steady states. We study the global stability analysis of models using Lyapunov method. The numerical simulations have shown that antibodies can reduce the pathogen progression.

The inclination of the dwarf irregular galaxy Holmberg II

NASA Astrophysics Data System (ADS)

Sánchez-Salcedo, F. J.; Hidalgo-Gámez, A. M.; Martínez-García, E. E.

2014-10-01

We provide constraints on the inclination angle of the H I disk of the dwarf irregular galaxy Holmberg II (Ho II) from a stability analysis of the outer gaseous disk. We point out that a mean inclination angle of 27(°) and thus a flat circular velocity of ≈ 60 km s(-1) , is required to have a level of gravitational stability similar to that found in other galaxies. Adopting this inclination angle, we find that Ho II lies on the right location in the baryonic Tully-Fisher relation. Moreover, for this inclination, its rotation curve is consistent with MOND. However, the corresponding analysis of the stability under MOND indicates that this galaxy could be problematic for MOND because its outer parts are marginally unstable in this gravity theory. We urge MOND simulators to study numerically the non-linear stability of gas-rich dwarf galaxies since this may provide a new key test for MOND.

Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves.

PubMed

Cuevas-Maraver, J; Kevrekidis, P G; Frantzeskakis, D J; Karachalios, N I; Haragus, M; James, G

2017-07-01

In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a nontrivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of the Peregrine soliton in the evolution variable, namely the Kuznetsov-Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations.

Dissipative stability analysis and control of two-dimensional Fornasini-Marchesini local state-space model

NASA Astrophysics Data System (ADS)

Wang, Lanning; Chen, Weimin; Li, Lizhen

2017-06-01

This paper is concerned with the problems of dissipative stability analysis and control of the two-dimensional (2-D) Fornasini-Marchesini local state-space (FM LSS) model. Based on the characteristics of the system model, a novel definition of 2-D FM LSS (Q, S, R)-α-dissipativity is given first, and then a sufficient condition in terms of linear matrix inequality (LMI) is proposed to guarantee the asymptotical stability and 2-D (Q, S, R)-α-dissipativity of the systems. As its special cases, 2-D passivity performance and 2-D H∞ performance are also discussed. Furthermore, by use of this dissipative stability condition and projection lemma technique, 2-D (Q, S, R)-α-dissipative state-feedback control problem is solved as well. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties.

PubMed

Song, Qiankun; Yu, Qinqin; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E

2018-07-01

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. Copyright © 2018 Elsevier Ltd. All rights reserved.

Launch window analysis of satellites in high eccentricity or large circular orbits

NASA Technical Reports Server (NTRS)

Renard, M. L.; Bhate, S. K.; Sridharan, R.

1973-01-01

Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions.

Stability and bifurcation for an SEIS epidemic model with the impact of media

NASA Astrophysics Data System (ADS)

Huo, Hai-Feng; Yang, Peng; Xiang, Hong

2018-01-01

A novel SEIS epidemic model with the impact of media is introduced. By analyzing the characteristic equation of equilibrium, the basic reproduction number is obtained and the stability of the steady states is proved. The occurrence of a forward, backward and Hopf bifurcation is derived. Numerical simulations and sensitivity analysis are performed. Our results manifest that media can regard as a good indicator in controlling the emergence and spread of the epidemic disease.

Dynamics and Statics of Nonaxisymmetric Liquid Bridges

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.; Resnick, Andrew H.; Slobozhanin, L. A.

1996-01-01

Theoretical and experimental investigation of the stability of nonaxisymmetric and nonaxisymmetric bridges contained between equal and unequal radii disks as a function of Bond and Weber number with emphasis on the transition from unstable axisymmetric to stable nonaxisymmetric shapes, are conducted. Numerical analysis of the stability of nonaxisymmetric bridges between unequal disks for various orientations of the gravity vector is performed. Experimental and theoretical investigation of large (nonaxisymmetric) oscillations and breaking of liquid bridges are also conducted.

Optimal subinterval selection approach for power system transient stability simulation

DOE PAGES

Kim, Soobae; Overbye, Thomas J.

2015-10-21

Power system transient stability analysis requires an appropriate integration time step to avoid numerical instability as well as to reduce computational demands. For fast system dynamics, which vary more rapidly than what the time step covers, a fraction of the time step, called a subinterval, is used. However, the optimal value of this subinterval is not easily determined because the analysis of the system dynamics might be required. This selection is usually made from engineering experiences, and perhaps trial and error. This paper proposes an optimal subinterval selection approach for power system transient stability analysis, which is based on modalmore » analysis using a single machine infinite bus (SMIB) system. Fast system dynamics are identified with the modal analysis and the SMIB system is used focusing on fast local modes. An appropriate subinterval time step from the proposed approach can reduce computational burden and achieve accurate simulation responses as well. As a result, the performance of the proposed method is demonstrated with the GSO 37-bus system.« less

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stability analysis of feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory

NASA Astrophysics Data System (ADS)

Sun, Di-Hua; Zhang, Geng; Zhao, Min; Cheng, Sen-Lin; Cao, Jian-Dong

2018-03-01

Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing transportation cyber-physical systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink-antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.

Numerical investigation of galloping instabilities in Z-shaped profiles.

PubMed

Gomez, Ignacio; Chavez, Miguel; Alonso, Gustavo; Valero, Eusebio

2014-01-01

Aeroelastic effects are relatively common in the design of modern civil constructions such as office blocks, airport terminal buildings, and factories. Typical flexible structures exposed to the action of wind are shading devices, normally slats or louvers. A typical cross-section for such elements is a Z-shaped profile, made out of a central web and two-side wings. Galloping instabilities are often determined in practice using the Glauert-Den Hartog criterion. This criterion relies on accurate predictions of the dependence of the aerodynamic force coefficients with the angle of attack. The results of a parametric analysis based on a numerical analysis and performed on different Z-shaped louvers to determine translational galloping instability regions are presented in this paper. These numerical analysis results have been validated with a parametric analysis of Z-shaped profiles based on static wind tunnel tests. In order to perform this validation, the DLR TAU Code, which is a standard code within the European aeronautical industry, has been used. This study highlights the focus on the numerical prediction of the effect of galloping, which is shown in a visible way, through stability maps. Comparisons between numerical and experimental data are presented with respect to various meshes and turbulence models.

Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh-Taylor instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reckinger, Scott James; Livescu, Daniel; Vasilyev, Oleg V.

A comprehensive numerical methodology has been developed that handles the challenges introduced by considering the compressive nature of Rayleigh-Taylor instability (RTI) systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification-dependent vorticity production. The computational framework is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

NASA Astrophysics Data System (ADS)

Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

2017-06-01

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

The Impact of Temperatures on the Stability of Rocks Surrounding a Single Fracture

NASA Astrophysics Data System (ADS)

Zhang, Yan; Li, Ning; Dai, Jun

2018-05-01

Research on the influence of temperature and the accompanying stress on the stability of the rocks surrounding an underground tunnel has become ever more important. This paper constructs a geometric model of a single-fracture tunnel by combining a high-temperature underground tunnel as the object of study with an example that uses a high-temperature tunnel segment in the water diversion tunnel of a hydropower station in Xinjiang. Based on the relevant theoretical analysis, with the consideration of different working conditions, a numerical experimental analysis was conducted to determine the two-dimensional transient temperature field distribution of the tunnel rock mass by using a numerical analysis software. The experimental data was consistent with the measured data. The calculated results show the following: a. when the temperature difference is greater, the stress concentration is higher near the fracture of the surrounding rock; b. the degree of the stress concentration in the crack tip region is not positively correlated to the distance, and there is a sensitive region where the stress varies.

The use of the modified Cholesky decomposition in divergence and classification calculations

NASA Technical Reports Server (NTRS)

Vanroony, D. L.; Lynn, M. S.; Snyder, C. H.

1973-01-01

The use of the Cholesky decomposition technique is analyzed as applied to the feature selection and classification algorithms used in the analysis of remote sensing data (e.g. as in LARSYS). This technique is approximately 30% faster in classification and a factor of 2-3 faster in divergence, as compared with LARSYS. Also numerical stability and accuracy are slightly improved. Other methods necessary to deal with numerical stablity problems are briefly discussed.

Harmonic Balance Computations of Fan Aeroelastic Stability

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Reddy, T. S. R.

2010-01-01

A harmonic balance (HB) aeroelastic analysis, which has been recently developed, was used to determine the aeroelastic stability (flutter) characteristics of an experimental fan. To assess the numerical accuracy of this HB aeroelastic analysis, a time-domain aeroelastic analysis was also used to determine the aeroelastic stability characteristics of the same fan. Both of these three-dimensional analysis codes model the unsteady flowfield due to blade vibrations using the Reynolds-averaged Navier-Stokes (RANS) equations. In the HB analysis, the unsteady flow equations are converted to a HB form and solved using a pseudo-time marching method. In the time-domain analysis, the unsteady flow equations are solved using an implicit time-marching approach. Steady and unsteady computations for two vibration modes were carried out at two rotational speeds: 100 percent (design) and 70 percent (part-speed). The steady and unsteady results obtained from the two analysis methods compare well, thus verifying the recently developed HB aeroelastic analysis. Based on the results, the experimental fan was found to have no aeroelastic instability (flutter) at the conditions examined in this study.

Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno's mathematical model

NASA Astrophysics Data System (ADS)

Wakif, Abderrahim; Boulahia, Zoubair; Mishra, S. R.; Mehdi Rashidi, Mohammad; Sehaqui, Rachid

2018-05-01

The onset of nanofluid convection in the presence of an externally applied magnetic field is investigated numerically based on the non-homogeneous Buongiorno's mathematical model. In this study, we use the latest experimental correlations and powerful analytical models for expressing the thermo-physical properties of some electrically conducting nanofluids, such as copper-water, sliver-water and gold-water nanofluids, in which the Brownian motion and thermophoresis effects on slip flow in nanofluids are taken into account in this model ( i.e., two-phase transport model). In this paper, we assume that the nanofluid has Newtonian behavior, confined horizontally between two infinite impermeable boundaries and heated from below, in such a way that the nanoparticles tend to concentrate near the upper wall. Considering the basic state of the nanofluidic system, the linear stability theory has been successfully applied to obtain the principal stability equations, which are solved numerically for an imposed volumetric fraction of nanoparticles and no-slip impermeable conditions at the isothermal walls bounding the nanofluid layer. The linear boundary-value problem obtained in this investigation is converted into a pure initial-value problem, so that we can solve it numerically by the fourth-fifth-order Runge-Kutta-Fehlberg method. The generalized Buongiorno's mathematical model proposed in this study allows performing a highly accurate computational analysis. In addition, the obtained results show that the stability of the studied nanofluidic system depends on several parameters, namely, the magnetic Chandrasekhar number Q , the reference value for the volumetric fraction of nanoparticles φ_0 and the size of nanoparticles d_p . In this analysis, the thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical thermal Rayleigh number R_{ac} , which characterizes the onset of convection cells, whose size is L_c=2π/a_c . Furthermore, the effects of various pertinent parameters on the critical stability parameters R_{ac} and a_c are discussed in more detail through graphical and tabular illustrations, for three types of nanofluids including copper-water, sliver-water, and gold-water.

Experimental and Numerical Study of the Buckling of Composite Profiles with Open Cross Section under Axial Compression

NASA Astrophysics Data System (ADS)

Rozylo, Patryk; Teter, Andrzej; Debski, Hubert; Wysmulski, Pawel; Falkowicz, Katarzyna

2017-10-01

The object of the research are short, thin-walled columns with an open top-hat cross section made of multilayer laminate. The walls of the investigated profiles are made of plate elements. The entire columns are subjected to uniform compression. A detailed analysis allowed us to determine critical forces and post-critical equilibrium paths. It is assumed that the columns are articulately supported on the edges forming their ends. The numerical investigation is performed by the finite element method. The study involves solving the problem of eigenvalue and the non-linear problem of stability of the structure. The numerical analysis is performed by the commercial simulation software ABAQUS®. The numerical results are then validated experimentally. In the discussed cases, it is assumed that the material operates within a linearly-elastic range, and the non-linearity of the FEM model is due to large displacements.

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

Analysis of the particle stability in a new designed ultrasonic levitation device.

PubMed

Baer, Sebastian; Andrade, Marco A B; Esen, Cemal; Adamowski, Julio Cezar; Schweiger, Gustav; Ostendorf, Andreas

2011-10-01

The use of acoustic levitation in the fields of analytical chemistry and in the containerless processing of materials requires a good stability of the levitated particle. However, spontaneous oscillations and rotation of the levitated particle have been reported in literature, which can reduce the applicability of the acoustic levitation technique. Aiming to reduce the particle oscillations, this paper presents the analysis of the particle stability in a new acoustic levitator device. The new acoustic levitator consists of a piezoelectric transducer with a concave radiating surface and a concave reflector. The analysis is conducted by determining numerically the axial and lateral forces that act on the levitated object and by measuring the oscillations of a sphere particle by a laser Doppler vibrometer. It is shown that the new levitator design allows to increase the lateral forces and reduce significantly the lateral oscillations of the levitated object.

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Correlation of Risk Analysis Method Results with Numerical and Limit Equilibrium Methods in Overall Slope Stability Analysis of Southern Wall of Chadormalu Iron Open Pit Mine-Iran / Korelacja wyników analizy ryzyka z wynikami obliczeń numerycznych oraz wynikami uzyskanymi w oparciu o metodę równowagi granicznej zastosowanych do badania stabilności wyrobiska pochyłego na południowej ścianie odkrywkowej kopalni rud żelaza w chadormalu w Iranie

NASA Astrophysics Data System (ADS)

Ahangari, Kaveh; Paji, Arman Gholinezhad; Behdani, Alireza Siami

2013-06-01

Slope stability analysis is one of the most important factors in designing open pit mines. Therefore an optimal slope design that supports both aspects of economy and safety is very significant. There are many different methods in slope stability analysis including empirical, limit equilibrium, block theory, numerical, and probabilistic methods. In this study, to analyze the overall slope stability of southern wall of Chadormalu iron open pit mine three numerical, limit equilibrium and probabilistic methods have been used. Software and methods that is used for analytical investigation in this study are FLAC software for numerical analysis, SLIDE software and circuit failure chart for limit equilibrium analysis and qualitative fault tree and semi-quantitative risk matrix for probabilistic analysis. The results of all above mentioned methods, was a circular failure occurrence in Metasomatite rock zone between 1405 to 1525 m levels. The main factors of failure occurrence in this range were heavily jointing and existing of faults. Safety factors resulted from numerical method; Circular chart method and SLIDE software are 1.16, 1.25 and 1.27 respectively. Regarding instability and safety factors in Metasomatite rock zone, in order to stabilize the given zone, some considerations such as bench angle and height reduction should be planned. In results of risk matrix method this zone was mentioned too as a high risk zone that numerical and limit equilibrium methods confirmed this. Badanie stabilności wyrobiska pochyłego jest jednym z najważniejszych czynników uwzględnianych przy projektowaniu kopalni odkrywkowych. Optymalne zaprojektowanie wyrobiska pochyłego z uwzględnieniem czynników ekonomicznych oraz bezpieczeństwa jest niezmiernie ważne. Istnieje wiele metod badania stabilności wyrobiska pochyłego, między innymi metody empiryczne, metoda równowagi granicznej, teoria bloków oraz metody numeryczne i probabilistyczne. W pracy tej omówiono zastosowanie trzech spośród tych metod: metody numerycznej, równowagi granicznej oraz metody probabilistycznej, do analizy stabilności wyrobiska pochyłego na południowej ścianie kopalni rud żelaza w Chadormalu w Iranie. Oprogramowanie wykorzystane w badaniach analitycznych to pakiet FLAK przy metodzie numerycznej, oprogramowanie SLIDE oraz wykresy kołowe przy metodzie równowagi granicznej oraz jakościowe drzewa określające występowanie uskoków i pół-jakościowe macierze ryzyka przy metodzie probabilistycznej. Wyniki uzyskane w oparciu o trzy wyżej wymienione metody wykazały wystąpienie zawalenia się skał metasomatycznych na poziomie od 1405 do 1525 m. Głównymi czynnikami warunkującymi zawalenie się skał w tym regionie była obecność licznych pęknięć oraz uskoków. Wskaźniki bezpieczeństwa uzyskane przy pomocy metod numerycznych, wykresu kołowego oraz oprogramowanie SLIDE wyniosły kolejno: 1.16, 1.25, 1.27. W odniesieniu do niestabilności w rejonie skał metasomatycznych, aby uczynić tę strefę bardziej stabilną należy uwzględnić takie czynniki jak kąt nachylenia ławy oraz obniżenie wysokości. Analiza przeprowadzona w oparciu o macierze ryzyka wykazała, że strefa ta jest strefą wysokiego ryzyka, zaś wyniki analizy numerycznej oraz wyników uzyskanych przy pomocy metody równowagi granicznej w pełni ten wniosek potwierdziły.

On the influence of tyre and structural properties on the stability of bicycles

NASA Astrophysics Data System (ADS)

Doria, Alberto; Roa Melo, Sergio Daniel

2018-06-01

In recent years the Whipple Carvallo Bicycle Model has been extended to analyse high speed stability of bicycles. Various researchers have developed models taking into account the effects of front frame compliance and tyre properties, nonetheless, a systematic analysis has not been yet carried out. This paper aims at analysing parametrically the influence of front frame compliance and tyre properties on the open loop stability of bicycles. Some indexes based on the eigenvalues of the dynamic system are defined to evaluate quantitatively bicycle stability. The parametric analysis is carried out with a factorial design approach to determine the most influential parameters. A commuting and a racing bicycle are considered and numerical results show different effects of the various parameters on each bicycle. In the commuting bicycle, the tyre properties have greater influence than front frame compliance, and the weave mode has the main effect on stability. Conversely, in the racing bicycle, the front frame compliance parameters have greater influence than tyre properties, and the wobble mode has the main effect on stability.

Slope Reinforcement with the Utilization of the Coal Waste Anthropogenic Material

NASA Astrophysics Data System (ADS)

Gwóźdź-Lasoń, Monika

2017-10-01

The protection of the environment, including waste management, is one of the pillars of the policy of the Europe. The application which is presented in that paper tries to show a trans-disciplinary way to design geotechnical constructions - slope stability analysis. The generally accepted principles that the author presents are numerous modelling patterns of earth retaining walls as slope stabilization system. The paper constitutes an attempt to summarise and generalise earlier researches which involved FEM numeric procedures and the Z_Soil package. The design of anthropogenic soil used as a material for reinforced earth retaining walls, are not only of commercial but of environmental importance as well and consistent with the concept of sustainable development and the need to redevelop brownfield. This paper tries to show conceptual and empirical modelling approaches to slope stability system used in anthropogenic soil formation such as heaps, resulting from mining, with a special focus on urban areas of South of Poland and perspectives of anthropogenic materials application in geotechnical engineering are discussed.

On the linear stability of blood flow through model capillary networks.

PubMed

Davis, Jeffrey M

2014-12-01

Under the approximation that blood behaves as a continuum, a numerical implementation is presented to analyze the linear stability of capillary blood flow through model tree and honeycomb networks that are based on the microvascular structures of biological tissues. The tree network is comprised of a cascade of diverging bifurcations, in which a parent vessel bifurcates into two descendent vessels, while the honeycomb network also contains converging bifurcations, in which two parent vessels merge into one descendent vessel. At diverging bifurcations, a cell partitioning law is required to account for the nonuniform distribution of red blood cells as a function of the flow rate of blood into each descendent vessel. A linearization of the governing equations produces a system of delay differential equations involving the discharge hematocrit entering each network vessel and leads to a nonlinear eigenvalue problem. All eigenvalues in a specified region of the complex plane are captured using a transformation based on contour integrals to construct a linear eigenvalue problem with identical eigenvalues, which are then determined using a standard QR algorithm. The predicted value of the dimensionless exponent in the cell partitioning law at the instability threshold corresponds to a supercritical Hopf bifurcation in numerical simulations of the equations governing unsteady blood flow. Excellent agreement is found between the predictions of the linear stability analysis and nonlinear simulations. The relaxation of the assumption of plug flow made in previous stability analyses typically has a small, quantitative effect on the stability results that depends on the specific network structure. This implementation of the stability analysis can be applied to large networks with arbitrary structure provided only that the connectivity among the network segments is known.

Dynamic stability of unidirectional fiber-reinforced viscoelastic composite plates

NASA Technical Reports Server (NTRS)

Chandiramani, N. K.; Librescu, L.

1989-01-01

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a three-dimensional viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi's micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Natural frequency and stability analysis of a pipe conveying fluid with axially moving supports immersed in fluid

NASA Astrophysics Data System (ADS)

Ni, Qiao; Luo, Yangyang; Li, Mingwu; Yan, Hao

2017-09-01

Structural model for a slender and uniform pipe conveying fluid, with axially moving supports on both ends, immersed in an incompressible fluid, is formulated. Free vibration and stability of the system are studied through numerical calculation. First, the equations of motion of the system are derived in an absolute coordinate system. An "axial added mass coefficient" is adopted to amend the forces caused by the external fluid. Boundary conditions are fixed by using coordinated conversion. Then, numerical results of the natural frequency are obtained via the Galerkin method, both for pinned-pinned and clamped-clamped supports. The critical speeds of supports and several instability types are discussed. Last, the effects of the system parameters on the dynamics and instability of the system are investigated.

A multilevel control system for the large space telescope. [numerical analysis/optimal control

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Sundareshan, S. K.; Vukcevic, M. B.

1975-01-01

A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques.

Spreading of a surfactant-laden droplet down an inclined and pre-wetted plane - Numerics, Asymptotics and Linear Stability Analysis

NASA Astrophysics Data System (ADS)

Goddard, Joseph

2012-11-01

Non-uniformities in surfactant concentration result in a surface shear stress, known as the Marangoni stress. This stress, if sufficiently large, can influence the flow at the interface. Naturally occurring surfactants in the mammalian lung reduce the surface tension within the liquid lining the airways and help to prevent collapse of smaller airways. Premature infants produce insufficient surfactant because the lungs are under developed. Resulting Respiratory Distress Syndrome is treated by Surfactant Replacement Therapy. Motivated by this medical application we theoretically investigate a model problem involving the spreading of a drop laden with an insoluble surfactant down an inclined and pre-wetted plane. Our focus is on understanding the mechanisms behind a ``fingering'' instability observed experimentally by high-resolution numerics revealing a multi-region asymptotic structure of the spreading droplet. Approximate solutions for each region are then derived using asymptotic analysis. In particular, a quasi-steady similarity solution is obtained for the leading edge of the droplet and a linear stability analysis shows that the base state is linearly unstable to long-wavelength perturbations for all inclination angles. The Marangoni effect is shown to be behind this instability at small inclination angles. A stability criterion is derived at small wave number and it's implication in the onset of the instability will be discussed.

Improved helicopter aeromechanical stability analysis using segmented constrained layer damping and hybrid optimization

NASA Astrophysics Data System (ADS)

Liu, Qiang; Chattopadhyay, Aditi

2000-06-01

Aeromechanical stability plays a critical role in helicopter design and lead-lag damping is crucial to this design. In this paper, the use of segmented constrained damping layer (SCL) treatment and composite tailoring is investigated for improved rotor aeromechanical stability using formal optimization technique. The principal load-carrying member in the rotor blade is represented by a composite box beam, of arbitrary thickness, with surface bonded SCLs. A comprehensive theory is used to model the smart box beam. A ground resonance analysis model and an air resonance analysis model are implemented in the rotor blade built around the composite box beam with SCLs. The Pitt-Peters dynamic inflow model is used in air resonance analysis under hover condition. A hybrid optimization technique is used to investigate the optimum design of the composite box beam with surface bonded SCLs for improved damping characteristics. Parameters such as stacking sequence of the composite laminates and placement of SCLs are used as design variables. Detailed numerical studies are presented for aeromechanical stability analysis. It is shown that optimum blade design yields significant increase in rotor lead-lag regressive modal damping compared to the initial system.

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

NASA Technical Reports Server (NTRS)

Beam, Richard M.; Warming, Robert F.

1991-01-01

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Study of a tri-trophic prey-dependent food chain model of interacting populations.

PubMed

Haque, Mainul; Ali, Nijamuddin; Chakravarty, Santabrata

2013-11-01

The current paper accounts for the influence of intra-specific competition among predators in a prey dependent tri-trophic food chain model of interacting populations. We offer a detailed mathematical analysis of the proposed food chain model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. Biologically feasible equilibria of the system are observed and the behaviours of the system around each of them are described. In particular, persistence, stability (local and global) and bifurcation (saddle-node, transcritical, Hopf-Andronov) analysis of this model are obtained. Relevant results from previous well known food chain models are compared with the current findings. Global stability analysis is also carried out by constructing appropriate Lyapunov functions. Numerical simulations show that the present system is capable enough to produce chaotic dynamics when the rate of self-interaction is very low. On the other hand such chaotic behaviour disappears for a certain value of the rate of self interaction. In addition, numerical simulations with experimented parameters values confirm the analytical results and shows that intra-specific competitions bears a potential role in controlling the chaotic dynamics of the system; and thus the role of self interactions in food chain model is illustrated first time. Finally, a discussion of the ecological applications of the analytical and numerical findings concludes the paper. Copyright © 2013 Elsevier Inc. All rights reserved.

Theoretical-Numerical Analysis of Boundary-Layer Stability with Combined Injection and Acoustic Absorptive Coating

DTIC Science & Technology

2014-01-01

stabilization of the boundary-layer flow. The foregoing model assumes that: • The number of pores per the instability wavelength ( porn ) is large...calculated ( ) porn x using the wavelength distribution ( )xλ∗ for the most unstable (vs. frequency) waves. Figure 45 shows that 100porn > downstream...instability wavelength ( ) porn x . Distribution A: Approved for public release; distribution is unlimited. 37 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 R e

Large deformation frictional contact analysis with immersed boundary method

NASA Astrophysics Data System (ADS)

Navarro-Jiménez, José Manuel; Tur, Manuel; Albelda, José; Ródenas, Juan José

2018-01-01

This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.

Local projection stabilization for linearized Brinkman-Forchheimer-Darcy equation

NASA Astrophysics Data System (ADS)

Skrzypacz, Piotr

2017-09-01

The Local Projection Stabilization (LPS) is presented for the linearized Brinkman-Forchheimer-Darcy equation with high Reynolds numbers. The considered equation can be used to model porous medium flows in chemical reactors of packed bed type. The detailed finite element analysis is presented for the case of nonconstant porosity. The enriched variant of LPS is based on the equal order interpolation for the velocity and pressure. The optimal error bounds for the velocity and pressure errors are justified numerically.

The feedback control research on straight and curved road with car-following model

NASA Astrophysics Data System (ADS)

Zheng, Yi-Ming; Cheng, Rong-Jun; Ge, Hong-Xia

2017-07-01

Taking account of the road consisting of curved part and straight part, an extended car-following model is proposed in this paper. A control signal including the velocity difference between the considered vehicle and the vehicle in front is taken into account. The control theory method is applied into analysis of the stability condition for the model. Numerical simulations are implemented to prove that the stability of the traffic flow strengthens effectively with an increase of the radius of curved road, and the control signal can suppress the traffic congestion. The results are in good agree with the theoretical analysis.

Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays.

PubMed

Wang, Leimin; Zeng, Zhigang; Ge, Ming-Feng; Hu, Junhao

2018-05-02

This paper deals with the stabilization problem of memristive recurrent neural networks with inertial items, discrete delays, bounded and unbounded distributed delays. First, for inertial memristive recurrent neural networks (IMRNNs) with second-order derivatives of states, an appropriate variable substitution method is invoked to transfer IMRNNs into a first-order differential form. Then, based on nonsmooth analysis theory, several algebraic criteria are established for the global stabilizability of IMRNNs under proposed feedback control, where the cases with both bounded and unbounded distributed delays are successfully addressed. Finally, the theoretical results are illustrated via the numerical simulations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies

PubMed Central

Borazjani, Iman; Ge, Liang; Sotiropoulos, Fotis

2010-01-01

The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782–1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken’s acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and an upper bound of the required for stability under-relaxation coefficient is derived. PMID:20981246

Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Ge, Liang; Sotiropoulos, Fotis

2008-08-01

The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries, Journal of Computational Physics 225 (2007) 1782-1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions the FSI algorithm is unconditionally unstable even when strong coupling FSI is employed. For such cases, however, combining the strong coupling iteration with under-relaxation in conjunction with the Aitken's acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and the upper bound of the under-relaxation coefficient, required for stability, is derived.

Development of Theoretical and Numerical Techniques for Achieving Stability in Gyrotron Traveling-Wave Amplifiers.

DTIC Science & Technology

1989-02-01

analysis methods diverge significantly. The electron current density found in Eq. 2.106 may be evaluated" as I J ...S..Y.v Yvt r t) (2.107) 0 ZO where 10...will be specified by the geometry and mode under consider- ation. It was noted earlier that the point of divergence between the two principle...techniques lies in the methods used to calculate the current density. Actually, the divergence is present only in theory. Theoreti- cally and numerically, Eq

Formal Solutions for Polarized Radiative Transfer. II. High-order Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Janett, Gioele; Steiner, Oskar; Belluzzi, Luca, E-mail: gioele.janett@irsol.ch

When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al., emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost.

Structured population dynamics: continuous size and discontinuous stage structures.

PubMed

Buffoni, Giuseppe; Pasquali, Sara

2007-04-01

A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the Eulerian formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of Eulerian and Lagrangian models are compared.

Analysis of an ultrasonically rotating droplet by moving particle semi-implicit and distributed point source method in a rotational coordinate

NASA Astrophysics Data System (ADS)

Wada, Yuji; Yuge, Kohei; Tanaka, Hiroki; Nakamura, Kentaro

2017-07-01

Numerical analysis on the rotation of an ultrasonically levitated droplet in centrifugal coordinate is discussed. A droplet levitated in an acoustic chamber is simulated using the distributed point source method and the moving particle semi-implicit method. Centrifugal coordinate is adopted to avoid the Laplacian differential error, which causes numerical divergence or inaccuracy in the global coordinate calculation. Consequently, the duration of calculation stability has increased 30 times longer than that in a the previous paper. Moreover, the droplet radius versus rotational acceleration characteristics show a similar trend to the theoretical and experimental values in the literature.

Stability and stabilisation of a class of networked dynamic systems

NASA Astrophysics Data System (ADS)

Liu, H. B.; Wang, D. Q.

2018-04-01

We investigate the stability and stabilisation of a linear time invariant networked heterogeneous system with arbitrarily connected subsystems. A new linear matrix inequality based sufficient and necessary condition for the stability is derived, based on which the stabilisation is provided. The obtained conditions efficiently utilise the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, a sufficient condition only dependent on each individual subsystem is also presented for the stabilisation of the networked systems with a large scale. Numerical simulations show that these conditions are computationally valid in the analysis and synthesis of a large-scale networked system.

Pharmacovigilance in Space: Stability Payload Compliance Procedures

NASA Technical Reports Server (NTRS)

Daniels, Vernie R.; Putcha, Lakshmi

2007-01-01

Pharmacovigilance is the science of, and activities relating to the detection, assessment, understanding, and prevention of drug-related problems. Over the lase decade, pharmacovigilance activities have contributed to the development of numerous technological and conventional advances focused on medication safety and regulatory intervention. The topics discussed include: 1) Proactive Pharmacovigilance; 2) A New Frontier; 3) Research Activities; 4) Project Purpose; 5) Methods; 6) Flight Stability Kit Components; 7) Experimental Conditions; 8) Research Project Logistics; 9) Research Plan; 10) Pharmaceutical Stability Research Project Pharmacovigilance Aspects; 11) Security / Control; 12) Packaging/Containment Actions; 13) Shelf-Life Assessments; 14) Stability Assessment Parameters; 15) Chemical Content Analysis; 16) Preliminary Results; 17) Temperature/Humidity; 18) Changes in PHysical and Chemical Assessment Parameters; 19) Observations; and 20) Conclusions.

An input-to-state stability approach to verify almost global stability of a synchronous-machine-infinite-bus system.

PubMed

Schiffer, Johannes; Efimov, Denis; Ortega, Romeo; Barabanov, Nikita

2017-08-13

Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)-Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS-Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

Numerical Modeling of Sliding Stability of RCC dam

NASA Astrophysics Data System (ADS)

Mughieda, O.; Hazirbaba, K.; Bani-Hani, K.; Daoud, W.

2017-06-01

Stability and stress analyses are the most important elements that require rigorous consideration in design of a dam structure. Stability of dams against sliding is crucial due to the substantial horizontal load that requires sufficient and safe resistance to develop by mobilization of adequate shearing forces along the base of the dam foundation. In the current research, the static sliding stability of a roller-compacted-concrete (RCC) dam was modelled using finite element method to investigate the stability against sliding. A commercially available finite element software (SAP 2000) was used to analyze stresses in the body of the dam and foundation. A linear finite element static analysis was performed in which a linear plane strain isoperimetric four node elements was used for modelling the dam-foundation system. The analysis was carried out assuming that no slip will occur at the interface between the dam and the foundation. Usual static loading condition was applied for the static analysis. The greatest tension was found to develop in the rock adjacent to the toe of the upstream slope. The factor of safety against sliding along the entire base of the dam was found to be greater than 1 (FS>1), for static loading conditions.

Hunting stability analysis of high-speed train bogie under the frame lateral vibration active control

NASA Astrophysics Data System (ADS)

Yao, Yuan; Wu, Guosong; Sardahi, Yousef; Sun, Jian-Qiao

2018-02-01

In this paper, we study a multi-objective optimal design of three different frame vibration control configurations and compare their performances in improving the lateral stability of a high-speed train bogie. The existence of the time-delay in the control system and its impact on the bogie hunting stability are also investigated. The continuous time approximation method is used to approximate the time-delay system dynamics and then the root locus curves of the system before and after applying control are depicted. The analysis results show that the three control cases could improve the bogie hunting stability effectively. But the root locus of low- frequency hunting mode of bogie which determinates the system critical speed is different, thus affecting the system stability with the increasing of speed. Based on the stability analysis at different bogie dynamics parameters, the robustness of the control case (1) is the strongest. However, the case (2) is more suitable for the dynamic performance requirements of bogie. For the case (1), the time-delay over 10 ms may lead to instability of the control system which will affect the bogie hunting stability seriously. For the case (2) and (3), the increasing time-delay reduces the hunting stability gradually over the high-speed range. At a certain speed, such as 200 km/h, an appropriate time-delay is favourable to the bogie hunting stability. The mechanism is proposed according to the root locus analysis of time-delay system. At last, the nonlinear bifurcation characteristics of the bogie control system are studied by the numerical integration methods to verify the effects of these active control configurations and the delay on the bogie hunting stability.

A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1976-01-01

The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.

Numerical stability of the error diffusion concept

NASA Astrophysics Data System (ADS)

Weissbach, Severin; Wyrowski, Frank

1992-10-01

The error diffusion algorithm is an easy implementable mean to handle nonlinearities in signal processing, e.g. in picture binarization and coding of diffractive elements. The numerical stability of the algorithm depends on the choice of the diffusion weights. A criterion for the stability of the algorithm is presented and evaluated for some examples.

The influence of geometric imperfections on the stability of three-layer beams with foam core

NASA Astrophysics Data System (ADS)

Wstawska, Iwona

2017-01-01

The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.

Direct Numerical Simulation of a Cavity-Stabilized Ethylene/Air Premixed Flame

NASA Astrophysics Data System (ADS)

Chen, Jacqueline; Konduri, Aditya; Kolla, Hemanth; Rauch, Andreas; Chelliah, Harsha

2016-11-01

Cavity flame holders have been shown to be important for flame stabilization in scramjet combustors. In the present study the stabilization of a lean premixed ethylene/air flame in a rectangular cavity at thermo-chemical conditions relevant to scramjet combustors is simulated using a compressible reacting multi-block direct numerical simulation solver, S3D, incorporating a 22 species ethylene-air reduced chemical model. The fuel is premixed with air to an equivalence ratio of 0.4 and enters the computational domain at Mach numbers between 0.3 and 0.6. An auxiliary inert channel flow simulation is used to provide the turbulent velocity profile at the inlet for the reacting flow simulation. The detailed interaction between intense turbulence, nonequilibrium concentrations of radical species formed in the cavity and mixing with the premixed main stream under density variations due to heat release rate and compressibility effects is quantified. The mechanism for flame stabilization is quantified in terms of relevant non-dimensional parameters, and detailed analysis of the flame and turbulence structure will be presented. We acknowledge the sponsorship of the AFOSR-NSF Joint Effort on Turbulent Combustion Model Assumptions and the DOE Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.

A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system

NASA Astrophysics Data System (ADS)

Lee, Hyun Geun; Choi, Jeong-Whan; Kim, Junseok

2012-02-01

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn-Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component Cahn-Hilliard system into a system of N-1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Does surface roughness influence the primary stability of acetabular cups? A numerical and experimental biomechanical evaluation.

PubMed

Le Cann, Sophie; Galland, Alexandre; Rosa, Benoît; Le Corroller, Thomas; Pithioux, Martine; Argenson, Jean-Noël; Chabrand, Patrick; Parratte, Sébastien

2014-09-01

Most acetabular cups implanted today are press-fit impacted cementless. Anchorage begins with the primary stability given by insertion of a slightly oversized cup. This primary stability is key to obtaining bone ingrowth and secondary stability. We tested the hypothesis that primary stability of the cup is related to surface roughness of the implant, using both an experimental and a numerical models to analyze how three levels of surface roughness (micro, macro and combined) affect the primary stability of the cup. We also investigated the effect of differences in diameter between the cup and its substrate, and of insertion force, on the cups' primary stability. The results of our study show that primary stability depends on the surface roughness of the cup. The presence of macro-roughness on the peripheral ring is found to decrease primary stability; there was excessive abrasion of the substrate, damaging it and leading to poor primary stability. Numerical modeling indicates that oversizing the cup compared to its substrate has an impact on primary stability, as has insertion force. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel.

PubMed

Baczewski, Andrew D; Bond, Stephen D

2013-07-28

Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.

Theoretical analyses of Baroclinic flows

NASA Technical Reports Server (NTRS)

Antar, B.

1982-01-01

A stability analysis of a thin horizontal rotating fluid layer which is subjected to arbitrary horizontal and vertical temperature gradients is presented. The basic state is a nonlinear Hadley cell which contains both Ekman and thermal boundary layers; it is given in closed form. The stability analysis is based on the linearized Navier-Stokes equations, and zonally symmetric perturbations in the form of waves propagating in the meridional direction are considered. Numerical methods were used for the stability problem. It was found that the instability sets in when the Richardson number is close to unity and that the critical Richardson number is a non-monotonic function of the Prandtl number. Further, it was found that the critical Richardson number decreases with increasing Ekman number until a critical value of the Ekman number is reached beyond which the fluid is stable.

Dynamical analysis of Lorenz System on traffic problem in Yogyakarta, Indonesia

NASA Astrophysics Data System (ADS)

Hartono; Saptaningtyas, F. Y.; Krisnawan, K. P.

2018-03-01

The traffic congestion becomes a routine problem which occurs in Yogyakarta. This study was to develop a mathematical model of traffic congestion using Lorenz System. This system was used to analyze the traffic condition in Yogyakarta road. The data was taken from the observation of the road and it had been validated. Routh Hourwith used to analyse the stability of free jamm equlibrium. The dynamic analysis showed that the system was stabil. Numerical solution showed that the bigger value of ratio of the distance relaxsation time to velocity relaxsation time resulting the more time to reach the stabil condition. It showed that more and more time to reach optimal velocity, needed more and more time as well to reach equilibrium. Traffic condition at the time of observation was ideal and there was no transition of traffic jam.

Instability and transition in rotating disk flow

NASA Technical Reports Server (NTRS)

Malik, M. R.

1981-01-01

The stability of three dimensional rotating disk flow and the effects of Coriolis forces and streamline curvature were investigated. It was shown that this analysis gives better growth rates than Orr-Sommerfeld equation. Results support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number.

Numerical Study of the Plasticity-Induced Stabilization Effect on Martensitic Transformations in Shape Memory Alloys

NASA Astrophysics Data System (ADS)

Junker, Philipp; Hempel, Philipp

2017-12-01

It is well known that plastic deformations in shape memory alloys stabilize the martensitic phase. Furthermore, the knowledge concerning the plastic state is crucial for a reliable sustainability analysis of construction parts. Numerical simulations serve as a tool for the realistic investigation of the complex interactions between phase transformations and plastic deformations. To account also for irreversible deformations, we expand an energy-based material model by including a non-linear isotropic hardening plasticity model. An implementation of this material model into commercial finite element programs, e.g., Abaqus, offers the opportunity to analyze entire structural components at low costs and fast computation times. Along with the theoretical derivation and expansion of the model, several simulation results for various boundary value problems are presented and interpreted for improved construction designing.

An optical fiber spool for laser stabilization with reduced acceleration sensitivity to 10-12/g

NASA Astrophysics Data System (ADS)

Hu, Yong-Qi; Dong, Jing; Huang, Jun-Chao; Li, Tang; Liu, Liang

2015-10-01

Environmental vibration causes mechanical deformation in optical fibers, which induces excess frequency noise in fiber-stabilized lasers. In order to solve such a problem, we propose an ultralow acceleration sensitivity fiber spool with symmetrically mounted structure. By numerical analysis with the finite element method, we obtain the optimal geometry parameters of the spool with which the horizontal and vertical acceleration sensitivity can be reduced to 3.25 × 10-12/g and 5.38 × 10-12/g respectively. Moreover, the structure features the insensitivity to the variation of geometry parameters, which will minimize the influence from numerical simulation error and manufacture tolerance. Project supported by the National Natural Science Foundation of China (Grant Nos. 11034008 and 11274324) and the Key Research Program of the Chinese Academy of Sciences (Grant No. KJZD-EW-W02).

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Lucero, John M.

1996-01-01

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2010-01-01

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Aeroelastic impact of above-rated wave-induced structural motions on the near-wake stability of a floating offshore wind turbine rotor

NASA Astrophysics Data System (ADS)

Rodriguez, Steven; Jaworski, Justin

2017-11-01

The impact of above-rated wave-induced motions on the stability of floating offshore wind turbine near-wakes is studied numerically. The rotor near-wake is generated using a lifting-line free vortex wake method, which is strongly coupled to a finite element solver for kinematically nonlinear blade deformations. A synthetic time series of relatively high-amplitude/high-frequency representative of above-rated conditions of the NREL 5MW referece wind turbine is imposed on the rotor structure. To evaluate the impact of these above-rated conditions, a linear stability analysis is first performed on the near wake generated by a fixed-tower wind turbine configuration at above-rated inflow conditions. The platform motion is then introduced via synthetic time series, and a stability analysis is performed on the wake generated by the floating offshore wind turbine at the same above-rated inflow conditions. The stability trends (disturbance modes versus the divergence rate of vortex structures) of the two analyses are compared to identify the impact that above-rated wave-induced structural motions have on the stability of the floating offshore wind turbine wake.

Analysis of ELM stability with extended MHD models in JET, JT-60U and future JT-60SA tokamak plasmas

NASA Astrophysics Data System (ADS)

Aiba, N.; Pamela, S.; Honda, M.; Urano, H.; Giroud, C.; Delabie, E.; Frassinetti, L.; Lupelli, I.; Hayashi, N.; Huijsmans, G.; JET Contributors, the; Research Unit, JT-60SA

2018-01-01

The stability with respect to a peeling-ballooning mode (PBM) was investigated numerically with extended MHD simulation codes in JET, JT-60U and future JT-60SA plasmas. The MINERVA-DI code was used to analyze the linear stability, including the effects of rotation and ion diamagnetic drift ({ω }* {{i}}), in JET-ILW and JT-60SA plasmas, and the JOREK code was used to simulate nonlinear dynamics with rotation, viscosity and resistivity in JT-60U plasmas. It was validated quantitatively that the ELM trigger condition in JET-ILW plasmas can be reasonably explained by taking into account both the rotation and {ω }* {{i}} effects in the numerical analysis. When deuterium poloidal rotation is evaluated based on neoclassical theory, an increase in the effective charge of plasma destabilizes the PBM because of an acceleration of rotation and a decrease in {ω }* {{i}}. The difference in the amount of ELM energy loss in JT-60U plasmas rotating in opposite directions was reproduced qualitatively with JOREK. By comparing the ELM affected areas with linear eigenfunctions, it was confirmed that the difference in the linear stability property, due not to the rotation direction but to the plasma density profile, is thought to be responsible for changing the ELM energy loss just after the ELM crash. A predictive study to determine the pedestal profiles in JT-60SA was performed by updating the EPED1 model to include the rotation and {ω }* {{i}} effects in the PBM stability analysis. It was shown that the plasma rotation predicted with the neoclassical toroidal viscosity degrades the pedestal performance by about 10% by destabilizing the PBM, but the pressure pedestal height will be high enough to achieve the target parameters required for the ITER-like shape inductive scenario in JT-60SA.

Elastic stability of biaxially loaded longitudinally stiffened composite structures.

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Tripp, L. L.

1973-01-01

A linear analysis method is presented for the elastic stability of structures of uniform cross section, that may be idealized as an assemblage of laminated plate-strips, flat and curved, and beams. Each plate-strip and beam covers the entire length of the structure and is simply supported on the edges normal to the longitudinal axis. Arbitrary boundary conditions may be specified on any external longitudinal side of plate-strips. The structure or selected plate-strips may be loaded in any desired combination of inplane biaxial loads. The analysis simultaneously considers all modes of instability and is applicable for the buckling of laminated composite structures. Some numerical results are presented to indicate possible applications.

Bright-dark and dark-dark solitons in coupled nonlinear Schrödinger equation with P T -symmetric potentials

NASA Astrophysics Data System (ADS)

Nath, Debraj; Gao, Yali; Babu Mareeswaran, R.; Kanna, T.; Roy, Barnana

2017-12-01

We explore different nonlinear coherent structures, namely, bright-dark (BD) and dark-dark (DD) solitons in a coupled nonlinear Schrödinger/Gross-Pitaevskii equation with defocusing/repulsive nonlinearity coefficients featuring parity-time ( P T )-symmetric potentials. Especially, for two choices of P T -symmetric potentials, we obtain the exact solutions for BD and DD solitons. We perform the linear stability analysis of the obtained coherent structures. The results of this linear stability analysis are well corroborated by direct numerical simulation incorporating small random noise. It has been found that there exists a parameter regime which can support stable BD and DD solitons.

Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay

NASA Astrophysics Data System (ADS)

Xu, Rui; Gan, Qintao; Ma, Zhien

2009-08-01

A ratio-dependent predator-prey model with time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and a semi-trivial boundary equilibrium is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semi-trivial equilibrium is also addressed. Numerical simulations are carried out to illustrate the main results.

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

NASA Technical Reports Server (NTRS)

Smith, L. L.; Morino, L.

1975-01-01

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.

PubMed

Cao, Hui; Zhou, Yicang; Ma, Zhien

2013-01-01

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

Analysis of the dynamics of multi-team Bertrand game with heterogeneous players

NASA Astrophysics Data System (ADS)

Ding, Zhanwen; Hang, Qinglan; Yang, Honglin

2011-06-01

In this article, we study the dynamics of a two-team Bertrand game with players having heterogeneous expectations. We study the equilibrium solutions and the conditions of their locally asymptotic stability. Numerical simulations are used to illustrate the complex behaviours of the proposed model of the Bertrand game. We demonstrate that some parameters of the model have great influence on the stability of Nash equilibrium and on the speed of convergence to Nash equilibrium. The chaotic behaviour of the model has been controlled by using feedback control method.

A stage structure pest management model with impulsive state feedback control

NASA Astrophysics Data System (ADS)

Pang, Guoping; Chen, Lansun; Xu, Weijian; Fu, Gang

2015-06-01

A stage structure pest management model with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

Numerical limitations in application of vector autoregressive modeling and Granger causality to analysis of EEG time series

NASA Astrophysics Data System (ADS)

Kammerdiner, Alla; Xanthopoulos, Petros; Pardalos, Panos M.

2007-11-01

In this chapter a potential problem with application of the Granger-causality based on the simple vector autoregressive (VAR) modeling to EEG data is investigated. Although some initial studies tested whether the data support the stationarity assumption of VAR, the stability of the estimated model is rarely (if ever) been verified. In fact, in cases when the stability condition is violated the process may exhibit a random walk like behavior or even be explosive. The problem is illustrated by an example.

Stability of equilibrium points in intraguild predation model with disease with SI model

NASA Astrophysics Data System (ADS)

Hassan, Aimi Nuraida binti Ali; Bujang, Noriham binti; Mahdi, Ahmad Faisal Bin

2017-04-01

Intraguild Predation (IGP) is classified as killing and eating among potential competitors. Intraguild Predation is a universal interaction, differing from competition or predation. Lotka Volterra competition model and Intraguild predation model has been analyze. The assumption for this model is no any immigration or migration involves. This paper is only considered IGP model for susceptible and infective (SI) only. The analysis of stability of the equilibrium points of Intraguild Predation Models with disease using Routh Hurwitz criteria will be illustrated using some numerical example.

Attitude stability of a spinning spacecraft during appendage deployment/retraction

NASA Technical Reports Server (NTRS)

Fitz-Coy, Norman; Fullerton, Wayne

1994-01-01

The work presented is motivated by the need for a national satellite rescue policy, not the ad hoc policy now in place. In studying different approaches for a national policy, the issue of capture and stabilization of a tumbling spacecraft must be addressed. For a rescue mission involving a tumbling spacecraft, it may be advantageous to have a rescue vehicle which is compact and 'rigid' during the rendezvous/capture phase. After capture, passive stabilization techniques could be utilized as an efficient means of detumbling the resulting system (i.e., both the rescue vehicle and captures spacecraft). Since the rescue vehicle is initially compact and 'rigid,' significant passive stabilization through energy dissipation can only be achieved through the deployment of flexible appendages. Once stabilization is accomplished, retraction of the appendages before maneuvering the system to its final destination may also prove advantageous. It is therefore of paramount interest that we study the effect of appendage deployment/retraction on the attitude stability of a spacecraft. Particular interest should be paid to appendage retraction, since if this process is destabilizing, passive stabilization as proposed may not be useful. Over the past three decades, it has been an 'on-again-off-again affair' with the problem of spacecraft appendage deployment. In most instances, these studies have been numerical simulations of specific spacecraft configurations for which there were specific concerns. The primary focus of these studies was the behavior of the appendage during deployment; the effects of appendage retraction was considered only in one of these studies. What is missing in the literature is a thorough study of the effects of appendage deployment/retraction on the attitude stability of a spacecraft. This paper presents a rigorous analysis of the stability of a spinning spacecraft during the deployment or the retraction of an appendage. The analysis is simplified such that meaningful insights into the problem can be inferred; it is not overly simplified such that critical dynamical behavior is neglected. The system is analyzed assuming that the spacecraft hub is rigid. The appendage deployment mechanism is modeled as a point mass on a massless rod whose length undergoes prescribed changes. Simplified flexibility effects of the appendage are included. The system is examined for stability by linearizing the equations in terms of small deviations from steady, noninterfering coning motion. Routh's procedure for analyzing small deviations from steady motion in dynamical systems is utilized in the analysis. The system of equations are nondimensionalized to facilitate parametric studies. The results are presented in terms of a reduced number of nondimensional parameters so that some general conclusions may be drawn. Verification of the linear analysis is presented through numerical simulations of the complete nonlinear, nonautonomous, coupled equations.

Finite element analysis and simulation of rheological properties of bulk molding compound (BMC)

NASA Astrophysics Data System (ADS)

Ergin, M. Fatih; Aydin, Ismail

2013-12-01

Bulk molding compound (BMC) is one of the important composite materials with various engineering applications. BMC is a thermoset plastic resin blend of various inert fillers, fiber reinforcements, catalysts, stabilizers and pigments that form a viscous, molding compound. Depending on the end-use application, bulk molding compounds are formulated to achieve close dimensional control, flame and scratch resistance, electrical insulation, corrosion and stain resistance, superior mechanical properties, low shrink and color stability. Its excellent flow characteristics, dielectric properties, and flame resistance make this thermoset material well-suited to a wide variety of applications requiring precision in detail and dimensions as well as high performance. When a BMC is used for these purposes, the rheological behavior and properties of the BMC is the main concern. In this paper, finite element analysis of rheological properties of bulk molding composite material was studied. For this purpose, standard samples of composite material were obtained by means of uniaxial hot pressing. 3 point flexural tests were then carried out by using a universal testing machine. Finite element analyses were then performed with defined material properties within a specific constitutive material behavior. Experimental and numerical results were then compared. Good correlation between the numerical simulation and the experimental results was obtained. It was expected with this study that effects of various process parameters and boundary conditions on the rheological behavior of bulk molding compounds could be determined by means of numerical analysis without detailed experimental work.

Long Term Analysis of Deformations in Salt Mines: Kłodawa Salt Mine Case Study, Central Poland

NASA Astrophysics Data System (ADS)

Cała, Marek; Tajduś, Antoni; Andrusikiewicz, Wacław; Kowalski, Michał; Kolano, Malwina; Stopkowicz, Agnieszka; Cyran, Katarzyna; Jakóbczyk, Joanna

2017-09-01

Located in central Poland, the Kłodawa salt dome is 26 km long and about 2 km wide. Exploitation of the dome started in 1956, currently rock salt extraction is carried out in 7 mining fields and the 12 mining levels at the depth from 322 to 625 meters below sea level (m.b.s.l.). It is planned to maintain the mining activity till 2052 and extend rock salt extraction to deeper levels. The dome is characterised by complex geological structure resulted from halokinetic and tectonic processes. Projection of the 3D numerical analysis took into account the following factors: mine working distribution within the Kłodawa mine (about 1000 rooms, 350 km of galleries), complex geological structure of the salt dome, complicated structure and geometry of mine workings and distinction in rocks mechanical properties e.g. rock salt and anhydrite. Analysis of past mine workings deformation and prediction of future rock mass behaviour was divided into four stages: building of the 3D model (state of mine workings in year 2014), model extension of the future mine workings planned for extraction in years 2015-2052, the 3D model calibration and stability analysis of all mine workings. The 3D numerical model of Kłodawa salt mine included extracted and planned mine workings in 7 mining fields and 14 mining levels (about 2000 mine workings). The dimensions of the model were 4200 m × 4700 m × 1200 m what was simulated by 33 million elements. The 3D model was calibrated on the grounds of convergence measurements and laboratory tests. Stability assessment of mine workings was based on analysis of the strength/stress ratio and vertical stress. The strength/stress ratio analysis enabled to indicate endangered area in mine workings and can be defined as the factor of safety. Mine workings in state close to collapse are indicated by the strength/stress ratio equals 1. Analysis of the vertical stress in mine workings produced the estimation of current state of stress in comparison to initial (pre-mining) conditions. The long-term deformation analysis of the Kłodawa salt mine for year 2014 revealed that stability conditions were fulfilled. Local disturbances indicated in the numerical analysis were connected with high chambers included in the mining field no 1 and complex geological structure in the vicinity of mine workings located in the mining fields no 2 and 3. Moreover, numerical simulations that projected the future extraction progress (till year 2052) showed positive performance. Local weakness zones in the mining field no 7 are associated with occurrence of carnallite layers and intensive mining which are planned in the mining field no 6 at the end of rock salt extraction.

Stability numerical analysis of soil cave in karst area to drawdown of underground water level

NASA Astrophysics Data System (ADS)

Mo, Yizheng; Xiao, Rencheng; Deng, Zongwei

2018-05-01

With the underground water level falling, the reliable estimates of the stability and deformation characteristics of soil caves in karst region area are required for analysis used for engineering design. Aimed at this goal, combined with practical engineering and field geotechnical test, detail analysis on vertical maximum displacement of top, vertical maximum displacement of surface, maximum principal stress and maximum shear stress were conducted by finite element software, with an emphasis on two varying factors: the size and the depth of soil cave. The calculations on the soil cave show that, its stability of soil cave is affected by both the size and depth, and only when extending a certain limit, the collapse occurred along with the falling of underground water; Additionally, its maximum shear stress is in arch toes, and its deformation curve trend of maximum displacement is similar to the maximum shear stress, which further verified that the collapse of soil cave was mainly due to shear-failure.

Stability of Capillary Surfaces in Rectangular Containers: The Right Square Cylinder

NASA Technical Reports Server (NTRS)

Weislogel, M. M.; Hsieh, K. C.

1998-01-01

The linearized governing equations for an ideal fluid are presented for numerical analysis for the stability of free capillary surfaces in rectangular containers against unfavorable disturbances (accelerations,i.e. Rayleigh-Taylor instability). The equations are solved for the case of the right square cylinder. The results are expressed graphically in term of a critical Bond number as a function of system contact angle. A critical wetting phenomena in the corners is shown to significantly alter the region of stability for such containers in contrast to simpler geometries such as the right circular cylinder or the infinite rectangular slot. Such computational results provide additional constraints for the design of fluids systems for space-based applications.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

NASA Technical Reports Server (NTRS)

Campbell, W.

1981-01-01

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

Stability of nonuniform rotor blades in hover using a mixed formulation

NASA Technical Reports Server (NTRS)

Stephens, W. B.; Hodges, D. H.; Avila, J. H.; Kung, R. M.

1980-01-01

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

NASA Astrophysics Data System (ADS)

Servan-Camas, Borja; Tsai, Frank T.-C.

2010-02-01

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).

Tilt angle measurement with a Gaussian-shaped laser beam tracking

NASA Astrophysics Data System (ADS)

Šarbort, Martin; Řeřucha, Šimon; Jedlička, Petr; Lazar, Josef; Číp, Ondrej

2014-05-01

We have addressed the challenge to carry out the angular tilt stabilization of a laser guiding mirror which is intended to route a laser beam with a high energy density. Such an application requires good angular accuracy as well as large operating range, long term stability and absolute positioning. We have designed an instrument for such a high precision angular tilt measurement based on a triangulation method where a laser beam with Gaussian profile is reflected off the stabilized mirror and detected by an image sensor. As the angular deflection of the mirror causes a change of the beam spot position, the principal task is to measure the position on the image chip surface. We have employed a numerical analysis of the Gaussian intensity pattern which uses the nonlinear regression algorithm. The feasibility and performance of the method were tested by numeric modeling as well as experimentally. The experimental results indicate that the assembled instrument achieves a measurement error of 0.13 microradian in the range +/-0.65 degrees over the period of one hour. This corresponds to the dynamic range of 1:170 000.

Free Body Dynamics of a Spinning Cylinder with Planar Restraint-(a.k.a. Barrel of Fun). Part 2

NASA Technical Reports Server (NTRS)

Moraru, Laurentiu; Dimofte, Florin; Hendricks, Robert C.

2011-01-01

The dynamic motion of a cylinder is analyzed based on rotation about its center of mass and is restrained by a plane normal to the axis passing through its center of mass at an angle. The first part of this work presented an analysis of the stability of the motion. In the current report, the governing equations are numerically integrated in time and the steady state is obtained as a limit of the transient numerical solution. The calculated data are compared with observed behaviors.

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

Stability analysis of the phytoplankton effect model on changes in nitrogen concentration on integrated multi-trophic aquaculture systems

NASA Astrophysics Data System (ADS)

Widowati; Putro, S. P.; Silfiana

2018-05-01

Integrated Multi-Trophic Aquaculture (IMTA) is a polyculture with several biotas maintained in it to optimize waste recycling as a food source. The interaction between phytoplankton and nitrogen as waste in fish cultivation including ammonia, nitrite, and nitrate studied in the form of mathematical models. The form model is non-linear systems of differential equations with the four variables. The analytical analysis was used to study the dynamic behavior of this model. Local stability analysis is performed at the equilibrium point with the first step linearized model by using Taylor series, then determined the Jacobian matrix. If all eigenvalues have negative real parts, then the equilibrium of the system is locally asymptotic stable. Some numerical simulations were also demonstrated to verify our analytical result.

Long-wave theory for a new convective instability with exponential growth normal to the wall.

PubMed

Healey, J J

2005-05-15

A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.

Numerical and experimental study of the dynamics of a superheated jet

NASA Astrophysics Data System (ADS)

Sinha, Avick; Gopalakrishnan, Shivasubramanian; Balasubramanian, Sridhar

2015-11-01

Flash-boiling is a phenomenon where a liquid experiences low pressures in a system resulting in it getting superheated. The sudden drop in pressures results in accelerated expansion and violent vapour formation. Understanding the physics behind the jet disintegration and flash-boiling phenomenon is still an open problem, with applications in automotive and aerospace combustors. The behaviour of a flash-boiling jet is highly dependent on the input parameters, inlet temperature and pressure. In the present study, the external (outside nozzle) and the internal (inside nozzle) flow characteristics of the two-phase flow has been studied numerically and experimentally. The phase change from liquid to vapour takes place over a finite period of time, modeled sing Homogeneous Relaxation Model (HRM). In order to validate the numerical results, controlled experiments were performed. Optical diagnostic techniques such as Particle Image Velocimetry (PIV) and Shadowgraphy were used to study the flow characteristics. Spray angle, penetration depth, droplet spectra were obtained which provides a better understanding of the break-up mechanism. Linear stability analysis is performed to study the stability characteristics of the jet.

Computer modeling of pulsed CO2 lasers for lidar applications

NASA Technical Reports Server (NTRS)

Spiers, Gary D.; Smithers, Martin E.; Murty, Rom

1991-01-01

The experimental results will enable a comparison of the numerical code output with experimental data. This will ensure verification of the validity of the code. The measurements were made on a modified commercial CO2 laser. Results are listed as following. (1) The pulse shape and energy dependence on gas pressure were measured. (2) The intrapulse frequency chirp due to plasma and laser induced medium perturbation effects were determined. A simple numerical model showed quantitative agreement with these measurements. The pulse to pulse frequency stability was also determined. (3) The dependence was measured of the laser transverse mode stability on cavity length. A simple analysis of this dependence in terms of changes to the equivalent fresnel number and the cavity magnification was performed. (4) An analysis was made of the discharge pulse shape which enabled the low efficiency of the laser to be explained in terms of poor coupling of the electrical energy into the vibrational levels. And (5) the existing laser resonator code was changed to allow it to run on the Cray XMP under the new operating system.

A spectral approach for the stability analysis of turbulent open-channel flows over granular beds

NASA Astrophysics Data System (ADS)

Camporeale, C.; Canuto, C.; Ridolfi, L.

2012-01-01

A novel Orr-Sommerfeld-like equation for gravity-driven turbulent open-channel flows over a granular erodible bed is here derived, and the linear stability analysis is developed. The whole spectrum of eigenvalues and eigenvectors of the complete generalized eigenvalue problem is computed and analyzed. The fourth-order eigenvalue problem presents singular non-polynomial coefficients with non-homogenous Robin-type boundary conditions that involve first and second derivatives. Furthermore, the Exner condition is imposed at an internal point. We propose a numerical discretization of spectral type based on a single-domain Galerkin scheme. In order to manage the presence of singular coefficients, some properties of Jacobi polynomials have been carefully blended with numerical integration of Gauss-Legendre type. The results show a positive agreement with the classical experimental data and allow one to relate the different types of instability to such parameters as the Froude number, wavenumber, and the roughness scale. The eigenfunctions allow two types of boundary layers to be distinguished, scaling, respectively, with the roughness height and the saltation layer for the bedload sediment transport.

Aeroelastic Stability of Rotor Blades Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Chopra, I.; Sivaneri, N.

1982-01-01

The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

Stability of a dragged viscous thread: Onset of ``stitching'' in a fluid-mechanical ``sewing machine''

NASA Astrophysics Data System (ADS)

Ribe, Neil M.; Lister, John R.; Chiu-Webster, Sunny

2006-12-01

A thin thread of viscous fluid that falls on a moving belt acts like a fluid-mechanical "sewing machine," exhibiting a rich variety of "stitch" patterns including meanders, translated coiling, slanted loops, braiding, figures-of-eight, W-patterns, side kicks, and period-doubled patterns. Using a numerical linear stability analysis, we determine the critical belt speed and oscillation frequency of the first bifurcation, at which a steady dragged viscous thread becomes unstable to transverse oscillations or "meandering." The predictions of the stability analysis agree closely with the experimental measurements of Chiu-Webster and Lister [J. Fluid Mech. 569, 89 (2006)]. Moreover, the critical belt speed and onset frequency for meandering are nearly identical to the contact-point migration speed and angular frequency, respectively, of steady coiling of a viscous thread on a stationary surface, implying a remarkable degree of dynamical similarity between the two phenomena.

Linear Stability of Binary Alloy Solidification for Unsteady Growth Rates

NASA Technical Reports Server (NTRS)

Mazuruk, K.; Volz, M. P.

2010-01-01

An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay.

PubMed

Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed

2017-02-01

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable. Copyright © 2016 Elsevier Ltd. All rights reserved.

Bright discrete solitons in spatially modulated DNLS systems

DOE PAGES

Kevrekidis, P. G.; Horne, R. L.; Whitaker, N.; ...

2015-08-04

In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the 'extended' solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Inmore » conclusion, the dynamics also reveal a tendency of the solution profiles to broaden, in line with the above findings. These results pave the way for further explorations of such states in discrete systems, including in higher dimensional settings.« less

Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales.

PubMed

Xiao, Qiang; Zeng, Zhigang

2017-10-01

The existed results of Lagrange stability and finite-time synchronization for memristive recurrent neural networks (MRNNs) are scale-free on time evolvement, and some restrictions appear naturally. In this paper, two novel scale-limited comparison principles are established by means of inequality techniques and induction principle on time scales. Then the results concerning Lagrange stability and global finite-time synchronization of MRNNs on time scales are obtained. Scaled-limited Lagrange stability criteria are derived, in detail, via nonsmooth analysis and theory of time scales. Moreover, novel criteria for achieving the global finite-time synchronization are acquired. In addition, the derived method can also be used to study global finite-time stabilization. The proposed results extend or improve the existed ones in the literatures. Two numerical examples are chosen to show the effectiveness of the obtained results.

Analysis and testing of numerical formulas for the initial value problem

NASA Technical Reports Server (NTRS)

Brown, R. L.; Kovach, K. R.; Popyack, J. L.

1980-01-01

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Numerical simulation of the cavitation characteristics of a mixed-flow pump

NASA Astrophysics Data System (ADS)

Chen, T.; Li, S. R.; Li, W. Z.; Liu, Y. L.; Wu, D. Z.; Wang, L. Q.

2013-12-01

As a kind of general equipment for fluid transportation, pumps were widely used in industry which includes many applications of high pressure, temperature and toxic fluids transportations. Performances of pumps affect the safety and reliability of the whole special equipment system. Cavitation in pumps cause the loss of performance and erosion of the blade, which could affect the running stability and reliability of the pump system. In this paper, a kind of numerical method for cavitaion performance prediction was presented. In order to investigate the accuracy of the method, CFD flow analysis and cavitation performance predictions of a mixed-flow pump were carried out. The numerical results were compared with the test results.

Numerical stability analysis of two-dimensional solute transport along a discrete fracture in a porous rock matrix

NASA Astrophysics Data System (ADS)

Watanabe, Norihiro; Kolditz, Olaf

2015-07-01

This work reports numerical stability conditions in two-dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective-dispersive problem described in Tang et al. (1981) and examine the stability of the Crank-Nicolson Galerkin finite element method (CN-GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method-flux corrected transport (FEM-FCT) method by Kuzmin () to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov-Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM-FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM-FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue.

The Effect of Stabilization Heat Treatments on the Tensile and Creep Behavior of an Advanced Nickel-Based Disk Alloy

NASA Technical Reports Server (NTRS)

Gayda, John

2003-01-01

As part of NASA s Advanced Subsonic Technology Program, a study of stabilization heat treatment options for an advanced nickel-base disk alloy, ME 209, was performed. Using a simple, physically based approach, the effect of stabilization heat treatments on tensile and creep properties was analyzed in this paper. Solutions temperature, solution cooling rate, and stabilization temperature/time were found to have a significant impact on tensile and creep properties. These effects were readily quantified using the following methodology. First, the effect of solution cooling rate was assessed to determine its impact on a given property. The as-cooled property was then modified by using two multiplicative factors which assess the impact of solution temperature and stabilization parameters. Comparison of experimental data with predicted values showed this physically based analysis produced good results that rivaled the statistical analysis employed, which required numerous changes in the form of the regression equation depending on the property and temperature in question. As this physically based analysis uses the data for input, it should be noted that predictions which attempt to extrapolate beyond the bounds of the data must be viewed with skepticism. Future work aimed at expanding the range of the stabilization/aging parameters explored in this study would be highly desirable, especially at the higher solution cooling rates.

Fate of Methane Emitted from Dissociating Marine Hydrates: Modeling, Laboratory, and Field Constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Juanes, Ruben

The overall goals of this research are: (1) to determine the physical fate of single and multiple methane bubbles emitted to the water column by dissociating gas hydrates at seep sites deep within the hydrate stability zone or at the updip limit of gas hydrate stability, and (2) to quantitatively link theoretical and laboratory findings on methane transport to the analysis of real-world field-scale methane plume data placed within the context of the degrading methane hydrate province on the US Atlantic margin. The project is arranged to advance on three interrelated fronts (numerical modeling, laboratory experiments, and analysis of field-basedmore » plume data) simultaneously. The fundamental objectives of each component are the following: Numerical modeling: Constraining the conditions under which rising bubbles become armored with hydrate, the impact of hydrate armoring on the eventual fate of a bubble’s methane, and the role of multiple bubble interactions in survival of methane plumes to very shallow depths in the water column. Laboratory experiments: Exploring the parameter space (e.g., bubble size, gas saturation in the liquid phase, “proximity” to the stability boundary) for formation of a hydrate shell around a free bubble in water, the rise rate of such bubbles, and the bubble’s acoustic characteristics using field-scale frequencies. Field component: Extending the results of numerical modeling and laboratory experiments to the field-scale using brand new, existing, public-domain, state-of-the-art real world data on US Atlantic margin methane seeps, without acquiring new field data in the course of this particular project. This component quantitatively analyzes data on Atlantic margin methane plumes and place those new plumes and their corresponding seeps within the context of gas hydrate degradation processes on this margin.« less

Determination of Global Stability of the Slosh Motion in a Spacecraft via Num Erical Experiment

NASA Astrophysics Data System (ADS)

Kang, Ja-Young

2003-12-01

The global stability of the attitude motion of a spin-stabilized space vehicle is investigated by performing numerical experiment. In the previous study, a stationary solution and a particular resonant condition for a given model were found by using analytical method but failed to represent the system stability over parameter values near and off the stationary points. Accordingly, as an extension of the previous work, this study performs numerical experiment to investigate the stability of the system across the parameter space and determines stable and unstable regions of the design parameters of the system.

Global stability of a multiple infected compartments model for waterborne diseases

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde

2014-10-01

In this paper, mathematical analysis is carried out for a multiple infected compartments model for waterborne diseases, such as cholera, giardia, and rotavirus. The model accounts for both person-to-person and water-to-person transmission routes. Global stability of the equilibria is studied. In terms of the basic reproduction number R0, we prove that, if R0⩽1, then the disease-free equilibrium is globally asymptotically stable and the infection always disappears; whereas if R0>1, there exists a unique endemic equilibrium which is globally asymptotically stable for the corresponding fast-slow system. Numerical simulations verify our theoretical results and present that the decay rate of waterborne pathogens has a significant impact on the epidemic growth rate. Also, we observe numerically that the unique endemic equilibrium is globally asymptotically stable for the whole system. This statement indicates that the present method need to be improved by other techniques.

MHD stagnation point flow and heat transfer of a nanofluid over a permeable nonlinear stretching/shrinking sheet with viscous dissipation effect

NASA Astrophysics Data System (ADS)

Jusoh, Rahimah; Nazar, Roslinda

2018-04-01

The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

Numerical modelling on stabilizing large magnetic island by RF current for disruption avoidance

NASA Astrophysics Data System (ADS)

Wang, Xiaojing; Yu, Qingquan; Zhang, Xiaodong; Zhu, Sizheng; Wang, Xiaoguang; Wu, Bin

2018-01-01

Numerical modelling on tearing mode stabilization by RF current due to electron cyclotron current drive (ECCD) has been carried out for the purposes of disruption avoidance, focusing on stabilizing the magnetic island which can grow to a large width and therefore, might cause plasma disruption. When the island has become large, a threshold in driven current for fully stabilizing the mode is found; below this threshold, the island width only slightly decreases. The island’s O-point shifts radially towards the magnetic axis as the mode grows, as a result, applying ECCD at the minor radius of the island’s O-point has a stronger effect than that at the original equilibrium rational surface for stabilizing a large island. During the island growth, the required driven current for mode stabilization increases with the island’s width, indicating that it is more effective to apply ECCD as early as possible for disruption avoidance, as observed in experiments. The numerical results have been compared with those obtained from the modified Rutherford equation.

A 3D staggered-grid finite difference scheme for poroelastic wave equation

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai

2014-10-01

Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko

2007-10-01

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.

On the wall-normal velocity of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Pruett, C. David

1991-01-01

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Numerical analysis of the performance of rock weirs: Effects of structure configuration on local hydraulics

USGS Publications Warehouse

Holmquist-Johnson, C. L.

2009-01-01

River spanning rock structures are being constructed for water delivery as well as to enable fish passage at barriers and provide or improve the aquatic habitat for endangered fish species. Current design methods are based upon anecdotal information applicable to a narrow range of channel conditions. The complex flow patterns and performance of rock weirs is not well understood. Without accurate understanding of their hydraulics, designers cannot address the failure mechanisms of these structures. Flow characteristics such as jets, near bed velocities, recirculation, eddies, and plunging flow govern scour pool development. These detailed flow patterns can be replicated using a 3D numerical model. Numerical studies inexpensively simulate a large number of cases resulting in an increased range of applicability in order to develop design tools and predictive capability for analysis and design. The analysis and results of the numerical modeling, laboratory modeling, and field data provide a process-based method for understanding how structure geometry affects flow characteristics, scour development, fish passage, water delivery, and overall structure stability. Results of the numerical modeling allow designers to utilize results of the analysis to determine the appropriate geometry for generating desirable flow parameters. The end product of this research will develop tools and guidelines for more robust structure design or retrofits based upon predictable engineering and hydraulic performance criteria. ?? 2009 ASCE.

Trajectory Prediction of Spin-Stabilized Projectiles With a Steady Liquid Payload

DTIC Science & Technology

2011-11-01

analysis assumes the effect of a liquid payload is similar to the Magnus effect . Spectral analysis used to numerically compute liquid-fill induced...the internal motion of a liquid payload can induce destabilizing moments on the projectile. This report creates a method to include the effect of... effect , liquid payload moments are added to the applied loads on the projectile. These loads are computed by solving the linearized Navier-Stokes

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1995-01-01

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Use of segmented constrained layer damping treatment for improved helicopter aeromechanical stability

NASA Astrophysics Data System (ADS)

Liu, Qiang; Chattopadhyay, Aditi; Gu, Haozhong; Liu, Qiang; Chattopadhyay, Aditi; Zhou, Xu

2000-08-01

The use of a special type of smart material, known as segmented constrained layer (SCL) damping, is investigated for improved rotor aeromechanical stability. The rotor blade load-carrying member is modeled using a composite box beam with arbitrary wall thickness. The SCLs are bonded to the upper and lower surfaces of the box beam to provide passive damping. A finite-element model based on a hybrid displacement theory is used to accurately capture the transverse shear effects in the composite primary structure and the viscoelastic and the piezoelectric layers within the SCL. Detailed numerical studies are presented to assess the influence of the number of actuators and their locations for improved aeromechanical stability. Ground and air resonance analysis models are implemented in the rotor blade built around the composite box beam with segmented SCLs. A classic ground resonance model and an air resonance model are used in the rotor-body coupled stability analysis. The Pitt dynamic inflow model is used in the air resonance analysis under hover condition. Results indicate that the surface bonded SCLs significantly increase rotor lead-lag regressive modal damping in the coupled rotor-body system.

Computational analysis of aerodynamic characteristics for wing in ground effect craft in lateral stability

NASA Astrophysics Data System (ADS)

Amir, M. A. U.; Maimun, A.; Mat, S.; Saad, M. R.

2016-10-01

Wing in-ground effect (WIG) crafts are becoming promising transportation over the last decade. However, stability and control problems faced by the WIG in earlier development are still unresolved. This paper objectively investigates the lateral stability of wing in ground effect craft. The wing encompasses a winglet at the end of the wingtip. Lift, drag and pressure were measured with the respect of the heeling angle of 100, 150 and 200, respectively, with the h/c of 0.3. Initial results from the computational studies show that the ground effect pressure distributions provide a natural righting moment when the WIG craft heels near ground. This initial result provides an insight to understand the current state of knowledge of stability for WIG, particularly on transverse or lateral stability of WIG where it plays important roles in the safety aspect. It is crucial to understand the stability and its component in order to avoid any unforeseen accident. This paper discusses the results obtained from the numerical studies.

On the stabilizing role of species diffusion in chemical enhanced oil recovery

NASA Astrophysics Data System (ADS)

Daripa, Prabir; Gin, Craig

2015-11-01

In this talk, the speaker will discuss a problem on the stability analysis related to the effect of species diffusion on stabilization of fingering in a Hele-Shaw model of chemical enhanced oil recovery. The formulation of the problem is motivated by a specific design principle of the immiscible interfaces in the hope that this will lead to significant stabilization of interfacial instabilities, there by improving oil recovery in the context of porous media flow. Testing the merits of this hypothesis poses some challenges which will be discussed along with some numerical results based on current formulation of this problem. Several open problems in this context will be discussed. This work is currently under progress. Supported by the grant NPRP 08-777-1-141 from the Qatar National Research Fund (a member of The Qatar Foundation).

Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons.

PubMed

Chen, Xiaofeng; Song, Qiankun; Li, Zhongshan; Zhao, Zhenjiang; Liu, Yurong

2018-07-01

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

NASA Technical Reports Server (NTRS)

Shaw, Stephen J.; Duck, Peter W.

1992-01-01

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

NASA Technical Reports Server (NTRS)

Shaw, Stephen J.; Duck, Peter W.

1990-01-01

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations. Chapter 1

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sjoegreen, B.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Truncation effect on Taylor-Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability

NASA Astrophysics Data System (ADS)

Ginzburg, Irina; Roux, Laetitia

2015-10-01

The Taylor dispersion in parabolic velocity field provides a well-known benchmark for advection-diffusion (ADE) schemes and serves as a first step towards accurate modeling of the high-order non-Gaussian effects in heterogeneous flow. While applying the Lattice Boltzmann ADE two-relaxation-times (TRT) scheme for a transport with given Péclet number (Pe) one should select six free-tunable parameters, namely, (i) molecular-diffusion-scale, equilibrium parameter; (ii) three families of equilibrium weights, assigned to the terms of mass, velocity and numerical-diffusion-correction, and (iii) two relaxation rates. We analytically and numerically investigate the respective roles of all these degrees of freedom in the accuracy and stability in the evolution of a Gaussian plume. For this purpose, the third- and fourth-order transient multi-dimensional analysis of the recurrence equations of the TRT ADE scheme is extended for a spatially-variable velocity field. The key point is in the coupling of the truncation and Taylor dispersion analysis which allows us to identify the second-order numerical correction δkT to Taylor dispersivity coefficient kT. The procedure is exemplified for a straight Poiseuille flow where δkT is given in a closed analytical form in equilibrium and relaxation parameter spaces. The predicted longitudinal dispersivity is in excellent agreement with the numerical experiments over a wide parameter range. In relatively small Pe-range, the relative dispersion error increases with Péclet number. This deficiency reduces in the intermediate and high Pe-range where it becomes Pe-independent and velocity-amplitude independent. Eliminating δkT by a proper parameter choice and employing specular reflection for zero flux condition on solid boundaries, the d2Q9 TRT ADE scheme may reproduce the Taylor-Aris result quasi-exactly, from very coarse to fine grids, and from very small to arbitrarily high Péclet numbers. Since free-tunable product of two eigenfunctions also controls stability of the model, the validity of the analytically established von Neumann stability diagram is examined in Poiseuille profile. The simplest coordinate-stencil subclass, which is the d2Q5 TRT bounce-back scheme, demonstrates the best performance and achieves the maximum accuracy for most stable relaxation parameters.

Pattern dynamics of the reaction-diffusion immune system.

PubMed

Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

2018-01-01

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

Mathematical analysis of a nutrient-plankton system with delay.

PubMed

Rehim, Mehbuba; Zhang, Zhenzhen; Muhammadhaji, Ahmadjan

2016-01-01

A mathematical model describing the interaction of nutrient-plankton is investigated in this paper. In order to account for the time needed by the phytoplankton to mature after which they can release toxins, a discrete time delay is incorporated into the system. Moreover, it is also taken into account discrete time delays which indicates the partially recycled nutrient decomposed by bacteria after the death of biomass. In the first part of our analysis the sufficient conditions ensuring local and global asymptotic stability of the model are obtained. Next, the existence of the Hopf bifurcation as time delay crosses a threshold value is established and, meanwhile, the phenomenon of stability switches is found under certain conditions. Numerical simulations are presented to illustrate the analytical results.

Front and pulse solutions for the complex Ginzburg-Landau equation with higher-order terms.

PubMed

Tian, Huiping; Li, Zhonghao; Tian, Jinping; Zhou, Guosheng

2002-12-01

We investigate one-dimensional complex Ginzburg-Landau equation with higher-order terms and discuss their influences on the multiplicity of solutions. An exact analytic front solution is presented. By stability analysis for the original partial differential equation, we derive its necessary stability condition for amplitude perturbations. This condition together with the exact front solution determine the region of parameter space where the uniformly translating front solution can exist. In addition, stable pulses, chaotic pulses, and attenuation pulses appear generally if the parameters are out of the range. Finally, applying these analysis into the optical transmission system numerically we find that the stable transmission of optical pulses can be achieved if the parameters are appropriately chosen.

Calculating Dynamics Of Helicopters And Slung Loads

NASA Technical Reports Server (NTRS)

Cicolani, Luigi; Kanning, Gerd

1991-01-01

General equations derived for numerical simulations of motions of multiple-lift, slung-load systems consisting of two or more lifting helicopters and loads slung from them by various combinations of spreader bars, cables, nets, and attaching hardware. Equations readily programmable for efficient computation of motions and lend themselves well to analysis and design of control strategies for stabilization and coordination.

Analysis of Serial and Parallel Algorithms for Use in Molecular Dynamics.. Review and Proposals

NASA Astrophysics Data System (ADS)

Mazzone, A. M.

This work analyzes the stability and accuracy of multistep methods, either for serial or parallel calculations, applied to molecular dynamics simulations. Numerical testing is made by evaluating the equilibrium configurations of mono-elemental crystalline lattices of metallic and semiconducting type (Ag and Si, respectively) and of a cubic CuY compound.

Ground effects on the stability of separated flow around an airfoil at low Reynolds numbers

NASA Astrophysics Data System (ADS)

He, Wei; Yu, Peng; Li, Larry K. B.

2017-11-01

We perform a BiGlobal stability analysis on the separated flow around a NACA 4415 airfoil at low Reynolds numbers (Re = 300 - 1000) and a high angle of attack α =20° with a focus on the effect of the airfoil's proximity to a moving ground. The results show that the most dominant perturbation is the Kelvin-Helmholtz mode and that this traveling mode becomes less unstable as the airfoil approaches the ground, although this stabilizing effect diminishes with increasing Reynolds number. By performing a Floquet analysis, we find that this ground effect can also stabilize secondary instabilities. This numerical-theoretical study shows that the ground can have a significant influence on the stability of separated flow around an airfoil at low Reynolds numbers, which could have implications for the design of micro aerial vehicles and for the understanding of natural flyers such as insects and birds. This work was supported by the Research Grants Council of Hong Kong (Project No. 16235716 and 26202815) and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) under Grant No.U1501501.

Robust stability for stochastic bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Shu, H. S.; Lv, Z. W.; Wei, G. L.

2008-02-01

In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

PubMed

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

Vibration and Stability of Pretwisted Spinning Thin-Walled Composite Beams Featuring BENDING-BENDING Elastic Coupling

NASA Astrophysics Data System (ADS)

SONG, O.; JEONG, N.-H.; LIBRESCU, L.

2000-10-01

A number of issues related to the modelling, vibration and stability of anisotropic pretwisted beams rotating at constant angular speed about the longitudinal body-axis fixed in the inertial space are investigated. The analysis is carried out in the framework of a refined theory of thin-walled anisotropic composite beams featuring bending-bending elastic coupling, and encompassing a number of non-classical features such as transverse-shear, anisotropy and pretwist. Special attention is paid to the effect of the spinning speed, pretwist angle, axial compressive load and symmetry/non-symmetry of the beam cross-section on natural frequencies and instability of the structural system. Numerical illustrations highlighting their implication on vibration and stability are displayed and pertinent conclusions are outlined.

Some problems of the solar wind interaction with Venus

NASA Astrophysics Data System (ADS)

Breus, T. K.; Krymskii, A. M.

1987-09-01

The aim of this paper is to analyze the effect of solar wind mass-loading due to hot-oxygen Venus corona photoionization on the plasma flow parameters in the nose part of the magnetosheath and the flow stability, taking into consideration the axial symmetry of the flow. The analysis has shown that the mass-loading effect increases the distance between the shock front and the ionopause and reduces the maximum magnetic field strength in the magnetic barrier in the vicinity of the stagnation region of the ionopause. The axial symmetry of the stream stabilizes the ionopause disturbances in the nose part. For shorter wavelengths the instability problem should be investigated numerically and should account for the stabilizing effect of the finite Larmor ion radius.

Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses.

PubMed

Yang, Wengui; Yu, Wenwu; Cao, Jinde; Alsaadi, Fuad E; Hayat, Tasawar

2018-02-01

This paper investigates the stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg bidirectional associative memory (BAM) neural networks with mixed delays (asynchronous time delays and continuously distributed delays) and impulses. By applying the inequality analysis technique, homeomorphism theory and some suitable Lyapunov-Krasovskii functionals, some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established. Furthermore, we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution, differential inclusion theory and control theory. In addition, some examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stability analysis for uncertain switched neural networks with time-varying delay.

PubMed

Shen, Wenwen; Zeng, Zhigang; Wang, Leimin

2016-11-01

In this paper, stability for a class of uncertain switched neural networks with time-varying delay is investigated. By exploring the mode-dependent properties of each subsystem, all the subsystems are categorized into stable and unstable ones. Based on Lyapunov-like function method and average dwell time technique, some delay-dependent sufficient conditions are derived to guarantee the exponential stability of considered uncertain switched neural networks. Compared with general results, our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being stable, thus getting less conservative criteria. Finally, two numerical examples are provided to show the validity and the advantages of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Aeolus high energy UV Laser wavelength measurement and frequency stability analysis

NASA Astrophysics Data System (ADS)

Mondin, Linda; Bravetti, Paolo

2017-11-01

The Aeolus mission is part of ESA's Earth Explorer program. The goal of the mission is to determine the first global wind data set in near real time to improve numerical weather prediction models. The only instrument on board Aeolus, Aladin, is a backscatter wind LIDAR in the ultraviolet (UV) frequency domain. Aeolus is a frequency limited mission, inasmuch as it relies on the measure of the backscattered signal frequency shift in order to deduce the wind velocity. As such the frequency stability of the LIDAR laser source is a key parameter for this mission. In the following, the characterization of the laser frequency stability, reproducibility and agility in vacuum shall be reported and compared to the mission requirements.

Prediction of dynamic and aerodynamic characteristics of the centrifugal fan with forward curved blades

NASA Astrophysics Data System (ADS)

Polanský, Jiří; Kalmár, László; Gášpár, Roman

2013-12-01

The main aim of this paper is determine the centrifugal fan with forward curved blades aerodynamic characteristics based on numerical modeling. Three variants of geometry were investigated. The first, basic "A" variant contains 12 blades. The geometry of second "B" variant contains 12 blades and 12 semi-blades with optimal length [1]. The third, control variant "C" contains 24 blades without semi-blades. Numerical calculations were performed by CFD Ansys. Another aim of this paper is to compare results of the numerical simulation with results of approximate numerical procedure. Applied approximate numerical procedure [2] is designated to determine characteristics of the turbulent flow in the bladed space of a centrifugal-flow fan impeller. This numerical method is an extension of the hydro-dynamical cascade theory for incompressible and inviscid fluid flow. Paper also partially compares results from the numerical simulation and results from the experimental investigation. Acoustic phenomena observed during experiment, during numerical simulation manifested as deterioration of the calculation stability, residuals oscillation and thus also as a flow field oscillation. Pressure pulsations are evaluated by using frequency analysis for each variant and working condition.

Soliton and kink jams in traffic flow with open boundaries.

PubMed

Muramatsu, M; Nagatani, T

1999-07-01

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.

Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1992-01-01

The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.

Nuclear-coupled thermal-hydraulic stability analysis of boiling water reactors

NASA Astrophysics Data System (ADS)

Karve, Atul A.

We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model we developed from: the space-time modal neutron kinetics equations based on spatial omega-modes, the equations for two-phase flow in parallel boiling channels, the fuel rod heat conduction equations, and a simple model for the recirculation loop. The model is represented as a dynamical system comprised of time-dependent nonlinear ordinary differential equations, and it is studied using stability analysis, modern bifurcation theory, and numerical simulations. We first determine the stability boundary (SB) in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value and then transform the SB to the practical power-flow map. Using this SB, we show that the normal operating point at 100% power is very stable, stability of points on the 100% rod line decreases as the flow rate is reduced, and that points are least stable in the low-flow/high-power region. We also determine the SB when the modal kinetics is replaced by simple point reactor kinetics and show that the first harmonic mode has no significant effect on the SB. Later we carry out the relevant numerical simulations where we first show that the Hopf bifurcation, that occurs as a parameter is varied across the SB is subcritical, and that, in the important low-flow/high-power region, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line. Hence, a point on the 100% rod line in the low-flow/high-power region, although stable, may nevertheless be a point at which a BWR should not be operated. Numerical simulations are then done to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is determined that the NRC requirement of DR < 0.75-0.8 is not rigorously satisfied in the low-flow/high-power region and hence these points should be avoided during normal startup and shutdown operations. The frequency of oscillation is shown to decrease as the flow rate is reduced and the frequency of 0.5Hz observed in the low-flow/high-power region is consistent with those observed during actual instability incidents. Additional numerical simulations show that in the low-flow/high-power region, for the same initial conditions, the use of point kinetics leads to damped oscillations, whereas the model that includes the modal kinetics equations results in growing nonlinear oscillations. Thus, we show that side-by-side out-of-phase growing power oscillations result due to the very important first harmonic mode effect and that the use of point kinetics, which fails to predict these growing oscillations, leads to dramatically nonconservative results. Finally, the effect of a simple recirculation loop model that we develop is studied by carrying out additional stability analyses and additional numerical simulations. It is shown that the loop has a stabilizing effect on certain points on the 100% rod line for time delays equal to integer multiples of the natural period of oscillation, whereas it has a destabilizing effect for half-integer multiples. However, for more practical time delays, it is determined that the overall effect generally is destabilizing.

A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks.

PubMed

Faydasicok, Ozlem; Arik, Sabri

2013-08-01

The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition. Copyright © 2013 Elsevier Ltd. All rights reserved.

Numerical FEM modeling in dental implantology

NASA Astrophysics Data System (ADS)

Roateşi, Iulia; Roateşi, Simona

2016-06-01

This paper is devoted to a numerical approach of the stress and displacement calculation of a system made up of dental implant, ceramic crown and surrounding bone. This is the simulation of a clinical situation involving both biological - the bone tissue, and non-biological - the implant and the crown, materials. On the other hand this problem deals with quite fine technical structure details - the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. The authors proposed a three-dimensional numerical model to assess the biomechanical behaviour of this complex structure in order to evaluate its stability by determining the risk zones. A comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained.

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

NASA Astrophysics Data System (ADS)

Sun, Y.; Taira, K.; Cattafesta, L. N.; Ukeiley, L. S.

2017-12-01

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of L/D=6 are analyzed at a free-stream Mach number of M_∞ =0.6 and depth-based Reynolds number of Re_D=502. In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of β =0. To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of W/D=1 and 2. We find that the 2D wake mode is not present in the 3D cavity flow with W/D=2, in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of λ /D=0.5{-}2.0 to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.

On adaptive modified projective synchronization of a supply chain management system

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2017-12-01

In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Robust rotation of rotor in a thermally driven nanomotor

PubMed Central

Cai, Kun; Yu, Jingzhou; Shi, Jiao; Qin, Qing-Hua

2017-01-01

In the fabrication of a thermally driven rotary nanomotor with the dimension of a few nanometers, fabrication and control precision may have great influence on rotor’s stability of rotational frequency (SRF). To investigate effects of uncertainty of some major factors including temperature, tube length, axial distance between tubes, diameter of tubes and the inward radial deviation (IRD) of atoms in stators on the frequency’s stability, theoretical analysis integrating with numerical experiments are carried out. From the results obtained via molecular dynamics simulation, some key points are illustrated for future fabrication of the thermal driven rotary nanomotor. PMID:28393898

Rock Slope Stability Evaluation in a Steep-Walled Canyon: Application to Elevator Construction in the Yunlong River Valley, Enshi, China

NASA Astrophysics Data System (ADS)

Xiao, Lili; Chai, Bo; Yin, Kunlong

2015-09-01

A passenger elevator is to be built on a nearly vertical slope in the National Geological Park in Enshi, Hubei province, China. Three steps comprise the construction: excavating the slope toe for the elevator platform, building the elevator on the platform, and affixing the elevator to the slope using anchors. To evaluate the rock slope stability in the elevator area and the safety of the elevator construction, we applied three techniques: qualitative analysis, formula calculation, and numerical simulation methods, based on field investigation and parameter selection, and considering both wet and dry conditions, pre- and post-construction. Qualitative stability factors for sliding and falling were calculated using the limit equilibrium method; the results show that the slope as a whole is stable, with a few unstable blocks, notably block BT1. Formula-based stability factors were calculated for four sections on block BT1, revealing the following: anchors will decrease the stability of certain rock pieces; the lowest average stability factor after anchoring will be K f = 1.36 in wet conditions; block BT1 should be reinforced during elevator construction, up to a first-class slope stability factor of K f = 1.40; and the slope as a whole is stable. Numerical simulation using FLAC3D indicated that the stress distribution will reach equilibrium for all steps before and after construction, and that the factor of safety (FOS) is within the general slope safety range (FOS > 1.05). We suggest that unstable pieces in block BT1 be reinforced during construction to a first-class slope safety range (FOS > 1.3), and that deformation monitoring on the slope surface be implemented.

Interface behavior of a multi-layer fluid configuration subject to acceleration in a microgravity environment, supplement 1. M.S. Thesis

NASA Technical Reports Server (NTRS)

Lyell, M. J.; Roh, Michael

1991-01-01

With the increasing opportunities for research in a microgravity environment, there arises a need for understanding fluid mechanics under such conditions. In particular, a number of material processing configurations involve fluid-fluid interfaces which may experience instabilities in the presence of external forcing. In a microgravity environment, these accelerations may be periodic or impulse-type in nature. This research investigates the behavior of a multi-layer idealized fluid configuration which is infinite in extent. The analysis is linear, and each fluid region is considered inviscid, incompressible, and immiscible. An initial parametric study of confiquration stability in the presence of a constant acceleration field is performed. The zero mean gravity limit case serves as the base state for the subsequent time-dependent forcing cases. A stability analysis of the multi-layer fluid system in the presence of periodic forcing is investigated. Floquet theory is utilized. A parameter study is performed, and regions of stability are identified. For the impulse-type forcing case, asymptotic stability is established for the configuration. Using numerical integration, the time response of the interfaces is determined.

An Aeroelastic Perspective of Floating Offshore Wind Turbine Wake Formation and Instability

NASA Astrophysics Data System (ADS)

Rodriguez, Steven N.; Jaworski, Justin W.

2015-11-01

The wake formation and wake stability of floating offshore wind turbines are investigated from an aeroelastic perspective. The aeroelastic model is composed of the Sebastian-Lackner free-vortex wake aerodynamic model coupled to the nonlinear Hodges-Dowell beam equations, which are extended to include the effects of blade profile asymmetry, higher-order torsional effects, and kinetic energy components associated with periodic rigid-body motions of floating platforms. Rigid-body platform motions are also assigned to the aerodynamic model as varying inflow conditions to emulate operational rotor-wake interactions. Careful attention is given to the wake formation within operational states where the ratio of inflow velocity to induced velocity is over 50%. These states are most susceptible to aerodynamic instabilities, and provide a range of states about which a wake stability analysis can be performed. In addition, the stability analysis used for the numerical framework is implemented into a standalone free-vortex wake aerodynamic model. Both aeroelastic and standalone aerodynamic results are compared to evaluate the level of impact that flexible blades have on the wake formation and wake stability.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Tianfeng

The goal of the proposed research is to create computational flame diagnostics (CFLD) that are rigorous numerical algorithms for systematic detection of critical flame features, such as ignition, extinction, and premixed and non-premixed flamelets, and to understand the underlying physicochemical processes controlling limit flame phenomena, flame stabilization, turbulence-chemistry interactions and pollutant emissions etc. The goal has been accomplished through an integrated effort on mechanism reduction, direct numerical simulations (DNS) of flames at engine conditions and a variety of turbulent flames with transport fuels, computational diagnostics, turbulence modeling, and DNS data mining and data reduction. The computational diagnostics are primarily basedmore » on the chemical explosive mode analysis (CEMA) and a recently developed bifurcation analysis using datasets from first-principle simulations of 0-D reactors, 1-D laminar flames, and 2-D and 3-D DNS (collaboration with J.H. Chen and S. Som at Argonne, and C.S. Yoo at UNIST). Non-stiff reduced mechanisms for transportation fuels amenable for 3-D DNS are developed through graph-based methods and timescale analysis. The flame structures, stabilization mechanisms, local ignition and extinction etc., and the rate controlling chemical processes are unambiguously identified through CFLD. CEMA is further employed to segment complex turbulent flames based on the critical flame features, such as premixed reaction fronts, and to enable zone-adaptive turbulent combustion modeling.« less

Absolute and convective instabilities of a film flow down a vertical fiber subjected to a radial electric field

NASA Astrophysics Data System (ADS)

Liu, Rong; Chen, Xue; Ding, Zijing

2018-01-01

We consider the motion of a gravity-driven flow down a vertical fiber subjected to a radial electric field. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the Maxwell stress at the interface. A spatiotemporal stability analysis is performed to investigate the effect of electric field on the absolute-convective instability (AI-CI) characteristics. We performed a numerical simulation on the nonlinear evolution of the film to examine the transition from CI to AI regime. The numerical results are in excellent agreement with the spatiotemporal stability analysis. The blowup behavior of nonlinear simulation predicts the formation of touchdown singularity of the interface due to the effect of electric field. We try to connect the blowup behavior with the AI-CI characteristics. It is found that the singularities mainly occur in the AI regime. The results indicate that the film may have a tendency to form very sharp tips due to the enhancement of the absolute instability induced by the electric field. We perform a theoretical analysis to study the behaviors of the singularities. The results show that there exists a self-similarity between the temporal and spatial distances from the singularities.

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

Modeling the effects of inflammation in bone fracture healing

NASA Astrophysics Data System (ADS)

Kojouharov, H. V.; Trejo, I.; Chen-Charpentier, B. M.

2017-10-01

A new mathematical model is presented to study the early inflammatory effects in bone healing. It consists of a system of nonlinear ordinary differential equations that represents the interactions among macrophages, mesenchymal stem cells, and osteoblasts. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. A set of numerical simulations is performed to support the theoretical results. The model is also used to numerically monitor the evolution of a broken bone for different types of fractures and to explore possible treatments to accelerate bone healing by administrating anti-inflammatory drugs.

Calculation of the aerodynamic loading of swept and unswept flexible wings of arbitrary stiffness

NASA Technical Reports Server (NTRS)

Diederich, Franklin W

1950-01-01

A method is presented for calculating the aerodynamic loading, the divergence speed, and certain stability derivatives of swept and unswept wings and tail surfaces of arbitrary stiffness. Provision is made for using either stiffness curves and root rotation constants or structural influence coefficients in the analysis. Computing forms, tables of numerical constants required in the analysis, and an illustrative example are included to facilitate calculations by means of the method.

Stabilization and analytical tuning rule of double-loop control scheme for unstable dead-time process

NASA Astrophysics Data System (ADS)

Ugon, B.; Nandong, J.; Zang, Z.

2017-06-01

The presence of unstable dead-time systems in process plants often leads to a daunting challenge in the design of standard PID controllers, which are not only intended to provide close-loop stability but also to give good performance-robustness overall. In this paper, we conduct stability analysis on a double-loop control scheme based on the Routh-Hurwitz stability criteria. We propose to use this unstable double-loop control scheme which employs two P/PID controllers to control first-order or second-order unstable dead-time processes typically found in process industries. Based on the Routh-Hurwitz stability necessary and sufficient criteria, we establish several stability regions which enclose within them the P/PID parameter values that guarantee close-loop stability of the double-loop control scheme. A systematic tuning rule is developed for the purpose of obtaining the optimal P/PID parameter values within the established regions. The effectiveness of the proposed tuning rule is demonstrated using several numerical examples and the result are compared with some well-established tuning methods reported in the literature.

A Dissipative Systems Theory for FDTD With Application to Stability Analysis and Subgridding

NASA Astrophysics Data System (ADS)

Bekmambetova, Fadime; Zhang, Xinyue; Triverio, Piero

2017-02-01

This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the magnetic and electric fields on the boundary as inputs and outputs. Suitable expressions for the energy stored in the region and the energy absorbed from the boundaries are introduced, and used to show that the FDTD system is dissipative under a generalized Courant-Friedrichs-Lewy condition. Based on the concept of dissipation, a powerful theoretical framework to investigate the stability of FDTD methods is devised. The new method makes FDTD stability proofs simpler, more intuitive, and modular. Stability conditions can indeed be given on the individual components (e.g. boundary conditions, meshes, embedded models) instead of the whole coupled setup. As an example of application, we derive a new subgridding method with material traverse, arbitrary grid refinement, and guaranteed stability. The method is easy to implement and has a straightforward stability proof. Numerical results confirm its stability, low reflections, and ability to handle material traverse.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

An optimal modeling of multidimensional wave digital filtering network for free vibration analysis of symmetrically laminated composite FSDT plates

NASA Astrophysics Data System (ADS)

Tseng, Chien-Hsun

2015-02-01

The technique of multidimensional wave digital filtering (MDWDF) that builds on traveling wave formulation of lumped electrical elements, is successfully implemented on the study of dynamic responses of symmetrically laminated composite plate based on the first order shear deformation theory. The philosophy applied for the first time in this laminate mechanics relies on integration of certain principles involving modeling and simulation, circuit theory, and MD digital signal processing to provide a great variety of outstanding features. Especially benefited by the conservation of passivity gives rise to a nonlinear programming problem (NLP) for the issue of numerical stability of a MD discrete system. Adopting the augmented Lagrangian genetic algorithm, an effective optimization technique for rapidly achieving solution spaces of NLP models, numerical stability of the MDWDF network is well received at all time by the satisfaction of the Courant-Friedrichs-Levy stability criterion with the least restriction. In particular, optimum of the NLP has led to the optimality of the network in terms of effectively and accurately predicting the desired fundamental frequency, and thus to give an insight into the robustness of the network by looking at the distribution of system energies. To further explore the application of the optimum network, more numerical examples are engaged in efforts to achieve a qualitative understanding of the behavior of the laminar system. These are carried out by investigating various effects based on different stacking sequences, stiffness and span-to-thickness ratios, mode shapes and boundary conditions. Results are scrupulously validated by cross referencing with early published works, which show that the present method is in excellent agreement with other numerical and analytical methods.

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

NASA Astrophysics Data System (ADS)

Grishin, Evgeni; Perets, Hagai B.; Zenati, Yossef; Michaely, Erez

2017-04-01

A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (˜120°), beyond which the agreement is marginal. At such high inclinations, the stability radius is larger, the ratio between the outer and inner periods becomes comparable and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non-co-planar systems, our results have direct implications for any triple systems and, in particular, binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.

Materials processing in a centrifuge - Numerical modeling of macrogravity effects

NASA Technical Reports Server (NTRS)

Ramachandran, N.; Downey, J. P.; Jones, J. C.; Curreri, P. A.

1992-01-01

The fluid mechanics associated with crystal growth processes on a centrifuge is investigated. A simple scaling analysis is used to examine the relative magnitudes of the forces acting on the system and good agreement is obtained with previous studies. A two-dimensional model of crystal growth on a centrifuge is proposed and calculations are undertaken to help in understanding the fundamental transport processes within the crystal growth cell. Results from three-dimensional calculations of actual centrifuge-based crystal growth systems are presented both for the thermodynamically stable and unstable configurations. The calculations show the existence of flow bifurcations in certain configurations but not in all instances. The numerical simulations also show that the centrifugal force is the dominant stabilizing force on fluid convection in the stable configuration. The stabilizing influence of the Coriolis force is found to be only secondary in nature. No significant impact of gravity gradient is found in the calculations. Simulations of unstable configurations show that the Coriolis force has a stabilizing influence on fluid motion by delaying the onset of unsteady convection. Detailed flow and thermal field characteristics are presented for all the different cases that are simulated.

The role of post-failure brittleness of soft rocks in the assessment of stability of intact masses: FDEM technique applications to ideal problems

NASA Astrophysics Data System (ADS)

Lollino, Piernicola; Andriani, Gioacchino Francesco; Fazio, Nunzio Luciano; Perrotti, Michele

2016-04-01

Strain-softening under low confinement stress, i.e. the drop of strength that occurs in the post-failure stage, represents a key factor of the stress-strain behavior of rocks. However, this feature of the rock behavior is generally underestimated or even neglected in the assessment of boundary value problems of intact soft rock masses. This is typically the case when the stability of intact rock masses is treated by means of limit equilibrium or finite element analyses, for which rigid-plastic or elastic perfectly-plastic constitutive models, generally implementing peak strength conditions of the rock, are respectively used. In fact, the aforementioned numerical techniques are characterized by intrinsic limitations that do not allow to account for material brittleness, either for the method assumptions or due to numerical stability problems, as for the case of the finite element method, unless sophisticated regularization techniques are implemented. However, for those problems that concern the stability of intact soft rock masses at low stress levels, as for example the stability of shallow underground caves or that of rock slopes, the brittle stress-strain response of rock in the post-failure stage cannot be disregarded due to the risk of overestimation of the stability factor. This work is aimed at highlighting the role of post-peak brittleness of soft rocks in the analysis of specific ideal problems by means of the use of a hybrid finite-discrete element technique (FDEM) that allows for the simulation of the rock stress-strain brittle behavior in a proper way. In particular, the stability of two ideal cases, represented by a shallow underground rectangular cave and a vertical cliff, has been analyzed by implementing a post-peak brittle behavior of the rock and the comparison with a non-brittle response of the rock mass is also explored. To this purpose, the mechanical behavior of a soft calcarenite belonging to the Calcarenite di Gravina formation, extensively outcropping in Puglia (Southern Italy), and the corresponding features of the post-peak behavior as measured in the laboratory, have been used as a reference in this work, as well as the typical geometrical features of underground cavities and rock cliffs, as observed in Southern Italy, have been adopted for the simulations. The numerical results indicate the strong impact for the assessment of stability when rock post-peak brittleness is accounted for, if compared with perfectly plastic assumptions, and the need for adopting numerical techniques, as the FDEM approach, to take properly into account this important aspect of the rock behavior is highlighted.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation.

PubMed

Lucas, Maxime; Newman, Julian; Stefanovska, Aneta

2018-04-01

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

NASA Astrophysics Data System (ADS)

Lucas, Maxime; Newman, Julian; Stefanovska, Aneta

2018-04-01

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canavan, G.H.

Optimizations of missile allocation based on linearized exchange equations produce accurate allocations, but the limits of validity of the linearization are not known. These limits are explored in the context of the upload of weapons by one side to initially small, equal forces of vulnerable and survivable weapons. The analysis compares analytic and numerical optimizations and stability induces based on aggregated interactions of the two missile forces, the first and second strikes they could deliver, and they resulting costs. This note discusses the costs and stability indices induced by unilateral uploading of weapons to an initially symmetrical low force configuration.more » These limits are quantified for forces with a few hundred missiles by comparing analytic and numerical optimizations of first strike costs. For forces of 100 vulnerable and 100 survivable missiles on each side, the analytic optimization agrees closely with the numerical solution. For 200 vulnerable and 200 survivable missiles on each side, the analytic optimization agrees with the induces to within about 10%, but disagrees with the allocation of the side with more weapons by about 50%. The disagreement comes from the interaction of the possession of more weapons with the shift of allocation from missiles to value that they induce.« less

Numerical Analysis of Ginzburg-Landau Models for Superconductivity.

NASA Astrophysics Data System (ADS)

Coskun, Erhan

Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.

Numerical Simulation And Experimental Investigation Of The Lift-Off And Blowout Of Enclosed Laminar Flames

NASA Technical Reports Server (NTRS)

Venuturmilli, Rajasekhar; Zhang, Yong; Chen, Lea-Der

2003-01-01

Enclosed flames are found in many industrial applications such as power plants, gas-turbine combustors and jet engine afterburners. A better understanding of the burner stability limits can lead to development of combustion systems that extend the lean and rich limits of combustor operations. This paper reports a fundamental study of the stability limits of co-flow laminar jet diffusion flames. A numerical study was conducted that used an adaptive mesh refinement scheme in the calculation. Experiments were conducted in two test rigs with two different fuels and diluted with three inert species. The numerical stability limits were compared with microgravity experimental data. Additional normal-gravity experimental results were also presented.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Stability and synchronization analysis of inertial memristive neural networks with time delays.

PubMed

Rakkiyappan, R; Premalatha, S; Chandrasekar, A; Cao, Jinde

2016-10-01

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

NASA Astrophysics Data System (ADS)

Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto

2016-05-01

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

On Thermal Instability of Kuvshiniski Fluid with Suspended Particles Saturated in a Porous Medium in the Presence of a Magnetic Field June 13, 2017

NASA Astrophysics Data System (ADS)

Singh, M.

2017-12-01

The thermal instability of a Kuvshiniski viscoelastic fluid is considered to include the effects of a uniform horizontal magnetic field, suspended particles saturated in a porous medium. The analysis is carried out within the framework of the linear stability theory and normal mode technique. For the case of stationary convection, the Kuvshiniski viscoelastic fluid behaves like a Newtonian fluid and the magnetic field has a stabilizing effect, whereas medium permeability and suspended particles are found to have a destabilizing effect on the system, oscillatory modes are introduced in the system, in the absence of these the principle of exchange of stabilities is valid. Graphs in each case have been plotted by giving numerical values to the parameters, depicting the stability characteristics. Sufficient conditions for the avoidance of overstability are also obtained.

Active vibration suppression of helicopter horizontal stabilizers

NASA Astrophysics Data System (ADS)

Cinquemani, Simone; Cazzulani, Gabriele; Resta, Ferruccio

2017-04-01

Helicopters are among the most complex machines ever made. While ensuring high performance from the aeronautical point of view, they are not very comfortable due to vibration mainly created by the main rotor and by the interaction with the surrounding air. One of the most solicited structural elements of the vehicle are the horizontal stabilizers. These elements are particularly stressed because of their composite structure which, while guaranteeing lightness and strength, is characterized by a low damping. This work makes a preliminary analysis on the dynamics of the structure and proposes different solutions to actively suppress vibrations. Among them, the best in terms of the relationship between performance and weight / complexity of the system is that based on inertial actuators mounted on the inside of the horizontal stabilizers. The work addresses the issue of the design of the device and its use in the stabilizer from both the numerical and the experimental points of view.

Dynamics of an advertising competition model with sales promotion

NASA Astrophysics Data System (ADS)

Jiang, Hui; Feng, Zhaosheng; Jiang, Guirong

2017-01-01

In this paper, an advertising competition model with sales promotion is constructed and investigated. Conditions of the existence and stability of period-T solutions are obtained by means of the discrete map. Flip bifurcation is analyzed by using the center manifold theory and three sales promotion strategies are discussed. Example and numerical simulations are illustrated which agree well with our theoretical analysis.

Vibrations in a moving flexible robot arm

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Wei, Jin-Duo

1987-01-01

The vibration in a flexible robot arm modeled by a moving slender prismatic beam is considered. It is found that the extending and contracting motions have destabilizing and stabilizing effects on the vibratory motions, respectively. The vibration analysis is based on a Galerkin approximation with time-dependent basis functions. Typical numerical results are presented to illustrate the qualitative features of vibrations.

The dynamics and control of large flexible space structures X, part 1

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R.; Li, Feiyue; Diarra, Cheick M.

1987-01-01

The effect of delay in the control system input on the stability of a continuously acting controller which is designed without considering the delay is studied. The stability analysis of a second order plant is studied analytically and verified numerically. For this example it is found that the system becomes unstable for a delay which is equivalent to only 16 percent of its natural period of motion. It is also observed that even a small amount of natural damping in the system can increase the amount of delay that can be tolerated before the onset of instability. The delay problem is formulated in the discrete time domain and an analysis procedure suggested. The maximum principle from optimal control theory is applied to minimize the time required for the slewing of a general rigid spacecraft. The slewing motion need not be restricted to a single axis maneuver. The minimum slewing time is calculated based on a quasi-linearization algorithm for the resulting two point boundary value problem. Numerical examples based on the rigidized in-orbit model of the SCOLE also include the more general reflector line-of-sight slewing maneuvers.

Analytical development of disturbed matrix eigenvalue problem applied to mixed convection stability analysis in Darcy media

NASA Astrophysics Data System (ADS)

Hamed, Haikel Ben; Bennacer, Rachid

2008-08-01

This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh-Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).

Ant Colony Optimization Analysis on Overall Stability of High Arch Dam Basis of Field Monitoring

PubMed Central

Liu, Xiaoli; Chen, Hong-Xin; Kim, Jinxie

2014-01-01

A dam ant colony optimization (D-ACO) analysis of the overall stability of high arch dams on complicated foundations is presented in this paper. A modified ant colony optimization (ACO) model is proposed for obtaining dam concrete and rock mechanical parameters. A typical dam parameter feedback problem is proposed for nonlinear back-analysis numerical model based on field monitoring deformation and ACO. The basic principle of the proposed model is the establishment of the objective function of optimizing real concrete and rock mechanical parameter. The feedback analysis is then implemented with a modified ant colony algorithm. The algorithm performance is satisfactory, and the accuracy is verified. The m groups of feedback parameters, used to run a nonlinear FEM code, and the displacement and stress distribution are discussed. A feedback analysis of the deformation of the Lijiaxia arch dam and based on the modified ant colony optimization method is also conducted. By considering various material parameters obtained using different analysis methods, comparative analyses were conducted on dam displacements, stress distribution characteristics, and overall dam stability. The comparison results show that the proposal model can effectively solve for feedback multiple parameters of dam concrete and rock material and basically satisfy assessment requirements for geotechnical structural engineering discipline. PMID:25025089

Stability switches of arbitrary high-order consensus in multiagent networks with time delays.

PubMed

Yang, Bo

2013-01-01

High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Numerical Boundary Condition Procedures

NASA Technical Reports Server (NTRS)

1981-01-01

Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.

Recursive regularization step for high-order lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

2017-09-01

A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear

NASA Astrophysics Data System (ADS)

Niu, Ben; Zhang, Jiaming; Wei, Junjie

2018-05-01

In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the stability boundary of the incoherent state is derived in multiple-parameter space. Moreover, very rich dynamical behavior such as stability switches inducing synchronization switches can occur in this equation. With the loss of stability, Hopf bifurcating coherent states arise, and the criticality of Hopf bifurcations is determined by applying the normal form theory and the center manifold theorem. On one hand, theoretical analysis indicates that the width of shear distribution and time delay can both eliminate the synchronization then lead the Kuramoto model to incoherence. On the other, time delay can induce several coexisting coherent states. Finally, some numerical simulations are given to support the obtained results where several bifurcation diagrams are drawn, and the effect of time delay and shear is discussed.

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

NASA Technical Reports Server (NTRS)

Antar, B. N.; Fowlis, W. W.

1985-01-01

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber.

Effect of turbulent eddy viscosity on the unstable surface mode above an acoustic liner

NASA Astrophysics Data System (ADS)

Marx, David; Aurégan, Yves

2013-07-01

Lined ducts are used to reduce noise radiation from ducts in turbofan engines. In certain conditions they may sustain hydrodynamic instabilities. A local linear stability analysis of the flow in a 2D lined channel is performed using a numerical integration of the governing equations. Several model equations are used, one of them taking into account turbulent eddy viscosity, and a realistic turbulent mean flow profile is used that vanishes at the wall. The stability analysis results are compared to published experimental results. Both the model and the experiments show the existence of an unstable mode, and the importance of taking into account eddy viscosity in the model is shown. When this is done, quantities such as the growth rate and the velocity eigenfunctions are shown to agree correctly.

Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability

NASA Astrophysics Data System (ADS)

Robinett, Rush D.; Wilson, David G.

2009-10-01

This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.

Stability of the discretization of the electron avalanche phenomenon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Villa, Andrea, E-mail: andrea.villa@rse-web.it; Barbieri, Luca, E-mail: luca.barbieri@rse-web.it; Gondola, Marco, E-mail: marco.gondola@rse-web.it

2015-09-01

The numerical simulation of the discharge inception is an active field of applied physics with many industrial applications. In this work we focus on the drift-reaction equation that describes the electron avalanche. This phenomenon is one of the basic building blocks of the streamer model. The main difficulty of the electron avalanche equation lies in the fact that the reaction term is positive when a high electric field is applied. It leads to exponentially growing solutions and this has a major impact on the behavior of numerical schemes. We analyze the stability of a reference finite volume scheme applied tomore » this latter problem. The stability of the method may impose a strict mesh spacing, therefore a proper stabilized scheme, which is stable whatever spacing is used, has been developed. The convergence of the scheme is treated as well as some numerical experiments.« less

Dynamic stability analysis for capillary channel flow: One-dimensional and three-dimensional computations and the equivalent steady state technique

NASA Astrophysics Data System (ADS)

Grah, Aleksander; Dreyer, Michael E.

2010-01-01

Spacecraft technology provides a series of applications for capillary channel flow. It can serve as a reliable means for positioning and transport of liquids under low gravity conditions. Basically, capillary channels provide liquid paths with one or more free surfaces. A problem may be flow instabilities leading to a collapse of the liquid surfaces. A result is undesired gas ingestion and a two phase flow which can in consequence cause several technical problems. The presented capillary channel consists of parallel plates with two free liquid surfaces. The flow rate is established by a pump at the channel outlet, creating a lower pressure within the channel. Owing to the pressure difference between the liquid phase and the ambient gas phase the free surfaces bend inwards and remain stable as long as they are able to resist the steady and unsteady pressure effects. For the numerical prediction of the flow stability two very different models are used. The one-dimensional unsteady model is mainly based on the Bernoulli equation, the continuity equation, and the Gauss-Laplace equation. For three-dimensional evaluations an open source computational fluid dynamics (CFD) tool is applied. For verifications the numerical results are compared with quasisteady and unsteady data of a sounding rocket experiment. Contrary to previous experiments this one results in a significantly longer observation sequence. Furthermore, the critical point of the steady flow instability could be approached by a quasisteady technique. As in previous experiments the comparison to the numerical model evaluation shows a very good agreement for the movement of the liquid surfaces and for the predicted flow instability. The theoretical prediction of the flow instability is related to the speed index, based on characteristic velocities of the capillary channel flow. Stable flow regimes are defined by stability criteria for steady and unsteady flow. The one-dimensional computation of the speed index is based on the technique of the equivalent steady system, which is published for the first time in the present paper. This approach assumes that for every unsteady state an equivalent steady state with a special boundary condition can be formulated. The equivalent steady state technique enables a reformulation of the equation system and an efficient and reliable speed index computation. Furthermore, the existence of the numerical singularity at the critical point of the steady flow instability, postulated in previous publication, is demonstrated in detail. The numerical singularity is related to the stability criterion for steady flow and represents the numerical consequence of the liquid surface collapse. The evaluation and generation of the pressure diagram is demonstrated in detail with a series of numerical dynamic flow studies. The stability diagram, based on one-dimensional computation, gives a detailed overview of the stable and instable flow regimes. This prediction is in good agreement with the experimentally observed critical flow conditions and results of three-dimensional CFD computations.

Dynamics Analysis of Anti-predator Model on Intermediate Predator With Ratio Dependent Functional Responses

NASA Astrophysics Data System (ADS)

Savitri, D.

2018-01-01

This articel discusses a predator prey model with anti-predator on intermediate predator using ratio dependent functional responses. Dynamical analysis performed on the model includes determination of equilibrium point, stability and simulation. Three kinds of equilibrium points have been discussed, namely the extinction of prey point, the extinction of intermediate predator point and the extinction of predator point are exists under certain conditions. It can be shown that the result of numerical simulations are in accordance with analitical results

Structural Analysis Computer Programs for Rigid Multicomponent Pavement Structures with Discontinuities--WESLIQID and WESLAYER. Report 1. Program Development and Numerical Presentations.

DTIC Science & Technology

1981-05-01

represented as a Winkler foundation. The program can treat any number of slabs connected by steel bars or other load trans- fer devices at the joints...dimensional finite element method. The inherent flexibility of such an approach permits the analysis of a rigid pavement with steel bars and stabilized...layers and provides an efficient tool for analyzing stress conditions at the joint. Unfor- tunately, such a procedure would require a tremendously

Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.

PubMed

Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong

2016-05-01

In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.

Detecting malicious chaotic signals in wireless sensor network

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Kumari, Sangeeta

2018-02-01

In this paper, an e-epidemic Susceptible-Infected-Vaccinated (SIV) model has been proposed to analyze the effect of node immunization and worms attacking dynamics in wireless sensor network. A modified nonlinear incidence rate with cyrtoid type functional response has been considered using sleep and active mode approach. Detailed stability analysis and the sufficient criteria for the persistence of the model system have been established. We also established different types of bifurcation analysis for different equilibria at different critical points of the control parameters. We performed a detailed Hopf bifurcation analysis and determine the direction and stability of the bifurcating periodic solutions using center manifold theorem. Numerical simulations are carried out to confirm the theoretical results. The impact of the control parameters on the dynamics of the model system has been investigated and malicious chaotic signals are detected. Finally, we have analyzed the effect of time delay on the dynamics of the model system.

Stability of the human respiratory control system. I. Analysis of a two-dimensional delay state-space model.

PubMed

Batzel, J J; Tran, H T

2000-07-01

A number of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing (including Cheyne-Stokes respiration and apneustic breathing) is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's [12]. The purpose of this paper is to study the stability characteristics of a feedback control system of five differential equations with delays in both the state and control variables presented by Khoo et al. [17] in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simplified mathematical model of two nonlinear state equations modeling arterial partial pressures of O2 and CO2 and a peripheral controller. Analysis was done on this model to illuminate the effect of delay on the stability. It shows that delay dependent stability is affected by the controller gain, compartmental volumes and the manner in which changes in the ventilation rate is produced (i.e., by deeper breathing or faster breathing). In addition, numerical simulations were performed to validate analytical results. Part II extends the model in Part I to include both peripheral and central controllers. This, however, necessitates the introduction of a third state equation modeling CO2 levels in the brain. In addition to analytical studies on delay dependent stability, it shows that the decreased cardiac output (and hence increased delay) resulting from the congestive heart condition can induce instability at certain control gain levels. These analytical results were also confirmed by numerical simulations.

Stability of the human respiratory control system. II. Analysis of a three-dimensional delay state-space model.

PubMed

Batzel, J J; Tran, H T

2000-07-01

A number of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing (including Cheyne-Stokes respiration and apneustic breathing) is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's [1]. The purpose of this paper is to study the stability characteristics of a feedback control system of five differential equations with delays in both the state and control variables presented by Khoo et al. [4] in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simplified mathematical model of two nonlinear state equations modeling arterial partial pressures of O2 and CO2 and a peripheral controller. Analysis was done on this model to illuminate the effect of delay on the stability. It shows that delay dependent stability is affected by the controller gain, compartmental volumes and the manner in which changes in the ventilation rate is produced (i.e., by deeper breathing or faster breathing). In addition, numerical simulations were performed to validate analytical results. Part II extends the model in Part I to include both peripheral and central controllers. This, however, necessitates the introduction of a third state equation modeling CO2 levels in the brain. In addition to analytical studies on delay dependent stability, it shows that the decreased cardiac output (and hence increased delay) resulting from the congestive heart condition can induce instability at certain control gain levels. These analytical results were also confirmed by numerical simulations.

Critical study of current situation of Vrănicioara tailing pond on Cavnicului Valley, risks and consequences

NASA Astrophysics Data System (ADS)

Bud, I.; Duma, S.; Gusat, D.; Pasca, I.; Bud, A.

2017-05-01

In northern Romania, there are numerous tailing ponds, resulting from mining activities that present significant environmental risks. Some of them, including Vrănicioara tailing pond, were the subject of technical projects for ecological rehabilitation. Vrănicioara pond is located on the right side of Cavnic Valley, downstream Cavnic town, about 4 kilometers far. It has about 500 m length and is located parallel to the road linking Baia Sprie and Cavnic localities. Chemical and physical stability of the tailing pond before rehabilitation interest the research, analysis and conclusions were published in several scientific meetings. In addition, close to the pond at less than 100 m, an open pit has developed, exploiting andesite by mining blast, increasing the risk of physical stability by continuous exposure to vibration. This activity currently continues, advancing towards the tailing pond body. The critical study addresses the current state of Vrănicioara Tailing Pond, analysis of some rehabilitation works done incorrectly, analysis of chemical stability that was not a priority during rehabilitation. Research intention is heading to water analysis confirming the existence of acid drainage that was not stopped or at least reduced. The scientific approach is based on the Technical Standards for Waste Deposits, in force in Romania, providing the rules to ensure physical and chemical stability.

Using phase locking for improving frequency stability and tunability of THz-band gyrotrons

NASA Astrophysics Data System (ADS)

Adilova, Asel B.; Gerasimova, Svetlana A.; Melnikova, Maria M.; Tyshkun, Alexandra V.; Rozhnev, Andrey G.; Ryskin, Nikita M.

2018-04-01

Medium-power (10-100 W) THz-band gyrotrons operating in a continuous-wave (CW) mode are of great importance for many applications such as NMR spectroscopy with dynamic nuclear polarization (DNP/NMR), plasma diagnostics, nondestructive inspection, stand-off detection of radioactive materials, biomedical applications, etc. For all these applications, high frequency stability and tunability within 1-2 GHz frequency range is typically required. Apart from different existing techniques for frequency stabilization, phase locking has recently attracted strong interest. In this paper, we present the results of theoretical analysis and numerical simulation for several phase locking techniques: (a) phase locking by injection of the external driving signal; (b) mutual phase locking of two coupled gyrotrons; and (c) selfinjection locking by a wave reflected from the remote load.

On the stability of equilibrium for a reformulated foreign trade model of three countries

NASA Astrophysics Data System (ADS)

Dassios, Ioannis K.; Kalogeropoulos, Grigoris

2014-06-01

In this paper, we study the stability of equilibrium for a foreign trade model consisting of three countries. As the gravity equation has been proven an excellent tool of analysis and adequately stable over time and space all over the world, we further enhance the problem to three masses. We use the basic Structure of Heckscher-Ohlin-Samuelson model. The national income equals consumption outlays plus investment plus exports minus imports. The proposed reformulation of the problem focus on two basic concepts: (1) the delay inherited in our economic variables and (2) the interaction effect along the three economies involved. Stability and stabilizability conditions are investigated while numerical examples provide further insight and better understanding. Finally, a generalization of the gravity equation is somehow obtained for the model.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Rui

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

DOE PAGES

Hu, Rui

2016-11-19

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

NASA Astrophysics Data System (ADS)

Pradipto; Purqon, Acep

2017-07-01

Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

NASA Astrophysics Data System (ADS)

Liu, Zhengguang; Li, Xiaoli

2018-05-01

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

A new numerical approximation of the fractal ordinary differential equation

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Dynamic strain aging and plastic instabilities

NASA Astrophysics Data System (ADS)

Mesarovic, Sinisa Dj.

1995-05-01

A constitutive model proposed by McCormick [(1988) Theory of flow localization due to dynamic strain ageing. Acta. Metall.36, 3061-3067] based on dislocation-solute interaction and describing dynamic strain aging behavior, is analyzed for the simple loading case of uniaxial tension. The model is rate dependent and includes a time-varying state variable, representing the local concentration of the impurity atoms at dislocations. Stability of the system and its post-instability behavior are considered. The methods used include analytical and numerical stability and bifurcation analysis with a numerical continuation technique. Yield point behavior and serrated yielding are found to result for well defined intervals of temperature and strain rate. Serrated yielding emerges as a branch of periodic solutions of the relaxation oscillation type, similar to frictional stick-slip. The distinction between the temporal and spatial (loss of homogeneity of strain) instability is emphasized. It is found that a critical machine stiffness exists above which a purely temporal instability cannot occur. The results are compared to the available experimental data.

H∞ memory feedback control with input limitation minimization for offshore jacket platform stabilization

NASA Astrophysics Data System (ADS)

Yang, Jia Sheng

2018-06-01

In this paper, we investigate a H∞ memory controller with input limitation minimization (HMCIM) for offshore jacket platforms stabilization. The main objective of this study is to reduce the control consumption as well as protect the actuator when satisfying the requirement of the system performance. First, we introduce a dynamic model of offshore platform with low order main modes based on mode reduction method in numerical analysis. Then, based on H∞ control theory and matrix inequality techniques, we develop a novel H∞ memory controller with input limitation. Furthermore, a non-convex optimization model to minimize input energy consumption is proposed. Since it is difficult to solve this non-convex optimization model by optimization algorithm, we use a relaxation method with matrix operations to transform this non-convex optimization model to be a convex optimization model. Thus, it could be solved by a standard convex optimization solver in MATLAB or CPLEX. Finally, several numerical examples are given to validate the proposed models and methods.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks

NASA Astrophysics Data System (ADS)

Wang, Xue-She; Mazzoleni, Michael J.; Mann, Brian P.

2018-03-01

This paper presents the results of an investigation on the dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. The full equation of motion for both rocking disks is derived from first principles. For unforced behavior, Lamb's method is used to derive the linear natural frequency of both disks, and harmonic balance is used to determine their amplitude-dependent rocking frequencies. A stability analysis then reveals that the equilibria and stability of the two disks are considerably different, as the semi-elliptical disk has a super-critical pitchfork bifurcation that enables it to exhibit bistable rocking behavior. Experimental studies were conducted to verify the trends. For vertically forced behavior, numerical investigations show the disk's responses to forward and reverse frequency sweeps. Three modes of periodicity were observed for the steady state behavior. Experiments were performed to verify the frequency responses and the presence of the three rocking modes. Comparisons between the experiments and numerical investigations show good agreement.

High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

NASA Astrophysics Data System (ADS)

He, Yang; Sun, Yajuan; Zhang, Ruili; Wang, Yulei; Liu, Jian; Qin, Hong

2016-09-01

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracy-enhancing processing technique, the explicit methods obtain high-order accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations.

A control problem for Burgers' equation with bounded input/output

NASA Technical Reports Server (NTRS)

Burns, John A.; Kang, Sungkwon

1990-01-01

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to show the theoretical results.

Study on Stability Analysis and Monitoring Technology of Deep Concave Open-Pit Mine Slope

NASA Astrophysics Data System (ADS)

Xue, Dinglong; Ren, Fenghua; Li, Yuan

2018-05-01

In this paper, using the FLAC3D software to establish the numerical model of the rock slope in the south of Washan stope and to compare and verify with the monitoring result, reference is made to the original engineering and hydrogeological data of Washan stope. The results show that the stability of the South slope is mainly affected by the dominant structural plane, and the potential slip surface and the dominant structure surface are the same. During the recovery period of -120m platform residual mine, the disturbance stress is increasing but the overall amplitude is small and the slope is relatively stable.

Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species.

PubMed

Meng, Xin-You; Qin, Ni-Ni; Huo, Hai-Feng

2018-12-01

In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

NASA Astrophysics Data System (ADS)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Stability analysis of host dynamics for hiv

NASA Astrophysics Data System (ADS)

Geetha, V.; Balamuralitharan, S.

2018-04-01

The phenomenon of disease modeling can be easily accomplished through mathematical framework. In this paper the transmission of disease in human is represented mathematically as a nonlinear system. We think about the components of the Human Immunodeficiency Virus (HIV) among the beginning periods of illness. Throughout this paper we have determined those logical representation of a three-compartmental HIV demonstrate for their stability evaluation. We tend to likewise explore the stimulating behavior of the model and acquire those Steady states for the disease-free and the endemic agreement. The framework can be evaluated by reproduction number R0. We additionally clarify the numerical recreation and their outcomes.

The importance of Thermo-Hydro-Mechanical couplings and microstructure to strain localization in 3D continua with application to seismic faults. Part II: Numerical implementation and post-bifurcation analysis

NASA Astrophysics Data System (ADS)

Rattez, Hadrien; Stefanou, Ioannis; Sulem, Jean; Veveakis, Manolis; Poulet, Thomas

2018-06-01

In this paper we study the phenomenon of localization of deformation in fault gouges during seismic slip. This process is of key importance to understand frictional heating and energy budget during an earthquake. A infinite layer of fault gouge is modeled as a Cosserat continuum taking into account Thermo-Hydro-Mechanical (THM) couplings. The theoretical aspects of the problem are presented in the companion paper (Rattez et al., 2017a), together with a linear stability analysis to determine the conditions of localization and estimate the shear band thickness. In this Part II of the study, we investigate the post-bifurcation evolution of the system by integrating numerically the full system of non-linear equations using the method of Finite Elements. The problem is formulated in the framework of Cosserat theory. It enables to introduce information about the microstructure of the material in the constitutive equations and to regularize the mathematical problem in the post-localization regime. We emphasize the influence of the size of the microstructure and of the softening law on the material response and the strain localization process. The weakening effect of pore fluid thermal pressurization induced by shear heating is examined and quantified. It enhances the weakening process and contributes to the narrowing of shear band thickness. Moreover, due to THM couplings an apparent rate-dependency is observed, even for rate-independent material behavior. Finally, comparisons show that when the perturbed field of shear deformation dominates, the estimation of the shear band thickness obtained from linear stability analysis differs from the one obtained from the finite element computations, demonstrating the importance of post-localization numerical simulations.

Comparison of eigenvectors for coupled seismo-electromagnetic layered-Earth modelling

NASA Astrophysics Data System (ADS)

Grobbe, N.; Slob, E. C.; Thorbecke, J. W.

2016-07-01

We study the accuracy and numerical stability of three eigenvector sets for modelling the coupled poroelastic and electromagnetic layered-Earth response. We use a known eigenvector set, its flux-normalized version and a newly derived flux-normalized set. The new set is chosen such that the system is properly uncoupled when the coupling between the poroelastic and electromagnetic fields vanishes. We carry out two different numerical stability tests: the first test focuses on the internal system, eigenvector and eigenvalue consistency; the second test investigates the stability and preciseness of the flux-normalized systems by looking at identity relations. We find that the known set shows the largest deviation for both tests, whereas the new set performs best. In two additional numerical modelling experiments, these numerical inaccuracies are shown to generate numerical noise levels comparable to small signals, such as signals coming from the important interface conversion responses, especially when the coupling coefficient is small. When coupling vanishes completely, the known set does not produce proper results. The new set produces numerically stable and accurate results in all situations. We therefore strongly recommend to use this newly derived set for future layered-Earth seismo-electromagnetic modelling experiments.

A numerical study of transition control by periodic suction-blowing

NASA Technical Reports Server (NTRS)

Biringen, Sedat

1987-01-01

The applicability of active control of transition by periodic suction-blowing is investigated via direct numerical simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that, for relatively small three dimensional amplitudes, a two dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the flow dynamics during transition.

An Accurate and Stable FFT-based Method for Pricing Options under Exp-Lévy Processes

NASA Astrophysics Data System (ADS)

Ding, Deng; Chong U, Sio

2010-05-01

An accurate and stable method for pricing European options in exp-Lévy models is presented. The main idea of this new method is combining the quadrature technique and the Carr-Madan Fast Fourier Transform methods. The theoretical analysis shows that the overall complexity of this new method is still O(N log N) with N grid points as the fast Fourier transform methods. Numerical experiments for different exp-Lévy processes also show that the numerical algorithm proposed by this new method has an accuracy and stability for the small strike prices K. That develops and improves the Carr-Madan method.

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

The dynamic behaviour of data-driven Δ-M and ΔΣ-M in sliding mode control

NASA Astrophysics Data System (ADS)

Almakhles, Dhafer; Swain, Akshya K.; Nasiri, Alireza

2017-11-01

In recent years, delta (Δ-M) and delta-sigma modulators (ΔΣ-M) are increasingly being used as efficient data converters due to numerous advantages they offer. This paper investigates various dynamical features of these modulators/systems (both in continuous and discrete time domain) and derives their stability conditions using the theory of sliding mode. The upper bound of the hitting time (step) has been estimated. The equivalent mode conditions, i.e. where the outputs of the modulators are equivalent to the inputs, are established. The results of the analysis are validated through simulations considering a numerical example.

The evolution and discharge of electric fields within a thunderstorm

NASA Technical Reports Server (NTRS)

Hager, William W.; Nisbet, John S.; Kasha, John R.

1989-01-01

An analysis of the present three-dimensional thunderstorm electrical model and its finite-difference approximations indicates unconditional stability for the discretization that results from the approximation of the spatial derivatives by a box-schemelike method and of the temporal derivative by either a backward-difference or Crank-Nicholson scheme. Lightning propagation is treated through numerical techniques based on the inverse-matrix modification formula and Cholesky updates. The model is applied to a storm observed at the Kennedy Space Center in 1978, and numerical comparisons are conducted between the model and the theoretical results obtained by Wilson (1920) and Holzer and Saxon (1952).

On the stability analysis of a pair of van der Pol oscillators with delayed self-connection, position and velocity couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Kun; Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon; Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk

2013-11-15

In this paper, we perform a stability analysis of a pair of van der Pol oscillators with delayed self-connection, position and velocity couplings. Bifurcation diagram of the damping, position and velocity coupling strengths is constructed, which gives insight into how stability boundary curves come into existence and how these curves evolve from small closed loops into open-ended curves. The van der Pol oscillator has been considered by many researchers as the nodes for various networks. It is inherently unstable at the zero equilibrium. Stability control of a network is always an important problem. Currently, the stabilization of the zero equilibriummore » of a pair of van der Pol oscillators can be achieved only for small damping strength by using delayed velocity coupling. An interesting question arises naturally: can the zero equilibrium be stabilized for an arbitrarily large value of the damping strength? We prove that it can be. In addition, a simple condition is given on how to choose the feedback parameters to achieve such goal. We further investigate how the in-phase mode or the out-of-phase mode of a periodic solution is related to the stability boundary curve that it emerges from a Hopf bifurcation. Analytical expression of a periodic solution is derived using an integration method. Some illustrative examples show that the theoretical prediction and numerical simulation are in good agreement.« less

Dynamic stability and bifurcation analysis in fractional thermodynamics

NASA Astrophysics Data System (ADS)

Béda, Péter B.

2018-02-01

In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity conditions are presented for constitutive relations under consideration.

Ferrofluids: Modeling, numerical analysis, and scientific computation

NASA Astrophysics Data System (ADS)

Tomas, Ignacio

This dissertation presents some developments in the Numerical Analysis of Partial Differential Equations (PDEs) describing the behavior of ferrofluids. The most widely accepted PDE model for ferrofluids is the Micropolar model proposed by R.E. Rosensweig. The Micropolar Navier-Stokes Equations (MNSE) is a subsystem of PDEs within the Rosensweig model. Being a simplified version of the much bigger system of PDEs proposed by Rosensweig, the MNSE are a natural starting point of this thesis. The MNSE couple linear velocity u, angular velocity w, and pressure p. We propose and analyze a first-order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier-Stokes equations. Moving onto the much more complex Rosensweig's model, we provide a definition (approximation) for the effective magnetizing field h, and explain the assumptions behind this definition. Unlike previous definitions available in the literature, this new definition is able to accommodate the effect of external magnetic fields. Using this definition we setup the system of PDEs coupling linear velocity u, pressure p, angular velocity w, magnetization m, and magnetic potential ϕ We show that this system is energy-stable and devise a numerical scheme that mimics the same stability property. We prove that solutions of the numerical scheme always exist and, under certain simplifying assumptions, that the discrete solutions converge. A notable outcome of the analysis of the numerical scheme for the Rosensweig's model is the choice of finite element spaces that allow the construction of an energy-stable scheme. Finally, with the lessons learned from Rosensweig's model, we develop a diffuse-interface model describing the behavior of two-phase ferrofluid flows and present an energy-stable numerical scheme for this model. For a simplified version of this model and the corresponding numerical scheme we prove (in addition to stability) convergence and existence of solutions as by-product . Throughout this dissertation, we will provide numerical experiments, not only to validate mathematical results, but also to help the reader gain a qualitative understanding of the PDE models analyzed in this dissertation (the MNSE, the Rosenweig's model, and the Two-phase model). In addition, we also provide computational experiments to illustrate the potential of these simple models and their ability to capture basic phenomenological features of ferrofluids, such as the Rosensweig instability for the case of the two-phase model. In this respect, we highlight the incisive numerical experiments with the two-phase model illustrating the critical role of the demagnetizing field to reproduce physically realistic behavior of ferrofluids.

Airfoil stall interpreted through linear stability analysis

NASA Astrophysics Data System (ADS)

Busquet, Denis; Juniper, Matthew; Richez, Francois; Marquet, Olivier; Sipp, Denis

2017-11-01

Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, M 0.2 and high Reynolds number, Re 1.8 ×106 . Steady RANS computation using a Spalart-Allmaras model is coupled with continuation methods (pseudo-arclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil.

Equal-area criterion in power systems revisited

NASA Astrophysics Data System (ADS)

Sun, Yong; Ma, Jinpeng; Kurths, Jürgen; Zhan, Meng

2018-02-01

The classic equal-area criterion (EAC) is of key importance in power system analysis, and provides a powerful, pictorial and quantitative means of analysing transient stability (i.e. the system's ability to maintain stable operation when subjected to a large disturbance). Based on the traditional EAC, it is common sense in engineering that there is a critical cleaning time (CCT); namely, a power system is stable (unstable) if a fault is cleared before (after) this CCT. We regard this form of CCT as bipartite. In this paper, we revisit the EAC theory and, surprisingly, find different kinds of transient stability behaviour. Based on these analyses, we discover that the bipartite CCT is only one type among four major types, and, actually, the forms of CCT can be diversified. In particular, under some circumstances, a system may have no CCT or show a periodic CCT. Our theoretical analysis is verified by numerical simulations in a single-machine-infinite-bus system and also in multi-machine systems. Thus, our study provides a panoramic framework for diverse transient stability behaviour in power systems and also may have a significant impact on applications of multi-stability in various other systems, such as neuroscience, climatology or photonics.

Unsteady characteristics of low-Re flow past two tandem cylinders

NASA Astrophysics Data System (ADS)

Zhang, Wei; Dou, Hua-Shu; Zhu, Zuchao; Li, Yi

2018-06-01

This study investigated the two-dimensional flow past two tandem circular or square cylinders at Re = 100 and D / d = 4-10, where D is the center-to-center distance and d is the cylinder diameter. Numerical simulation was performed to comparably study the effect of cylinder geometry and spacing on the aerodynamic characteristics, unsteady flow patterns, time-averaged flow characteristics and flow unsteadiness. We also provided the first global linear stability analysis and sensitivity analysis on the physical problem for the potential application of flow control. The objective of this work is to quantitatively identify the effect of the cylinder geometry and spacing on the characteristic quantities. Numerical results reveal that there is wake flow transition for both geometries depending on the spacing. The characteristic quantities, including the time-averaged and fluctuating streamwise velocity and pressure coefficient, are quite similar to that of the single cylinder case for the upstream cylinder, while an entirely different variation pattern is observed for the downstream cylinder. The global linear stability analysis shows that the spatial structure of perturbation is mainly observed in the wake of the downstream cylinder for small spacing, while moves upstream with reduced size and is also observed after the upstream cylinder for large spacing. The sensitivity analysis reflects that the temporal growth rate of perturbation is the most sensitive to the near-wake flow of downstream cylinder for small spacing and upstream cylinder for large spacing.

Modelling and stability analysis of switching impulsive power systems with multiple equilibria

NASA Astrophysics Data System (ADS)

Zhu, Liying; Qiu, Jianbin; Chadli, Mohammed

2017-12-01

This paper tries to model power systems accompanied with a series of faults in the form of switched impulsive Hamiltonian systems (SIHSs) with multiple equilibria (ME) and unstable subsystems (US), and then analyze long-term stability issues of the power systems from the viewpoint of mathematics. According to the complex phenomena of switching actions of stages and generators, impulses of state, and existence of multiple equilibria, this paper first introduces an SIHS with ME and US to formulate a switching impulsive power system composed of an active generator, a standby generator, and an infinite load. Then, based on special system structures, a unique compact region containing all ME is determined, and novel stability concepts of region stability (RS), asymptotic region stability (ARS), and exponential region stability (ERS) are defined for such SIHS with respect to the region. Third, based on the introduced stability concepts, this paper proposes a necessary and sufficient condition of RS and ARS and a sufficient condition of ERS for the power system with respect to the region via the maximum energy function method. Finally, numerical simulations are carried out for a power system to show the effectiveness and practicality of the obained novel results.

Quasi-laminar stability and sensitivity analyses for turbulent flows: Prediction of low-frequency unsteadiness and passive control

NASA Astrophysics Data System (ADS)

Mettot, Clément; Sipp, Denis; Bézard, Hervé

2014-04-01

This article presents a quasi-laminar stability approach to identify in high-Reynolds number flows the dominant low-frequencies and to design passive control means to shift these frequencies. The approach is based on a global linear stability analysis of mean-flows, which correspond to the time-average of the unsteady flows. Contrary to the previous work by Meliga et al. ["Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability," Phys. Fluids 24, 061701 (2012)], we use the linearized Navier-Stokes equations based solely on the molecular viscosity (leaving aside any turbulence model and any eddy viscosity) to extract the least stable direct and adjoint global modes of the flow. Then, we compute the frequency sensitivity maps of these modes, so as to predict before hand where a small control cylinder optimally shifts the frequency of the flow. In the case of the D-shaped cylinder studied by Parezanović and Cadot [J. Fluid Mech. 693, 115 (2012)], we show that the present approach well captures the frequency of the flow and recovers accurately the frequency control maps obtained experimentally. The results are close to those already obtained by Meliga et al., who used a more complex approach in which turbulence models played a central role. The present approach is simpler and may be applied to a broader range of flows since it is tractable as soon as mean-flows — which can be obtained either numerically from simulations (Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), unsteady Reynolds-Averaged-Navier-Stokes (RANS), steady RANS) or from experimental measurements (Particle Image Velocimetry - PIV) — are available. We also discuss how the influence of the control cylinder on the mean-flow may be more accurately predicted by determining an eddy-viscosity from numerical simulations or experimental measurements. From a technical point of view, we finally show how an existing compressible numerical simulation code may be used in a black-box manner to extract the global modes and sensitivity maps.

A general MHD formulation for plasmas with flow and resistive walls

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guazzotto, L.; Freidberg, J. P.; Betti, R.

2006-11-30

Toroidal rotation, either induced by means of neutral beams (e.g. in NSTX and DIII-D) or appearing spontaneously (e.g. in Alcator C-Mod, JET and Tore Supra) is routinely observed in modem tokamak experiments. Poloidal rotation is also commonly observed, in particular in the edge region of the plasma. Plasma rotation has a major effect on plasma stability. Flow and flow shear stabilize external modes such as the resistive wall mode (as observed e.g. in DIII-D), suppress turbulence when the flow shear is large enough, and also have a significant influence on the stability and nonlinear evolution of the internal kink andmore » ballooning modes. Flow shear can in particular have both a stabilizing (by breaking up unstable structures) and destabilizing (through the Kelvin-Helmoltz mechanism) effect. A self-consistent analysis of the effect of rotation requires the use of numerical tools. In this work, we present a general eigenvalue formulation based on a variational principle stability analysis, including arbitrary (both toroidal and poloidal) plasma rotation and a thin resistive wall of arbitrary shape and resistivity. It is shown that the problem can always be reduced to a classic eigenvalue formulation of the kind i{omega}A double underbar {center_dot} {zeta}-vector = B double underbar {center_dot} {zeta}-vector, where {zeta}-vector is the unknown eigenvector related to the plasma displacement, and {omega} the (complex) evolution frequency of the perturbation. The formulation is well suited for a finite element analysis.« less

Vortex sheet modeling with higher order curved panels. Ph.D Thesis Final Technical Report

NASA Technical Reports Server (NTRS)

Nagati, M. G.

1985-01-01

A numerical technique is presented for modeling the vortex sheet with a deformable surface definition, along which a continuous vortex strength distribution in the spanwise direction is applied, so that by repeatedly modifying its shape, its true configuration is approached, in the proximity of its generating wing. Design problems requiring the inclusion of a realistic configuration of the vortex sheet are numerous. Examples discussed include: control effectiveness and stability derivatives, longitudinal stability, lateral stability, canards, propellers and helicopter rotors, and trailing vortex hazards.

Mixed time integration methods for transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Liu, W. K.

1982-01-01

The computational methods used to predict and optimize the thermal structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a different yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Mixed time integration methods for transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Liu, W. K.

1983-01-01

The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally-useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Quasi-Static Analysis of Round LaRC THUNDER Actuators

NASA Technical Reports Server (NTRS)

Campbell, Joel F.

2007-01-01

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of round LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Quasi-Static Analysis of LaRC THUNDER Actuators

NASA Technical Reports Server (NTRS)

Campbell, Joel F.

2007-01-01

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Straight velocity boundaries in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Latt, Jonas; Chopard, Bastien; Malaspinas, Orestis; Deville, Michel; Michler, Andreas

2008-05-01

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

Fault stability under conditions of variable normal stress

USGS Publications Warehouse

Dieterich, J.H.; Linker, M.F.

1992-01-01

The stability of fault slip under conditions of varying normal stress is modelled as a spring and slider system with rate- and state-dependent friction. Coupling of normal stress to shear stress is achieved by inclining the spring at an angle, ??, to the sliding surface. Linear analysis yields two conditions for unstable slip. The first, of a type previously identified for constant normal stress systems, results in instability if stiffness is below a critical value. Critical stiffness depends on normal stress, constitutive parameters, characteristic sliding distance and the spring angle. Instability of the first type is possible only for velocity-weakening friction. The second condition yields instability if spring angle ?? <-cot-1??ss, where ??ss is steady-state sliding friction. The second condition can arise under conditions of velocity strengthening or weakening. Stability fields for finite perturbations are investigated by numerical simulation. -Authors

Observations and Numerical Modeling of the Jovian Ribbon

NASA Technical Reports Server (NTRS)

Cosentino, R. G.; Simon, A.; Morales-Juberias, R.; Sayanagi, K. M.

2015-01-01

Multiple wavelength observations made by the Hubble Space Telescope in early 2007 show the presence of a wavy, high-contrast feature in Jupiter's atmosphere near 30 degrees North. The "Jovian Ribbon," best seen at 410 nanometers, irregularly undulates in latitude and is time-variable in appearance. A meridional intensity gradient algorithm was applied to the observations to track the Ribbon's contour. Spectral analysis of the contour revealed that the Ribbon's structure is a combination of several wavenumbers ranging from k equals 8-40. The Ribbon is a dynamic structure that has been observed to have spectral power for dominant wavenumbers which vary over a time period of one month. The presence of the Ribbon correlates with periods when the velocity of the westward jet at the same location is highest. We conducted numerical simulations to investigate the stability of westward jets of varying speed, vertical shear, and background static stability to different perturbations. A Ribbon-like morphology was best reproduced with a 35 per millisecond westward jet that decreases in amplitude for pressures greater than 700 hectopascals and a background static stability of N equals 0.005 per second perturbed by heat pulses constrained to latitudes south of 30 degrees North. Additionally, the simulated feature had wavenumbers that qualitatively matched observations and evolved throughout the simulation reproducing the Jovian Ribbon's dynamic structure.

Towards the prediction of multiple necking during dynamic extension of round bar : linear stability approach versus finite element calculations

NASA Astrophysics Data System (ADS)

El Maï, S.; Mercier, S.; Petit, J.; Molinari, A.

2014-05-01

The fragmentation of structures subject to dynamic conditions is a matter of interest for civil industries as well as for Defence institutions. Dynamic expansions of structures, such as cylinders or rings, have been performed to obtain crucial information on fragment distributions. Many authors have proposed to capture by FEA the experimental distribution of fragment size by introducing in the FE model a perturbation. Stability and bifurcation analyses have also been proposed to describe the evolution of the perturbation growth rate. In the proposed contribution, the multiple necking of a round bar in dynamic tensile loading is analysed by the FE method. A perturbation on the initial flow stress is introduced in the numerical model to trigger instabilities. The onset time and the dominant mode of necking have been characterized precisely and showed power law evolutions, with the loading velocities and moderately with the amplitudes and the cell sizes of the perturbations. In the second part of the paper, the development of linear stability analysis and the use of salient criteria in terms of the growth rate of perturbations enabled comparisons with the numerical results. A good correlation in terms of onset time of instabilities and of number of necks is shown.

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

High Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Lanteri, S.; Maman, N.; Piperno, S.; Gumaste, U.

1994-01-01

In order to predict the dynamic response of a flexible structure in a fluid flow, the equations of motion of the structure and the fluid must be solved simultaneously. In this paper, we present several partitioned procedures for time-integrating this focus coupled problem and discuss their merits in terms of accuracy, stability, heterogeneous computing, I/O transfers, subcycling, and parallel processing. All theoretical results are derived for a one-dimensional piston model problem with a compressible flow, because the complete three-dimensional aeroelastic problem is difficult to analyze mathematically. However, the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two-dimensional transient aeroelastic response of a flexible panel in a transonic nonlinear Euler flow regime.

Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Baker, L. L.

1974-01-01

A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution.

A Cartesian parametrization for the numerical analysis of material instability

DOE PAGES

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

2016-02-25

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

A Cartesian parametrization for the numerical analysis of material instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

Application of the results of experimental and numerical turbulent flow researches based on pressure pulsations analysis

NASA Astrophysics Data System (ADS)

Kovalnogov, Vladislav N.; Fedorov, Ruslan V.; Khakhalev, Yuri A.; Khakhaleva, Larisa V.; Chukalin, Andrei V.

2017-07-01

The numerical investigation of the turbulent flow with the impacts, based on a modified Prandtl mixing-length model with using of the analysis of pulsations of pressure, calculation of structure and a friction factor of a turbulent flow is made. These results under the study allowed us to propose a new design of a cooled turbine blade and gas turbine mobile. The turbine blade comprises a combined cooling and cylindrical cavity on the blade surface, and on the inner surfaces of the cooling channels too damping cavity located on the guide vanes of the compressor of a gas turbine engine, increase the supply of gas-dynamic stability of the compressor of a gas turbine engine, reduce the resistance of the guide blades, and increase the efficiency of the turbine engine.

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

Effect of baffle size and orientation on lateral sloshing of partially filled containers: a numerical study

NASA Astrophysics Data System (ADS)

Ali, Sajid; Kamran, Muhammad Ali; Khan, Sikandar

2017-11-01

The fluid sloshing in partially filled road tankers has significantly increased the number of road accidents for the last few decades. Significant research is needed to investigate and to come up with optimum baffles designs that can help to increase the rollover stability of the partially filled tankers. In this investigation, a detailed analysis of the anti-slosh effectiveness of different baffle configurations is presented. This investigation extends the already available studies in the literature by introducing new modified rectangular tank's shapes that correspond to maximum rollover stability as compared to the already available standard tank designs. The various baffles configurations that are analysed in this study are horizontal, vertical, vertical-horizontal and diagonal. In the current study, numerical investigations are performed for rectangular, elliptical and circular tank shapes. Lateral sloshing, caused by constant radius turn manoeuvre, was simulated numerically using the volume-of-fluid method, and effect of the different baffle configurations was analysed. The effect of tank fill levels on sloshing measured in terms of horizontal force and pressure moments is also reported for with and without baffles configurations. Vertical baffles were the most effective at reducing sloshing in modified rectangular tanks, whereas a combination of horizontal and vertical baffles gave better results for the circular and elliptical tanks geometries.

Stabilization of the Rayleigh-Taylor instability in quantum magnetized plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, L. F.; Ye, W. H.; He, X. T.

2012-07-15

In this research, stabilization of the Rayleigh-Taylor instability (RTI) due to density gradients, magnetic fields, and quantum effects, in an ideal incompressible plasma, is studied analytically and numerically. A second-order ordinary differential equation (ODE) for the RTI including quantum corrections, with a continuous density profile, in a uniform external magnetic field, is obtained. Analytic expressions of the linear growth rate of the RTI, considering modifications of density gradients, magnetic fields, and quantum effects, are presented. Numerical approaches are performed to solve the second-order ODE. The analytical model proposed here agrees with the numerical calculation. It is found that the densitymore » gradients, the magnetic fields, and the quantum effects, respectively, have a stabilizing effect on the RTI (reduce the linear growth of the RTI). The RTI can be completely quenched by the magnetic field stabilization and/or the quantum effect stabilization in proper circumstances leading to a cutoff wavelength. The quantum effect stabilization plays a central role in systems with large Atwood number and small normalized density gradient scale length. The presence of external transverse magnetic fields beside the quantum effects will bring about more stability on the RTI. The stabilization of the linear growth of the RTI, for parameters closely related to inertial confinement fusion and white dwarfs, is discussed. Results could potentially be valuable for the RTI treatment to analyze the mixing in supernovas and other RTI-driven objects.« less

Navier-Stokes Analysis of the Flowfield Characteristics of an Ice Contaminated Aircraft Wing

NASA Technical Reports Server (NTRS)

Chung, J.; Choo, Y.; Reehorst, A.; Potapczuk, M.; Slater, J.

1999-01-01

An analytical study was performed as part of the NASA Lewis support of a National Transportation Safety Board (NTSB) aircraft accident investigation. The study was focused on the performance degradation associated with ice contamination on the wing of a commercial turbo-prop-powered aircraft. Based upon the results of an earlier numerical study conducted by the authors, a prominent ridged-ice formation on the subject aircraft wing was selected for detailed flow analysis using 2-dimensional (2-D), as well as, 3-dimensional (3-D) Navier-Stokes computations. This configuration was selected because it caused the largest lift decrease and drag increase among all the ice shapes investigated in the earlier study. A grid sensitivity test was performed to find out the influence of grid spacing on the lift, drag, and associated angle-of-attack for the maximum lift (C(sub lmax)). This study showed that grid resolution is important and a sensitivity analysis is an essential element of the process in order to assure that the final solution is independent of the grid. The 2-D results suggested that a severe stability and control difficulty could have occurred at a slightly higher angle-of-attack (AOA) than the one recorded by the Flight Data Recorder (FDR). This stability and control problem was thought to have resulted from a decreased differential lift on the wings with respect to the normal loading for the configuration. The analysis also indicated that this stability and control problem could have occurred whether or not natural ice shedding took place. Numerical results using an assumed 3-D ice shape showed an increase of the angle at which this phenomena occurred of about 4 degrees. As it occurred with the 2-D case, the trailing edge separation was observed but started only when the AOA was very close to the angle at which the maximum lift occurred.

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1990-01-01

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Linear stability analysis of laminar flow near a stagnation point in the slip flow regime

NASA Astrophysics Data System (ADS)

Essaghir, E.; Oubarra, A.; Lahjomri, J.

2017-12-01

The aim of the present contribution is to analyze the effect of slip parameter on the stability of a laminar incompressible flow near a stagnation point in the slip flow regime. The analysis is based on the traditional normal mode approach and assumes parallel flow approximation. The Orr-Sommerfeld equation that governs the infinitesimal disturbance of stream function imposed to the steady main flow, which is an exact solution of the Navier-Stokes equation satisfying slip boundary conditions, is obtained by using the powerful spectral Chebyshev collocation method. The results of the effect of slip parameter K on the hydrodynamic characteristics of the base flow, namely the velocity profile, the shear stress profile, the boundary layer, displacement and momentum thicknesses are illustrated and discussed. The numerical data for these characteristics, as well as those of the eigenvalues and the corresponding wave numbers recover the results of the special case of no-slip boundary conditions. They are found to be in good agreement with previous numerical calculations. The effects of slip parameter on the neutral curves of stability, for two-dimensional disturbances in the Reynolds-wave number plane, are then obtained for the first time in the slip flow regime for stagnation point flow. Furthermore, the evolution of the critical Reynolds number against the slip parameter is established. The results show that the critical Reynolds number for instability is significantly increased with the slip parameter and the flow turn out to be more stable when the effect of rarefaction becomes important.

Dark-bright soliton pairs in nonlocal nonlinear media.

PubMed

Lin, Yuan Yao; Lee, Ray-Kuang

2007-07-09

We study the formation of dark-bright vector soliton pairs in nonlocal Kerr-type nonlinear medium. We show, by analytical analysis and direct numerical calculation, that in addition to stabilize of vector soliton pairs nonlocal nonlinearity also helps to reduce the threshold power for forming a guided bright soliton. With help of the nonlocality, it is expected that the observation of dark-bright vector soliton pairs in experiments becomes more workable.

Laboratory and 3-D distinct element analysis of the failure mechanism of a slope under external surcharge

NASA Astrophysics Data System (ADS)

Li, N.; Cheng, Y. M.

2015-01-01

Landslide is a major disaster resulting in considerable loss of human lives and property damages in hilly terrain in Hong Kong, China and many other countries. The factor of safety and the critical slip surface for slope stabilization are the main considerations for slope stability analysis in the past, while the detailed post-failure conditions of the slopes have not been considered in sufficient detail. There is however increasing interest in the consequences after the initiation of failure that includes the development and propagation of the failure surfaces, the amount of failed mass and runoff and the affected region. To assess the development of slope failure in more detail and to consider the potential danger of slopes after failure has initiated, the slope stability problem under external surcharge is analyzed by the distinct element method (DEM) and a laboratory model test in the present research. A more refined study about the development of failure, microcosmic failure mechanisms and the post-failure mechanisms of slopes will be carried out. The numerical modeling method and the various findings from the present work can provide an alternate method of analysis of slope failure, which can give additional information not available from the classical methods of analysis.

Laboratory and 3-D-distinct element analysis of failure mechanism of slope under external surcharge

NASA Astrophysics Data System (ADS)

Li, N.; Cheng, Y. M.

2014-09-01

Landslide is a major disaster resulting in considerable loss of human lives and property damages in hilly terrain in Hong Kong, China and many other countries. The factor of safety and the critical slip surface for slope stabilization are the main considerations for slope stability analysis in the past, while the detailed post-failure conditions of the slopes have not been considered in sufficient details. There are however increasing interest on the consequences after the initiation of failure which includes the development and propagation of the failure surfaces, the amount of failed mass and runoff and the affected region. To assess the development of slope failure in more details and to consider the potential danger of slopes after failure has initiated, the slope stability problem under external surcharge is analyzed by the distinct element method (DEM) and laboratory model test in the present research. A more refined study about the development of failure, microcosmic failure mechanism and the post-failure mechanism of slope will be carried out. The numerical modeling method and the various findings from the present work can provide an alternate method of analysis of slope failure which can give additional information not available from the classical methods of analysis.

Wave Journal Bearing. Part 2: Experimental Pressure Measurements and Fractional Frequency Whirl Threshold for Wave and Plain Journal Bearings

NASA Technical Reports Server (NTRS)

Walker, James F.; Dimofte, Florin; Addy, Harold E., Jr.

1995-01-01

A new hydrodynamic bearing concept, the wave journal bearing, is being developed because it has better stability characteristics than plain journal bearings while maintaining similar load capacity. An analysis code to predict the steady state and dynamic performance of the wave journal bearing is also part of the development. To verify numerical predictions and contrast the wave journal bearing's stability characteristics to a plain journal bearing, tests were conducted at NASA Lewis Research Center using an air bearing test rig. Bearing film pressures were measured at 16 ports located around the bearing circumference at the middle of the bearing length. The pressure measurements for both a plain journal bearing and a wave journal bearing compared favorably with numerical predictions. Both bearings were tested with no radial load to determine the speed threshold for self-excited fractional frequency whirl. The plain journal bearing started to whirl immediately upon shaft start-up. The wave journal did not incur self-excited whirl until 800 to 900 rpm as predicted by the analysis. Furthermore, the wave bearing's geometry limited the whirl orbit to less than the bearing's clearance. In contrast, the plain journal bearing did not limit the whirl orbit, causing it to rub.

MI-Sim: A MATLAB package for the numerical analysis of microbial ecological interactions.

PubMed

Wade, Matthew J; Oakley, Jordan; Harbisher, Sophie; Parker, Nicholas G; Dolfing, Jan

2017-01-01

Food-webs and other classes of ecological network motifs, are a means of describing feeding relationships between consumers and producers in an ecosystem. They have application across scales where they differ only in the underlying characteristics of the organisms and substrates describing the system. Mathematical modelling, using mechanistic approaches to describe the dynamic behaviour and properties of the system through sets of ordinary differential equations, has been used extensively in ecology. Models allow simulation of the dynamics of the various motifs and their numerical analysis provides a greater understanding of the interplay between the system components and their intrinsic properties. We have developed the MI-Sim software for use with MATLAB to allow a rigorous and rapid numerical analysis of several common ecological motifs. MI-Sim contains a series of the most commonly used motifs such as cooperation, competition and predation. It does not require detailed knowledge of mathematical analytical techniques and is offered as a single graphical user interface containing all input and output options. The tools available in the current version of MI-Sim include model simulation, steady-state existence and stability analysis, and basin of attraction analysis. The software includes seven ecological interaction motifs and seven growth function models. Unlike other system analysis tools, MI-Sim is designed as a simple and user-friendly tool specific to ecological population type models, allowing for rapid assessment of their dynamical and behavioural properties.

Noncolocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum

NASA Astrophysics Data System (ADS)

Ciuonzo, Domenico; Rossi, Pierluigi Salvo

2017-04-01

We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario and several TR-MUSIC variants are here investigated. The analysis builds upon the 1st-order perturbation of the singular value decomposition and allows a simple characterization of null-spectrum moments (up to the 2nd order). This enables a comparison in terms of spectrums stability. Finally, a numerical analysis is provided to confirm the theoretical findings.

Atomic orbitals in molecules: general electronegativity and improvement of Mulliken population analysis.

PubMed

Lu, Haigang; Dai, Dadi; Yang, Pin; Li, Lemin

2006-01-21

An approach of atomic orbitals in molecules (AOIM) has been developed to study the atomic properties in molecules, in which the molecular orbitals are expressed in terms of the optimized minimal atomic orbitals. The atomic electronegativities are calculated using Pauling's electronegativity of free atom and are employed to find the electronegativity equilibrium in molecules and to describe the amphoteric properties of the transition metals from the groups 4 to 10. AOIM can also improve the numerical stability and accuracy of the original Mulliken population analysis.

Role of delay and screening in controlling AIDS

NASA Astrophysics Data System (ADS)

Chauhan, Sudipa; Bhatia, Sumit Kaur; Gupta, Surbhi

2016-06-01

We propose a non-linear HIV/ AIDS model to analyse the spread and control of HIV/AIDS. The population is divided into three classes, susceptible, infective and AIDS patients. The model is developed under the assumptions of vertical transmission and time delay in infective class. Time delay is also included to show sexual maturity period of infected newborns. We study dynamics of the model and obtain the reproduction number. Now to control the epidemic, we study the model where aware infective class is also added, i.e., people are made aware of their medical status by way of screening. To make the model more realistic, we consider the situation where aware infective class also interacts with other people. The model is analysed qualitatively by stability theory of ODE. Stability analysis of both disease-free and endemic equilibrium is studied based on reproduction number. Also, it is proved that if (R0)1, R1 ≤ 1 then, disease free equilibrium point is locally asymptotically stable and if (R0)1, R1 > 1 then, disease free equilibrium is unstable. Also, the stability analysis of endemic equilibrium point has been done and it is shown that for (R0)1 > 1 endemic equilibrium point is stable. Global stability analysis of endemic equilibrium point has also been done. At last, it is shown numerically that the delay in sexual maturity of infected individuals result in less number of AIDS patients.

Method for transition prediction in high-speed boundary layers, phase 2

NASA Astrophysics Data System (ADS)

Herbert, T.; Stuckert, G. K.; Lin, N.

1993-09-01

The parabolized stability equations (PSE) are a new and more reliable approach to analyzing the stability of streamwise varying flows such as boundary layers. This approach has been previously validated for idealized incompressible flows. Here, the PSE are formulated for highly compressible flows in general curvilinear coordinates to permit the analysis of high-speed boundary-layer flows over fairly general bodies. Vigorous numerical studies are carried out to study convergence and accuracy of the linear-stability code LSH and the linear/nonlinear PSE code PSH. Physical interfaces are set up to analyze the M = 8 boundary layer over a blunt cone calculated by using a thin-layer Navier Stokes (TNLS) code and the flow over a sharp cone at angle of attack calculated using the AFWAL parabolized Navier-Stokes (PNS) code. While stability and transition studies at high speeds are far from routine, the method developed here is the best tool available to research the physical processes in high-speed boundary layers.

Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach.

PubMed

Huang, Chuangxia; Cao, Jie; Cao, Jinde

2016-10-01

This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Flutter suppression and stability analysis for a variable-span wing via morphing technology

NASA Astrophysics Data System (ADS)

Li, Wencheng; Jin, Dongping

2018-01-01

A morphing wing can enhance aerodynamic characteristics and control authority as an alternative to using ailerons. To use morphing technology for flutter suppression, the dynamical behavior and stability of a variable-span wing subjected to the supersonic aerodynamic loads are investigated numerically in this paper. An axially moving cantilever plate is employed to model the variable-span wing, in which the governing equations of motion are established via the Kane method and piston theory. A morphing strategy based on axially moving rates is proposed to suppress the flutter that occurs beyond the critical span length, and the flutter stability is verified by Floquet theory. Furthermore, the transient stability during the morphing motion is analyzed and the upper bound of the morphing rate is obtained. The simulation results indicate that the proposed morphing law, which is varying periodically with a proper amplitude, could accomplish the flutter suppression. Further, the upper bound of the morphing speed decreases rapidly once the span length is close to its critical span length.

A Kinetic Approach to Propagation and Stability of Detonation Waves

NASA Astrophysics Data System (ADS)

Monaco, R.; Bianchi, M. Pandolfi; Soares, A. J.

2008-12-01

The problem of the steady propagation and linear stability of a detonation wave is formulated in the kinetic frame for a quaternary gas mixture in which a reversible bimolecular reaction takes place. The reactive Euler equations and related Rankine-Hugoniot conditions are deduced from the mesoscopic description of the process. The steady propagation problem is solved for a Zeldovich, von Neuman and Doering (ZND) wave, providing the detonation profiles and the wave thickness for different overdrive degrees. The one-dimensional stability of such detonation wave is then studied in terms of an initial value problem coupled with an acoustic radiation condition at the equilibrium final state. The stability equations and their initial data are deduced from the linearized reactive Euler equations and related Rankine-Hugoniot conditions through a normal mode analysis referred to the complex disturbances of the steady state variables. Some numerical simulations for an elementary reaction of the hydrogen-oxygen chain are proposed in order to describe the time and space evolution of the instabilities induced by the shock front perturbation.

Two-Relaxation-Time Lattice Boltzmann Method for Advective-Diffusive-Reactive Transport

NASA Astrophysics Data System (ADS)

Yan, Z.; Hilpert, M.

2016-12-01

The lattice Boltzmann method (LBM) has been applied to study a wide range of reactive transport in porous and fractured media. The single-relaxation-time (SRT) LBM, employing single relaxation time, is the most popular LBM due to its simplicity of understanding and implementation. Nevertheless, the SRT LBM may suffer from numerical instability for small value of the relaxation time. By contrast, the multiple-relaxation-time (MRT) LBM, employing multiple relaxation times, can improve the numerical stability through tuning the multiple relaxation times, but the complexity of implementing this method restricts its applications. The two-relaxation-time (TRT) LBM, which employs two relaxation times, combines the advantages of SRT and MRT LBMs. The TRT LBM can produce simulations with better accuracy and stability than the SRT one, and is easier to implement than the MRT one. This work evaluated the numerical accuracy and stability of the TRT method by comparing the simulation results with analytical solutions of Gaussian hill transport and Taylor dispersion under different advective velocities. The accuracy generally increased with the tunable relaxation time τ, and the stability first increased and then decreased as τ increased, showing an optimal TRT method emerging the best numerical stability. The free selection of τ enabled the TRT LBM to simulate the Gaussian hill transport and Taylor dispersion under relatively high advective velocity, under which the SRT LBM suffered from numerical instability. Finally, the TRT method was applied to study the contaminant degradation by chemotactic microorganisms in porous media, which acted as a reprehensive of reactive transport in this study, and well predicted the evolution of microorganisms and degradation of contaminants for different transport scenarios. To sum up, the TRT LBM produced simulation results with good accuracy and stability for various advective-diffusive-reactive transport through tuning the relaxation time τ, illustrating its potential to study various biogeochemical behaviors in the subsurface environment.

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

NASA Astrophysics Data System (ADS)

Gavish, Nir

2018-04-01

We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

NASA Astrophysics Data System (ADS)

Camacho, Erika T.; Radulescu, Anca; Wirkus, Stephen

2016-09-01

Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

Positional stability and radial dynamics of sonoluminescent bubbles under bi-harmonic driving: Effect of the high-frequency component and its relative phase.

PubMed

Rosselló, J M; Dellavale, D; Bonetto, F J

2016-07-01

The use of bi-frequency driving in sonoluminescence has proved to be an effective way to avoid the spatial instability (pseudo-orbits) developed by bubbles in systems with high viscous liquids like sulfuric or phosphoric acids. In this work, we present extensive experimental and numerical evidence in order to assess the effect of the high frequency component (PAc(HF)) of a bi-harmonic acoustic pressure field on the dynamic of sonoluminescent bubbles in an aqueous solution of sulfuric acid. The present study is mainly focused on the role of the harmonic frequency (Nf0) and the relative phase between the two frequency components (φb) of the acoustic field on the spatial, positional and diffusive stability of the bubbles. The results presented in this work were analyzed by means of three different approaches. First, we discussed some qualitative considerations about the changes observed in the radial dynamics, and the stability of similar bubbles under distinct bi-harmonic drivings. Later, we have investigated, through a series of numerical simulations, how the use of high frequency harmonic components of different order N, affects the positional stability of the SL bubbles. Furthermore, the influence of φb in their radius temporal evolution is systematically explored for harmonics ranging from the second to the fifteenth harmonic (N=2-15). Finally, a multivariate analysis based on the covariance method is performed to study the dependences among the parameters characterizing the SL bubble. Both experimental and numerical results indicate that the impact of PAc(HF) on the positional instability and the radial dynamics turns to be progressively negligible as the order of the high frequency harmonic component grows (i.e. N ≫ 1), however its effectiveness on the reduction of the spatial instability remains unaltered or even improved. Copyright © 2016 Elsevier B.V. All rights reserved.

PMU-Aided Voltage Security Assessment for a Wind Power Plant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Huaiguang; Zhang, Yingchen; Zhang, Jun Jason

2015-10-05

Because wind power penetration levels in electric power systems are continuously increasing, voltage stability is a critical issue for maintaining power system security and operation. The traditional methods to analyze voltage stability can be classified into two categories: dynamic and steady-state. Dynamic analysis relies on time-domain simulations of faults at different locations; however, this method needs to exhaust faults at all locations to find the security region for voltage at a single bus. With the widely located phasor measurement units (PMUs), the Thevenin equivalent matrix can be calculated by the voltage and current information collected by the PMUs. This papermore » proposes a method based on a Thevenin equivalent matrix to identify system locations that will have the greatest impact on the voltage at the wind power plant's point of interconnection. The number of dynamic voltage stability analysis runs is greatly reduced by using the proposed method. The numerical results demonstrate the feasibility, effectiveness, and robustness of the proposed approach for voltage security assessment for a wind power plant.« less

Design and Analysis of Morpheus Lander Flight Control System

NASA Technical Reports Server (NTRS)

Jang, Jiann-Woei; Yang, Lee; Fritz, Mathew; Nguyen, Louis H.; Johnson, Wyatt R.; Hart, Jeremy J.

2014-01-01

The Morpheus Lander is a vertical takeoff and landing test bed vehicle developed to demonstrate the system performance of the Guidance, Navigation and Control (GN&C) system capability for the integrated autonomous landing and hazard avoidance system hardware and software. The Morpheus flight control system design must be robust to various mission profiles. This paper presents a design methodology for employing numerical optimization to develop the Morpheus flight control system. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics and propellant slosh. Under the assumption that the Morpheus time-varying dynamics and control system can be frozen over a short period of time, the flight controllers are designed to stabilize all selected frozen-time control systems in the presence of parametric uncertainty. Both control gains in the inner attitude control loop and guidance gains in the outer position control loop are designed to maximize the vehicle performance while ensuring robustness. The flight control system designs provided herein have been demonstrated to provide stable control systems in both Draper Ares Stability Analysis Tool (ASAT) and the NASA/JSC Trick-based Morpheus time domain simulation.

Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays

NASA Astrophysics Data System (ADS)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

The effect of pressure anisotropy on ballooning modes in tokamak plasmas

NASA Astrophysics Data System (ADS)

Johnston, A.; Hole, M. J.; Qu, Z. S.; Hezaveh, H.

2018-06-01

Edge Localised Modes are thought to be caused by a spectrum of magnetohydrodynamic instabilities, including the ballooning mode. While ballooning modes have been studied extensively both theoretically and experimentally, the focus of the vast majority of this research has been on isotropic plasmas. The prevalence of pressure anisotropy in modern tokamaks thus motivates further study of these modes. This paper presents a numerical analysis of ballooning modes in anisotropic equilibria. The investigation was conducted using the newly-developed codes HELENA+ATF and MISHKA-A, which adds anisotropic physics to equilibria and stability analysis. We have examined the impact of anisotropy on the stability of an n = 30 ballooning mode, confirming results conform to previous calculations in the isotropic limit. Growth rates of ballooning modes in equilibria with different levels of anisotropy were then calculated using the stability code MISHKA-A. The key finding was that the level of anisotropy had a significant impact on ballooning mode growth rates. For {T}\\perp > {T}| | , typical of ICRH heating, the growth rate increases, while for {T}\\perp < {T}| | , typical of neutral beam heating, the growth rate decreases.

The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer

NASA Astrophysics Data System (ADS)

Griffiths, P. T.; Gallagher, M. T.; Stephen, S. O.

2016-07-01

We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results obtained from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation, that shear-thinning destabilises the boundary layer flow, is further supported by our calculations regarding the development of the streamwise eigenfunctions and the relative magnitude of the temporal growth rates.

Polyhedral meshing in numerical analysis of conjugate heat transfer

NASA Astrophysics Data System (ADS)

Sosnowski, Marcin; Krzywanski, Jaroslaw; Grabowska, Karolina; Gnatowska, Renata

2018-06-01

Computational methods have been widely applied in conjugate heat transfer analysis. The very first and crucial step in such research is the meshing process which consists in dividing the analysed geometry into numerous small control volumes (cells). In Computational Fluid Dynamics (CFD) applications it is desirable to use the hexahedral cells as the resulting mesh is characterized by low numerical diffusion. Unfortunately generating such mesh can be a very time-consuming task and in case of complicated geometry - it may not be possible to generate cells of good quality. Therefore tetrahedral cells have been implemented into commercial pre-processors. Their advantage is the ease of its generation even in case of very complex geometry. On the other hand tetrahedrons cannot be stretched excessively without decreasing the mesh quality factor, so significantly larger number of cells has to be used in comparison to hexahedral mesh in order to achieve a reasonable accuracy. Moreover the numerical diffusion of tetrahedral elements is significantly higher. Therefore the polyhedral cells are proposed within the paper in order to combine the advantages of hexahedrons (low numerical diffusion resulting in accurate solution) and tetrahedrons (rapid semi-automatic generation) as well as to overcome the disadvantages of both the above mentioned mesh types. The major benefit of polyhedral mesh is that each individual cell has many neighbours, so gradients can be well approximated. Polyhedrons are also less sensitive to stretching than tetrahedrons which results in better mesh quality leading to improved numerical stability of the model. In addition, numerical diffusion is reduced due to mass exchange over numerous faces. This leads to a more accurate solution achieved with a lower cell count. Therefore detailed comparison of numerical modelling results concerning conjugate heat transfer using tetrahedral and polyhedral meshes is presented in the paper.

Exact and Approximate Stability of Solutions to Traveling Salesman Problems.

PubMed

Niendorf, Moritz; Girard, Anouck R

2018-02-01

This paper presents the stability analysis of an optimal tour for the symmetric traveling salesman problem (TSP) by obtaining stability regions. The stability region of an optimal tour is the set of all cost changes for which that solution remains optimal and can be understood as the margin of optimality for a solution with respect to perturbations in the problem data. It is known that it is not possible to test in polynomial time whether an optimal tour remains optimal after the cost of an arbitrary set of edges changes. Therefore, this paper develops tractable methods to obtain under and over approximations of stability regions based on neighborhoods and relaxations. The application of the results to the two-neighborhood and the minimum 1 tree (M1T) relaxation are discussed in detail. For Euclidean TSPs, stability regions with respect to vertex location perturbations and the notion of safe radii and location criticalities are introduced. Benefits of this paper include insight into robustness properties of tours, minimum spanning trees, M1Ts, and fast methods to evaluate optimality after perturbations occur. Numerical examples are given to demonstrate the methods and achievable approximation quality.

Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels

PubMed Central

Camacho-Bello, César; Padilla-Vivanco, Alfonso; Toxqui-Quitl, Carina; Báez-Rojas, José Javier

2016-01-01

Abstract. A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters α and β of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented. PMID:27014716

A numerical study of the thermal stability of low-lying coronal loops

NASA Technical Reports Server (NTRS)

Klimchuk, J. A.; Antiochos, S. K.; Mariska, J. T.

1986-01-01

The nonlinear evolution of loops that are subjected to a variety of small but finite perturbations was studied. Only the low-lying loops are considered. The analysis was performed numerically using a one-dimensional hydrodynamical model developed at the Naval Research Laboratory. The computer codes solve the time-dependent equations for mass, momentum, and energy transport. The primary interest is the active region filaments, hence a geometry appropriate to those structures was considered. The static solutions were subjected to a moderate sized perturbation and allowed to evolve. The results suggest that both hot and cool loops of the geometry considered are thermally stable against amplitude perturbations of all kinds.

Numerical Modeling of Pot-Hole Subsidence Due to Shallow Underground Coal Mining in Structurally Disturbed Ground

NASA Astrophysics Data System (ADS)

Lokhande, Ritesh D.; Murthy, V. M. S. R.; Singh, K. B.; Verma, Chandan Prasad; Verma, A. K.

2018-04-01

Stability analysis of underground mining is, generally, complex in nature and is difficult to carry out through analytical solutions more so in case of pot-hole subsidence prediction. Thus, application of numerical modeling technique for simulating and finding a solution is preferred. This paper reports the development of a methodology for simulating the pot-hole subsidence using FLAC3D. This study is restricted to geologically disturbed areas where presence of fault was dominating factor for occurrence of pot-hole subsidence. The results demonstrate that the variation in the excavation geometry and properties of immediate roof rocks play a vital role in the occurrence of pot-hole subsidence.

Dynamical and fractal properties in periodically forced stretch-twist-fold (STF) flow

NASA Astrophysics Data System (ADS)

Aqeel, Muhammad; Ahmad, Salman; Azam, Anam; Ahmed, Faizan

2017-05-01

The periodically forced stretch-twist-fold (STF) flow is introduced in this article. The nonlinear behavior of the STF flow with periodic force along the y -axis is investigated analytically and numerically. The STF flow is a prototype of the dynamo theory that proposes a mechanism of magnetic field generation continuously. The stability analysis is done by Routh Huwritz criteria and Cardano method. Chasing chaos through numerical simulation is determined to demonstrate the chaotic behavior of the forced STF flow. With the help of fractal processes based on the forced STF flow, a multi-wing forced STF flow is obtained that gives a n -wing forced STF flow system.

Stability analysis of flexible wind turbine blades using finite element method

NASA Technical Reports Server (NTRS)

Kamoulakos, A.

1982-01-01

Static vibration and flutter analysis of a straight elastic axis blade was performed based on a finite element method solution. The total potential energy functional was formulated according to linear beam theory. The inertia and aerodynamic loads were formulated according to the blade absolute acceleration and absolute velocity vectors. In vibration analysis, the direction of motion of the blade during the first out-of-lane and first in-plane modes was examined; numerical results involve NASA/DOE Mod-0, McCauley propeller, north wind turbine and flat plate behavior. In flutter analysis, comparison cases were examined involving several references. Vibration analysis of a nonstraight elastic axis blade based on a finite element method solution was performed in a similar manner with the straight elastic axis blade, since it was recognized that a curved blade can be approximated by an assembly of a sufficient number of straight blade elements at different inclinations with respect to common system of axes. Numerical results involve comparison between the behavior of a straight and a curved cantilever beam during the lowest two in-plane and out-of-plane modes.

Motion stability of high-speed maglev systems in consideration of aerodynamic effects: a study of a single magnetic suspension system

NASA Astrophysics Data System (ADS)

Wu, Han; Zeng, Xiao-Hui; Yu, Yang

2017-12-01

In this study, the intrinsic mechanism of aerodynamic effects on the motion stability of a high-speed maglev system was investigated. The concept of a critical speed for maglev vehicles considering the aerodynamic effect is proposed. The study was carried out based on a single magnetic suspension system, which is convenient for proposing relevant concepts and obtaining explicit expressions. This study shows that the motion stability of the suspension system is closely related to the vehicle speed when aerodynamic effects are considered. With increases of the vehicle speed, the stability behavior of the system changes. At a certain vehicle speed, the stability of the system reaches a critical state, followed by instability. The speed corresponding to the critical state is the critical speed. Analysis reveals that when the system reaches the critical state, it takes two forms, with two critical speeds, and thus two expressions for the critical speed are obtained. The conditions of the existence of the critical speed were determined, and the effects of the control parameters and the lift coefficient on the critical speed were analyzed by numerical analysis. The results show that the first critical speed appears when the aerodynamic force is upward, and the second critical speed appears when the aerodynamic force is downward. Moreover, both critical speeds decrease with the increase of the lift coefficient.

Static and dynamic stability of pneumatic vibration isolators and systems of isolators

NASA Astrophysics Data System (ADS)

Ryaboy, Vyacheslav M.

2014-01-01

Pneumatic vibration isolation is the most widespread effective method for creating vibration-free environments that are vital for precise experiments and manufacturing operations in optoelectronics, life sciences, microelectronics, nanotechnology and other areas. The modeling and design principles of a dual-chamber pneumatic vibration isolator, basically established a few decades ago, continue to attract attention of researchers. On the other hand, behavior of systems of such isolators was never explained in the literature in sufficient detail. This paper covers a range of questions essential for understanding the mechanics of pneumatic isolation systems from both design and application perspectives. The theory and a model of a single standalone isolator are presented in concise form necessary for subsequent analysis. Then the dynamics of a system of isolators supporting a payload is considered with main attention directed to two aspects of their behavior: first, the static stability of payloads with high positions of the center of gravity; second, dynamic stability of the feedback system formed by mechanical leveling valves. The direct method of calculating the maximum stable position of the center of gravity is presented and illustrated by three-dimensional stability domains; analytic formulas are given that delineate these domains. A numerical method for feedback stability analysis of self-leveling valve systems is given, and the results are compared with the analytical estimates for a single isolator. The relation between the static and dynamic phenomena is discussed.

Stabilization of ring dark solitons in Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Wenlong; Kevrekidis, P. G.; Carretero-González, R.

Earlier work has shown that ring dark solitons in two-dimensional Bose-Einstein condensates are generically unstable. In this work, we propose a way of stabilizing the ring dark soliton via a radial Gaussian external potential. We investigate the existence and stability of the ring dark soliton upon variations of the chemical potential and also of the strength of the radial potential. Numerical results show that the ring dark soliton can be stabilized in a suitable interval of external potential strengths and chemical potentials. Furthermore, we also explore different proposed particle pictures considering the ring as a moving particle and find, wheremore » appropriate, results in very good qualitative and also reasonable quantitative agreement with the numerical findings.« less

Stabilization of ring dark solitons in Bose-Einstein condensates

DOE PAGES

Wang, Wenlong; Kevrekidis, P. G.; Carretero-González, R.; ...

2015-09-14

Earlier work has shown that ring dark solitons in two-dimensional Bose-Einstein condensates are generically unstable. In this work, we propose a way of stabilizing the ring dark soliton via a radial Gaussian external potential. We investigate the existence and stability of the ring dark soliton upon variations of the chemical potential and also of the strength of the radial potential. Numerical results show that the ring dark soliton can be stabilized in a suitable interval of external potential strengths and chemical potentials. Furthermore, we also explore different proposed particle pictures considering the ring as a moving particle and find, wheremore » appropriate, results in very good qualitative and also reasonable quantitative agreement with the numerical findings.« less

Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

NASA Astrophysics Data System (ADS)

Sun, Dihua; Chen, Dong; Zhao, Min; Liu, Weining; Zheng, Linjiang

2018-07-01

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

Bioconvection in spatially extended domains

NASA Astrophysics Data System (ADS)

Karimi, A.; Paul, M. R.

2013-05-01

We numerically explore gyrotactic bioconvection in large spatially extended domains of finite depth using parameter values from available experiments with the unicellular alga Chlamydomonas nivalis. We numerically integrate the three-dimensional, time-dependent continuum model of Pedley [J. Fluid Mech.10.1017/S0022112088002393 195, 223 (1988)] using a high-order, parallel, spectral-element approach. We explore the long-time nonlinear patterns and dynamics found for layers with an aspect ratio of 10 over a range of Rayleigh numbers. Our results yield the pattern wavelength and pattern dynamics which we compare with available theory and experimental measurement. There is good agreement for the pattern wavelength at short times between numerics, experiment, and a linear stability analysis. At long times we find that the general sequence of patterns given by the nonlinear evolution of the governing equations correspond qualitatively to what has been described experimentally. However, at long times the patterns in numerics grow to larger wavelengths, in contrast to what is observed in experiment where the wavelength is found to decrease with time.

Domain decomposition and matching for time-domain analysis of motions of ships advancing in head sea

NASA Astrophysics Data System (ADS)

Tang, Kai; Zhu, Ren-chuan; Miao, Guo-ping; Fan, Ju

2014-08-01

A domain decomposition and matching method in the time-domain is outlined for simulating the motions of ships advancing in waves. The flow field is decomposed into inner and outer domains by an imaginary control surface, and the Rankine source method is applied to the inner domain while the transient Green function method is used in the outer domain. Two initial boundary value problems are matched on the control surface. The corresponding numerical codes are developed, and the added masses, wave exciting forces and ship motions advancing in head sea for Series 60 ship and S175 containership, are presented and verified. A good agreement has been obtained when the numerical results are compared with the experimental data and other references. It shows that the present method is more efficient because of the panel discretization only in the inner domain during the numerical calculation, and good numerical stability is proved to avoid divergence problem regarding ships with flare.

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Combined analytical and numerical approaches in Dynamic Stability analyses of engineering systems

NASA Astrophysics Data System (ADS)

Náprstek, Jiří

2015-03-01

Dynamic Stability is a widely studied area that has attracted many researchers from various disciplines. Although Dynamic Stability is usually associated with mechanics, theoretical physics or other natural and technical disciplines, it is also relevant to social, economic, and philosophical areas of our lives. Therefore, it is useful to occasionally highlight the general aspects of this amazing area, to present some relevant examples and to evaluate its position among the various branches of Rational Mechanics. From this perspective, the aim of this study is to present a brief review concerning the Dynamic Stability problem, its basic definitions and principles, important phenomena, research motivations and applications in engineering. The relationships with relevant systems that are prone to stability loss (encountered in other areas such as physics, other natural sciences and engineering) are also noted. The theoretical background, which is applicable to many disciplines, is presented. In this paper, the most frequently used Dynamic Stability analysis methods are presented in relation to individual dynamic systems that are widely discussed in various engineering branches. In particular, the Lyapunov function and exponent procedures, Routh-Hurwitz, Liénard, and other theorems are outlined together with demonstrations. The possibilities for analytical and numerical procedures are mentioned together with possible feedback from experimental research and testing. The strengths and shortcomings of these approaches are evaluated together with examples of their effective complementing of each other. The systems that are widely encountered in engineering are presented in the form of mathematical models. The analyses of their Dynamic Stability and post-critical behaviour are also presented. The stability limits, bifurcation points, quasi-periodic response processes and chaotic regimes are discussed. The limit cycle existence and stability are examined together with their separating roles as attractors and repulsers. Two levels of stability loss (recovery of the system is possible or final collapse is inevitable) as can be observed in softening systems are noted. Time-limited excitation and relevant transition effects (e.g., seismic excitation) are also discussed, together with the evaluation of possible system reliability improvement. The Dynamic Stability investigation of two degrees-of-freedom aero-elastic systems in a linear formulation using several approaches is briefly highlighted. Further systems modelling problems that arise in transport engineering are also outlined. A few hints for applications are given. Some open problems and possible future research strategies are outlined.

Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis

NASA Astrophysics Data System (ADS)

Sakata, Ayaka; Xu, Yingying

2018-03-01

We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show that the stability condition corresponds to the de Almeida-Thouless condition in spin glass literature. Through asymptotic analysis, we show the correspondence between the density evolution of SCAD-AMP and the replica symmetric (RS) solution. Numerical experiments confirm that for a sufficiently large system size, SCAD-AMP achieves the optimal performance predicted by the replica method. Through replica analysis, a phase transition between replica symmetric and replica symmetry breaking (RSB) region is found in the parameter space of SCAD. The appearance of the RS region for a nonconvex penalty is a significant advantage that indicates the region of smooth landscape of the optimization problem. Furthermore, we analytically show that the statistical representation performance of the SCAD penalty is better than that of \

A pertinent approach to solve nonlinear fuzzy integro-differential equations.

PubMed

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

Stability analysis for acoustic wave propagation in tilted TI media by finite differences

NASA Astrophysics Data System (ADS)

Bakker, Peter M.; Duveneck, Eric

2011-05-01

Several papers in recent years have reported instabilities in P-wave modelling, based on an acoustic approximation, for inhomogeneous transversely isotropic media with tilted symmetry axis (TTI media). In particular, instabilities tend to occur if the axis of symmetry varies rapidly in combination with strong contrasts of medium parameters, which is typically the case at the foot of a steeply dipping salt flank. In a recent paper, we have proposed and demonstrated a P-wave modelling approach for TTI media, based on rotated stress and strain tensors, in which the wave equations reduce to a coupled set of two second-order partial differential equations for two scalar stress components: a normal component along the variable axis of symmetry and a lateral component of stress in the plane perpendicular to that axis. Spatially constant density is assumed in this approach. A numerical discretization scheme was proposed which uses discrete second-derivative operators for the non-mixed second-order derivatives in the wave equations, and combined first-derivative operators for the mixed second-order derivatives. This paper provides a complete and rigorous stability analysis, assuming a uniformly sampled grid. Although the spatial discretization operator for the TTI acoustic wave equation is not self-adjoint, this operator still defines a complete basis of eigenfunctions of the solution space, provided that the solution space is somewhat restricted at locations where the medium is elliptically anisotropic. First, a stability analysis is given for a discretization scheme, which is purely based on first-derivative operators. It is shown that the coefficients of the central difference operators should satisfy certain conditions. In view of numerical artefacts, such a discretization scheme is not attractive, and the non-mixed second-order derivatives of the wave equation are discretized directly by second-derivative operators. It is shown that this modification preserves stability, provided that the central difference operators of the second-order derivatives dominate over the twice applied operators of the first-order derivatives. In practice, it turns out that this is almost the case. Stability of the desired discretization scheme is enforced by slightly weighting down the mixed second-order derivatives in the wave equation. This has a minor, practically negligible, effect on the kinematics of wave propagation. Finally, it is shown that non-reflecting boundary conditions, enforced by applying a taper at the boundaries of the grid, do not harm the stability of the discretization scheme.

Research in computational fluid dynamics and analysis of algorithms

NASA Technical Reports Server (NTRS)

Gottlieb, David

1992-01-01

Recently, higher-order compact schemes have seen increasing use in the DNS (Direct Numerical Simulations) of the Navier-Stokes equations. Although they do not have the spatial resolution of spectral methods, they offer significant increases in accuracy over conventional second order methods. They can be used on any smooth grid, and do not have an overly restrictive CFL dependence as compared with the O(N(exp -2)) CFL dependence observed in Chebyshev spectral methods on finite domains. In addition, they are generally more robust and less costly than spectral methods. The issue of the relative cost of higher-order schemes (accuracy weighted against physical and numerical cost) is a far more complex issue, depending ultimately on what features of the solution are sought and how accurately they must be resolved. In any event, the further development of the underlying stability theory of these schemes is important. The approach of devising suitable boundary clusters and then testing them with various stability techniques (such as finding the norm) is entirely the wrong approach when dealing with high-order methods. Very seldom are high-order boundary closures stable, making them difficult to isolate. An alternative approach is to begin with a norm which satisfies all the stability criteria for the hyperbolic system, and look for the boundary closure forms which will match the norm exactly. This method was used recently by Strand to isolate stable boundary closure schemes for the explicit central fourth- and sixth-order schemes. The norm used was an energy norm mimicking the norm for the differential equations. Further research should be devoted to BC for high order schemes in order to make sure that the results obtained are reliable. The compact fourth order and sixth order finite difference scheme had been incorporated into a code to simulate flow past circular cylinders. This code will serve as a verification of the full spectral codes. A detailed stability analysis by Carpenter (from the fluid Mechanics Division) and Gottlieb gave analytic conditions for stability as well as asymptotic stability. This had been incorporated in the code in form of stable boundary conditions. Effects of the cylinder rotations had been studied. The results differ from the known theoretical results. We are in the middle of analyzing the results. A detailed analysis of the effects of the heating of the cylinder on the shedding frequency had been studied using the above schemes. It has been found that the shedding frequency decreases when the wire was heated. Experimental work is being carried out to affirm this result.

Stability analysis for a delay differential equations model of a hydraulic turbine speed governor

NASA Astrophysics Data System (ADS)

Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.

2017-01-01

The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.

Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential.

PubMed

Li, Min; Xu, Tao

2015-03-01

Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.

Perturbative stability of SFT-based cosmological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galli, Federico; Koshelev, Alexey S., E-mail: fgalli@tena4.vub.ac.be, E-mail: alexey.koshelev@vub.ac.be

2011-05-01

We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numericallymore » that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.« less

Onset of `stitching' in the fluid mechanical `sewing machine'

NASA Astrophysics Data System (ADS)

Ribe, Neil; Lister, John; Chiu-Webster, Sunny

2006-11-01

A thin thread of viscous fluid that falls on a moving belt acts like a fluid mechanical `sewing machine', exhibiting a rich variety of `stitch' patterns including meanders, side kicks, slanted loops, braiding, figures-of-eight, W-patterns, and period-doubled patterns (Chiu-Webster and Lister, J. Fluid Mech., in press). Using a numerical linear stability analysis based on asymptotic `slender thread' theory, we determine the critical belt speed and frequency of the first bifurcation, at which a steady dragged viscous thread becomes unstable to sideways oscillations (`meanders'). The predictions of the stability analysis agree closely with experimental measurements. Moreover, we find that the critical belt speed and frequency for meandering are nearly identical to the contact point migration speed and the frequency, respectively, of steady coiling of a viscous thread on a stationary surface, implying a remarkable degree of dynamical similarity between the two phenomena.

Stability Analysis of the Planetary System Orbiting Upsilon Andromedae

NASA Technical Reports Server (NTRS)

Lissauer, Jack J.; Rivera, Eugenio J.; DeVincenzi, Donald (Technical Monitor)

2000-01-01

We present results of long-term numerical orbital integrations designed to test the stability of the three-planet system orbiting Upsilon Andromedae and short-term integrations to test whether mutual perturbations among the planets can be used to determine planetary masses. Our initial conditions are based on the latest fits to the radial velocity data obtained by the planet-search group at Lick Observatory. The new fits result in significantly more stable systems than did the initially announced planetary parameters. An analytic analysis of the star and the two outer planets shows that this subsystem is Hill stable up to five. Our integrations involving all three planets show that the system is stable for at least 100 Myr for up to four. In our simulations, we still see a secular resonance between the outer two planets and in some cases large oscillations in the eccentricity of the inner planet.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ibraheem, S. O.; Demuren, A. O.

1994-01-01

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

Delay-dependent dynamical analysis of complex-valued memristive neural networks: Continuous-time and discrete-time cases.

PubMed

Wang, Jinling; Jiang, Haijun; Ma, Tianlong; Hu, Cheng

2018-05-01

This paper considers the delay-dependent stability of memristive complex-valued neural networks (MCVNNs). A novel linear mapping function is presented to transform the complex-valued system into the real-valued system. Under such mapping function, both continuous-time and discrete-time MCVNNs are analyzed in this paper. Firstly, when activation functions are continuous but not Lipschitz continuous, an extended matrix inequality is proved to ensure the stability of continuous-time MCVNNs. Furthermore, if activation functions are discontinuous, a discontinuous adaptive controller is designed to acquire its stability by applying Lyapunov-Krasovskii functionals. Secondly, compared with techniques in continuous-time MCVNNs, the Halanay-type inequality and comparison principle are firstly used to exploit the dynamical behaviors of discrete-time MCVNNs. Finally, the effectiveness of theoretical results is illustrated through numerical examples. Copyright © 2018 Elsevier Ltd. All rights reserved.

Stability Formulation for Integrated Opto-mechanic Phase Shifters.

PubMed

Ozer, Yigit; Kocaman, Serdar

2018-01-31

Stability of opto-mechanical phase shifters consisting of waveguides and non-signal carrying control beams is investigated thoroughly and a formula determining the physical limitations has been proposed. Suggested formulation is not only beneficial to determine physical strength of the system but also advantageous to guess the response of the output to the fabrication errors. In the iterative analysis of cantilever and double-clamped beam geometrical configurations, the stability condition is revealed under the strong inter-dependence of the system parameters such as input power, device length and waveguide separation. Numerical calculations involving effective index modifications and opto-mechanic movements show that well-known cantilever beams are unstable and inadequate to generate φ = 180° phase difference, while double-clamped beam structures can be utilized to build functional devices. Ideal operation conditions are also presented in terms of both the device durability and the controllability of phase evolution.

HADY-I, a FORTRAN program for the compressible stability analysis of three-dimensional boundary layers. [on swept and tapered wings

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1981-01-01

A computer program HADY-I for calculating the linear incompressible or compressible stability characteristics of the laminar boundary layer on swept and tapered wings is described. The eigenvalue problem and its adjoint arising from the linearized disturbance equations with the appropriate boundary conditions are solved numerically using a combination of Newton-Raphson interative scheme and a variable step size integrator based on the Runge-Kutta-Fehlburh fifth-order formulas. The integrator is used in conjunction with a modified Gram-Schmidt orthonormalization procedure. The computer program HADY-I calculates the growth rates of crossflow or streamwise Tollmien-Schlichting instabilities. It also calculates the group velocities of these disturbances. It is restricted to parallel stability calculations, where the boundary layer (meanflow) is assumed to be parallel. The meanflow solution is an input to the program.

Delay-feedback control strategy for reducing CO2 emission of traffic flow system

NASA Astrophysics Data System (ADS)

Zhang, Li-Dong; Zhu, Wen-Xing

2015-06-01

To study the signal control strategy for reducing traffic emission theoretically, we first presented a kind of discrete traffic flow model with relative speed term based on traditional coupled map car-following model. In the model, the relative speed difference between two successive running cars is incorporated into following vehicle's acceleration running equation. Then we analyzed its stability condition with discrete control system stability theory. Third, we designed a delay-feedback controller to suppress traffic jam and decrease traffic emission based on modern controller theory. Last, numerical simulations are made to support our theoretical results, including the comparison of models' stability analysis, the influence of model type and signal control on CO2 emissions. The results show that the temporal behavior of our model is superior to other models, and the traffic signal controller has good effect on traffic jam suppression and traffic CO2 emission, which fully supports the theoretical conclusions.

Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bisset, R. N.; Wang, Wenlong; Ticknor, C.

Here, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach and find good qualitative and quantitative agreement with our Bogoliubov–de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortex-ring states. We systematically capture these as stationary states of the system and quantifymore » their BdG spectra numerically. We found that although the vortex ring may be unstable when bifurcating, its instabilities weaken and may even eventually disappear for sufficiently large chemical potentials and suitable trap settings. For instance, we demonstrate the stability of the vortex ring for an isotropic trap in the large-chemical-potential regime.« less

Stabilization of solitons under competing nonlinearities by external potentials

NASA Astrophysics Data System (ADS)

Zegadlo, Krzysztof B.; Wasak, Tomasz; Malomed, Boris A.; Karpierz, Miroslaw A.; Trippenbach, Marek

2014-12-01

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

Rumor spreading model with the different attitudes towards rumors

NASA Astrophysics Data System (ADS)

Hu, Yuhan; Pan, Qiuhui; Hou, Wenbing; He, Mingfeng

2018-07-01

Rumor spreading has a profound influence on people's well-being and social stability. There are many factors influencing rumor spreading. In this paper, we recommended an assumption that among the common mass there are three attitudes towards rumors: to like rumor spreading, to dislike rumor spreading, and to be hesitant (or neutral) to rumor spreading. Based on such an assumption, a Susceptible-Hesitating-Affected-Resistant(SHAR) model is established, which considered individuals' different attitudes towards rumor spreading. We also analyzed the local and global stability of rumor-free equilibrium and rumor-existence equilibrium, calculated the basic reproduction number of our model. With numerical simulations, we illustrated the effect of parameter changes on rumor spreading, analyzing the parameter sensitivity of the model. The results of the theoretical analysis and numerical simulations illustrated the conclusions of this study. People having different attitudes towards rumors may play different roles in the process of rumor spreading. It was surprising to find, in our research, that people who hesitate to spread rumors have a positive effect on the spread of rumors.

The dynamics of a harvested predator-prey system with Holling type IV functional response.

PubMed

Liu, Xinxin; Huang, Qingdao

2018-05-31

The paper aims to investigate the dynamical behavior of a predator-prey system with Holling type IV functional response in which both the species are subject to capturing. We mainly consider how the harvesting affects equilibria, stability, limit cycles and bifurcations in this system. We adopt the method of qualitative and quantitative analysis, which is based on the dynamical theory, bifurcation theory and numerical simulation. The boundedness of solutions, the existence and stability of equilibrium points of the system are further studied. Based on the Sotomayor's theorem, the existence of transcritical bifurcation and saddle-node bifurcation are derived. We use the normal form theorem to analyze the Hopf bifurcation. Simulation results show that the first Lyapunov coefficient is negative and a stable limit cycle may bifurcate. Numerical simulations are performed to make analytical studies more complete. This work illustrates that using the harvesting effort as control parameter can change the behaviors of the system, which may be useful for the biological management. Copyright © 2018 Elsevier B.V. All rights reserved.

Impact of a single drop on the same liquid: formation, growth and disintegration of jets

NASA Astrophysics Data System (ADS)

Agbaglah, G. Gilou; Deegan, Robert

2015-11-01

One of the simplest splashing scenarios results from the impact of a single drop on on the same liquid. The traditional understanding of this process is that the impact generates a jet that later breaks up into secondary droplets. Recently it was shown that even this simplest of scenarios is more complicated than expected because multiple jets can be generated from a single impact event and there are bifurcations in the multiplicity of jets. First, we study the formation, growth and disintegration of jets following the impact of a drop on a thin film of the same liquid using a combination of numerical simulations and linear stability theory. We obtain scaling relations from our simulations and use these as inputs to our stability analysis. We also use experiments and numerical simulations of a single drop impacting on a deep pool to examine the bifurcation from a single jet into two jets. Using high speed X-ray imaging methods we show that vortex separation within the drop leads to the formation of a second jet long after the formation of the ejecta sheet.

Numerical Modelling and Analysis of Hydrostatic Thrust Air Bearings for High Loading Capacities and Low Air Consumption

NASA Astrophysics Data System (ADS)

Yu, Yunluo; Pu, Guang; Jiang, Kyle

2017-12-01

The paper presents a numerical simulation study on hydrostatic thrust air bearings to assess the load capacity, compressed air consumptions, and the dynamic response. Finite Difference Method (FDM) and Finite Volume Method (FVM) are combined to solve the non-linear Reynolds equation to find the pressure distribution of the air bearing gas film and the total loading capacity of the bearing. The influence of design parameters on air film gap characteristics, including the air film thickness, supplied pressure, depth of the groove and external load, are investigated based on the proposed FDM model. The simulation results show that the thrust air bearings with a groove have a higher load capacity and air consumption than without a groove, and the load capacity and air consumption both increase with the depth of the groove. Bearings without the groove are better damped than those with the grooves, and the stability of thrust bearing decreases when the groove depth increases. The stability of the thrust bearings is also affected by their loading.

Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates

DOE PAGES

Bisset, R. N.; Wang, Wenlong; Ticknor, C.; ...

2015-10-01

Here, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach and find good qualitative and quantitative agreement with our Bogoliubov–de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortex-ring states. We systematically capture these as stationary states of the system and quantifymore » their BdG spectra numerically. We found that although the vortex ring may be unstable when bifurcating, its instabilities weaken and may even eventually disappear for sufficiently large chemical potentials and suitable trap settings. For instance, we demonstrate the stability of the vortex ring for an isotropic trap in the large-chemical-potential regime.« less

Analysis of EDZ Development of Columnar Jointed Rock Mass in the Baihetan Diversion Tunnel

NASA Astrophysics Data System (ADS)

Hao, Xian-Jie; Feng, Xia-Ting; Yang, Cheng-Xiang; Jiang, Quan; Li, Shao-Jun

2016-04-01

Due to the time dependency of the crack propagation, columnar jointed rock masses exhibit marked time-dependent behaviour. In this study, in situ measurements, scanning electron microscope (SEM), back-analysis method and numerical simulations are presented to study the time-dependent development of the excavation damaged zone (EDZ) around underground diversion tunnels in a columnar jointed rock mass. Through in situ measurements of crack propagation and EDZ development, their extent is seen to have increased over time, despite the fact that the advancing face has passed. Similar to creep behaviour, the time-dependent EDZ development curve also consists of three stages: a deceleration stage, a stabilization stage, and an acceleration stage. A corresponding constitutive model of columnar jointed rock mass considering time-dependent behaviour is proposed. The time-dependent degradation coefficient of the roughness coefficient and residual friction angle in the Barton-Bandis strength criterion are taken into account. An intelligent back-analysis method is adopted to obtain the unknown time-dependent degradation coefficients for the proposed constitutive model. The numerical modelling results are in good agreement with the measured EDZ. Not only that, the failure pattern simulated by this time-dependent constitutive model is consistent with that observed in the scanning electron microscope (SEM) and in situ observation, indicating that this model could accurately simulate the failure pattern and time-dependent EDZ development of columnar joints. Moreover, the effects of the support system provided and the in situ stress on the time-dependent coefficients are studied. Finally, the long-term stability analysis of diversion tunnels excavated in columnar jointed rock masses is performed.

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Scalar Hairy Black Holes in Four Dimensions are Unstable

NASA Astrophysics Data System (ADS)

Ganchev, Bogdan; Santos, Jorge E.

2018-04-01

We present a numerical analysis of the stability properties of the black holes with scalar hair constructed by Herdeiro and Radu. We prove the existence of a novel gauge where the scalar field perturbations decouple from the metric perturbations, and analyze the resulting quasinormal mode spectrum. We find unstable modes with characteristic growth rates which for uniformly small hair are almost identical to those of a massive scalar field on a fixed Kerr background.