Showing papers on "Constant (mathematics) published in 2000"
Book•
24 Jan 2000
TL;DR: In this article, one item with a constant demand rate and time-varying demands is described. But, the model is based on a single item with constant lead times.
Abstract: 1 General Introduction2 Systems and Models3 One Item with a Constant Demand Rate4 Time-Varying Demands5 Several Products and Locations6 Stochastic Demand: One Item with Constant Leadtimes7 Stochastic Leadtimes: The Structure of the Supply System8 Several Items with Stochastic Demands9 Time-Varying, Stochastic Demand: Policy Optimization Bibliography Appendix A: Optimization and Convexity Appendix B: Dynamical Systems Appendix C: Probability and Stochastic Processes Appendix D: Notational Conventions
1,709 citations
TL;DR: In this paper, an analytical expression for the error in the sub-pixel displacement is derived, which relates the error to the second and fourth order moments of the intensity probability density function, which can both be expressed in terms of the source density.
Abstract: An analytical expression for the error in the sub-pixel displacement is derived. The expression relates the error to the second- and fourth-order moments of the intensity probability density function, which can both be expressed in terms of the source density. Scaling relations for the error as a function of the particle-image diameter are determined by means of the Cramer–Rao lower bound, for both constant image density and constant source density. The analytical expression is evaluated for the error as a function of the sub-pixel displacement, the particle-image diameter, and the image density, and the results are validated against results from Monte-Carlo simulations. It is demonstrated that results obtained from synthetic PIV images that do not represent the correct image intensity probability density function systematically underestimate the displacement measurement error.
410 citations
TL;DR: In this article, the authors consider the flow of gas in an N-dimensional porous medium with initial density v 0NxO 0.1, and prove that the L 1 -distance decays at a rate t 1=NNNC2Om NO.
Abstract: We consider the flow of gas in an N-dimensional porous medium with initial density v0NxO 0. The density vNx;tO then satisfies the nonlinear degenerate parabolic equa- tion vt E —v m where m> 1 is a physical constant. Assum- ing that R N1 Cj x j 2 Ov0NxOdx < 1, we prove that vNx;tO be- haves asymptotically, as t !1 , like the Barenblatt-Pattle solu- tion VNjxj;tO. We prove that the L 1 -distance decays at a rate t 1=NNNC2Om NO .M oreover, if N E1, we obtain an explicit time decay for the L 1 -distance at a suboptimal rate. The method we use is based on recent results we obtained for the Fokker-Planck equation (2), (3).
316 citations
TL;DR: In this paper, a simple method requiring only hardness and modulus of elasticity is proposed for estimation of the strain-life curve, and the prediction capability of this method is evaluated for steels with hardness between 150 and 700 HB.
314 citations
TL;DR: In this paper, the authors used the particle tracking technique to study turbulent diffusion of particle pairs in a three-dimensional turbulent flow generated by two oscillating grids, and compared the predictions of three models: Richardson (1926), Batchelor (1952) and Kraichnan (1966a).
Abstract: The particle tracking (PT) technique is used to study turbulent diffusion of particle pairs in a three-dimensional turbulent flow generated by two oscillating grids. The experimental data show a range where the Richardson–Obukhov law 〈r2〉 = Cet3 is satisfied, and the Richardson–Obukhov constant is found to be C = 0.5. A number of models predict much larger values. Furthermore, the distance–neighbour function is studied in detail in order to determine its general shape. The results are compared with the predictions of three models: Richardson (1926), Batchelor (1952) and Kraichnan (1966a). These three models predict different behaviours of the distance–neighbour function, and of the three, only Richardson's model is found to be consistent with the measurements. We have corrected a minor error in Kraichnan's (1996a) Lagrangian history direct interaction calculations with the result that we had to increase his theoretical value from C = 2.42 to C = 5.5.
299 citations
TL;DR: EJIIM generalizes the class of problems for which FIIIM is applicable and handles interfaces between constant and variable coefficients and extends the immersed interface method (IIM) to BVPs on irregular domains with Neumann and Dirichlet boundary conditions.
Abstract: Many boundary value problems (BVPs) or initial BVPs have nonsmooth solutions, with jumps along lower-dimensional interfaces. The explicit-jump immersed interface method (EJIIM) was developed following Li's fast iterative immersed interface method (FIIIM), recognizing that the foundation for the efficient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for which FIIIM is applicable. It handles interfaces between constant and variable coefficients and extends the immersed interface method (IIM) to BVPs on irregular domains with Neumann and Dirichlet boundary conditions. Proofs of second order convergence for a one-dimensional (1D) problem with piecewise constant coefficients and for two-dimensional (2D) problems with singular sources are given. Other problems are reduced to the singular sources case, with additional equations determining the source strengths. The advantages of EJIIM are high quality of solutions even on coarse grids and easy adaptation to many problems with complicated geometries, while still maintaining the efficiency of the FIIIM.
289 citations
TL;DR: In this article, a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI) is presented. But the only information about the nonlinearity is that it satisfies a linear constraint, and the major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the non-linearity which the system can tolerate without going unstable.
Abstract: This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI). The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable.
260 citations
TL;DR: Drift is one of the most serious impairments afflicting gas sensors and it can be seen as a gradual change in the sensor response over a long period of time when the external conditions an constant as mentioned in this paper.
Abstract: Drift is one of the most serious impairments afflicting gas sensors. It can be seen as a gradual change in the sensor response over a long period of time when the external conditions an constant. T ...
259 citations
TL;DR: The time-dependence of the climate response has implications for the use of simpler models in scaling GCM results to different scenarios of forcing as discussed by the authors, and has been shown to be associated with differences in cloud feedback arising from inter-hemispheric temperature differences due to the slower warming rate of the Southern Ocean.
Abstract: A doubled CO2 coupled ocean-atmosphere experiment has been run for over 800 years. The ‘effective’ equilibrium climate sensitivity to a doubling of CO2 (the equilibrium response of the model assuming the feedbacks remained constant at the value found at any given point of the transient response) is calculated throughout the run and found to increase by around 40%. The time-dependence is associated with differences in cloud feedback arising from inter-hemispheric temperature differences due to the slower warming rate of the Southern Ocean. The time-dependence of the climate response has implications for the use of simpler models in scaling GCM results to different scenarios of forcing.
253 citations
TL;DR: In this paper, a method is presented for examining dissipated energy to select a consistent level of material behavior that is indicative of the damage accumulation in the mixture, showing the similarity between the constant stress and constant strain modes of testing and providing the potential for unifying the now phenomenological description of fatigue.
Abstract: Determination of the failure limit in a repeated-load fatigue test in the laboratory has relied entirely on the arbitrary selection of a fixed criterion. The constant strain and constant stress modes of fatigue loading have been described by a consistent definition of failure in flexural fatigue testing because of the distinctly different application of energy during the loading history. The most widely accepted definition is a decrease in initial stiffness by 50 percent. Procedures examining energy input and dissipated energy have required different schemes for each mode in an attempt to describe similar states of damage in the mixture. A proposed method is presented for examining dissipated energy to select a consistent level of material behavior that is indicative of the damage accumulation in the mixture. This procedure shows the similarity between the constant stress and constant strain modes of testing and is shown to provide the potential for unifying the now phenomenological description of fatigue...
251 citations
TL;DR: In this article, the authors studied the general asymptotic behavior of critical points, including those of non-minimal energy type, of the functional for the van der Waals-Cahn-Hilliard theory of phase transitions.
Abstract: We study the general asymptotic behavior of critical points, including those of non-minimal energy type, of the functional for the van der Waals-Cahn-Hilliard theory of phase transitions. We prove that the interface is close to a hypersurface with mean curvature zero when no Lagrange multiplier is present, and with locally constant mean curvature in general. The energy density of the limiting measure has integer multiplicity almost everywhere modulo division by a surface energy constant.
TL;DR: In this article, it was shown that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere", provided that the data are in a certain sense outside the range of the operator to be inverted.
Abstract: In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.
TL;DR: In this article, the authors compared theories formulated on the basis of the classical Principle of Virtual Displacements (PVD) to mixed theories formulated by the Reissner Mixed Variational Theorem (RMVT) to evaluate the thermal response of orthotropic laminated plates.
Abstract: This article compares theories formulated on the basis of the classical Principle of Virtual Displacements (PVD) to mixed theories formulated on the basis of the Reissner Mixed Variational Theorem (RMVT) to evaluate the thermal response of orthotropic laminated plates. So-called layer-wise (LW) and equivalent single-layer (ESL) modelings have been developed for both classical and mixed approaches (each layer is considered as a single plate for LW analysis, while the unknown variables are independent of the number of the constitutive layers for the ESL cases). Linear up-to fourth-order displacement and stress field cases have been implemented to derive thermomechanical governing equations, consistent with the used variational statements. All the theories have been presented in a unified manner by referring to findings recently presented by the author. The numerical investigation has been restricted to a simply supported plate loaded by harmonic distribution of in-plane temperature fields. Constant and line...
TL;DR: This work designs an output feedback integral controller that asymptotically regulates the output to a bounded time-varying reference signal with a constant limit and shows that, for relative degree one and two systems, the proposed integral controller reduces to the classical PI and PID controllers.
Abstract: We consider a single-input-single-output (SISO) nonlinear system that has a well-defined normal form with asymptotically stable zero dynamics. Using only knowledge of the relative degree and the sign of the high-frequency gain, we design an output feedback integral controller that asymptotically regulates the output to a bounded time-varying reference signal with a constant limit. We give regional as well as semi-global results. We also show that, for relative degree one and two systems, the proposed integral controller reduces to the classical PI and PID controllers, respectively.
TL;DR: In this paper, a new Monte Carlo method for solving the population balance problem with multiple growth processes is presented, which samples a constant number of particles regardless of whether the actual growth process results in increase or decrease of the particle concentration.
TL;DR: In this paper, the Enskog-Boltzmann equation is simulated for a spatially uniform system of smooth inelastic spheres, where the particles are assumed to be under the action of an external driving force which does work to compensate for the collisional loss of energy.
Abstract: Direct Monte Carlo simulations of the Enskog-Boltzmann equation for a spatially uniform system of smooth inelastic spheres are performed. In order to reach a steady state, the particles are assumed to be under the action of an external driving force which does work to compensate for the collisional loss of energy. Three different types of external driving are considered: (a) a stochastic force, (b) a deterministic force proportional to the particle velocity and (c) a deterministic force parallel to the particle velocity but constant in magnitude. The Enskog-Boltzmann equation in case (b) is fully equivalent to that of the homogeneous cooling state (where the thermal velocity monotonically decreases with time) when expressed in terms of the particle velocity relative to the thermal velocity. Comparison of the simulation results for the fourth cumulant and the high energy tail with theoretical predictions derived in cases (a) and (b) [T. P. C. van Noije and M. H. Ernst, Gran. Matt. 1, 57 (1998)] shows a good agreement. In contrast to these two cases, the deviation from the Maxwell-Boltzmann distribution is not well represented by Sonine polynomials in case (c), even for low dissipation. In addition, the high energy tail exhibits an underpopulation effect in this case.
TL;DR: In this article, it was shown that no conformally flat foliations of the Kerr spacetime can exist, and that the standard Boyer-Lindquist time spatial slices of the spacetime are not conformal flat, so that using the Bowen-York approach is limited in dealing with rotating holes.
Abstract: Initial data for black hole collisions are commonly generated using the Bowen-York approach based on conformally flat 3-geometries. The standard (constant Boyer-Lindquist time) spatial slices of the Kerr spacetime are not conformally flat, so that use of the Bowen-York approach is limited in dealing with rotating holes. We investigate here whether there exist foliations of the Kerr spacetime that are conformally flat. We limit our considerations to foliations that are axisymmetric and that smoothly reduce in the Schwarzschild limit to slices of constant Schwarzschild time. With these restrictions, we show that no conformally flat slices can exist.
TL;DR: In this paper, the authors identify large classes of theories in which this assumption is justified and show that the a priori probability distribution for the cosmological constant is essentially constant in the very narrow range that is anthropically allowed.
Abstract: In calculations of the probability distribution for the cosmological constant, it has been previously assumed that the a priori probability distribution is essentially constant in the very narrow range that is anthropically allowed. This assumption has recently been challenged. Here we identify large classes of theories in which this assumption is justified.
TL;DR: In this article, a unified numerical method is developed for the analysis of deformations and stresses in elastic-plastic rotating disks with arbitrary cross-sections of continuously variable thickness and arbitrarily variable density made of nonlinear strain-hardening materials.
02 Mar 2000
TL;DR: In this article, a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open was given, which is similar to a theorem of Landau on bounded holomorphic functions.
Abstract: We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic functions as a special case. Also, for bounded planar harmonic mappings, we obtain results similar to a theorem of Landau on bounded holomorphic functions.
TL;DR: In this article, Bahri and Brezis [BB], Bahri [B], and Schoen [S2-3] showed that a large class of compact Riemannian manifolds with boundary are conformally equivalent to one with constant scalar curvature and zero mean curvature on the boundary.
Abstract: Let (M,g) be an n dimensional compact, smooth, Riemannian manifold without boundary. For n = 2, the Uniformization Theorem of Poincare says that there exist metrics on M which are pointwise conformal to g and have constant Gauss curvature. For n > 3, the well known Yamabe conjecture states that there exist metrics on M which are pointwise conformal to g and have constant scalar curvature. The Yamabe conjecture has been proved through the work of Yamabe [Y], Trudinger [T], Aubin [A], and Schoen [SI]. See Lee and Parker [LP] for a survey. See also Bahri and Brezis [BB], Bahri [B], and Schoen [S2-3] for works on the problem and related ones. Analogues of the Yamabe problem for compact Riemannian manifolds with boundary have been studied by Cherrier, Escobar, and others. In particular, Escobar proved in [E2] that a large class of compact Riemannian manifolds with boundary are conformally equivalent to one with constant scalar curvature and zero mean curvature on the boundary. See also [E3][E5] for related results. From now on in the paper, (M, g) denotes some smooth compact n dimensional Riemannian manifold with boundary, unless we specify otherwise. We use M to denote the interior of M, and dM the boundary of M. We use n — 2 d n — 2 La to denote An—c(n)Ra, where c(n) is — —, BQ to denote ——I—-—hQ, y y * 4(n -1) y du 2 y where u is the outward unit normal on dM with respect to 5, and hg to denote the mean curvature of dM with respect to the inner normal (balls in R have positive mean curvatures).
Posted Content•
22 Dec 2000
TL;DR: In this paper, the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time are derived, in two different frameworks, whether the scaling dependences of these constants spoil primordial nucleosynthesis.
Abstract: In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the ``cosmological constant'' is not a constant in a quantum field theory context, still less should be zero. In this paper we continue with previous work, and derive the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time. At higher energies the calculation is performed in a sharp cut off approximation. We assess, in two different frameworks, whether the scaling dependences of the cosmological and gravitational constants spoil primordial nucleosynthesis. Finally, the cosmological implications of the running of the cosmological constant are discussed.
TL;DR: In this article, the derivative corrections to the effective action for a single Dbrane in type II superstring theory coupled to constant background fields were studied. And the results were obtained via string sigma-model loop calculations using the boundary state operator language.
Abstract: We study derivative corrections to the effective action for a single D-brane in type II superstring theory coupled to constant background fields. In particular, within this setting we determine the complete expression for the (disk level) four-derivative corrections to the Born-Infeld part of the action. We also determine 2n-form 2n-derivative corrections to the Wess-Zumino term. Both types of corrections involve all orders of the gauge field strength, F. The results are obtained via string sigma-model loop calculations using the boundary state operator language. The corrections can be succinctly written in terms of the Riemann tensor for a non-symmetric metric.
TL;DR: In this paper, the authors derived the isothermal mechanical response of a 4-element rheological model for shape memory polymers (SMP) in the context of constant stress, constant strain, constant stress rate, and periodic strain.
Abstract: In this paper, we derive the isothermal mechanical response of a 4-element rheological model for shape memory polymers (SMP) in the context of (i) constant stress, (ii) constant strain, (iii) constant stress rate, (iv) constant strain rate, (v) periodic strain. The effect of shape memory strain (modeled by a friction element) and the temperature dependence of the material properties on the SMP response are examined for a polyurethane shape memory polymer of the polyester polypole series. In particular, it is possible to identify a threshold frequency during periodic loading, near which the damping capacity of the SMP is strongly affected by an increasing shape memory strain. On the other hand, when the applied frequency is much greater than the threshold value, an increasing shape memory strain ceases to have any effect on the damping. It is also shown that at a given frequency (significantly greater than the threshold value), the damping capacity as a function of temperature attains a maximum. While this maximum value is frequency-dependent (being inversely proportional), the temperature at which the maximum is attained is frequency-independent, and is analytically shown to be the glass transition temperature.
15 Jul 2000
TL;DR: In classical timed automata, as defined by Alur and Dill and since widely studied, the only operation allowed to modify the clocks is the reset operation, and in details such updates are studied.
Abstract: In classical timed automata, as defined by Alur and Dill [AD90,AD94] and since widely studied, the only operation allowed to modify the clocks is the reset operation. For instance, a clock can neither be set to a non-null constant value, nor be set to the value of another clock nor, in a non-deterministic way, to some value lower or higher than a given constant. In this paper we study in details such updates.
TL;DR: In this article, the R/sub 2/ estimation in the transient state without signal injection to the stator current is proposed, which uses the least mean square algorithm and the adaptive algorithm.
Abstract: In the speed sensorless control of the induction motor, the machine parameters (especially rotor resistance R/sub 2/) have a strong influence on the speed estimation. It is known that the simultaneous estimation of the rotor speed and R/sub 2/ is impossible in the slip frequency type vector control, because the rotor flux is constant. But the rotor flux is not always constant in the speed transient state. In this paper, the R/sub 2/ estimation in the transient state without signal injection to the stator current is proposed. This algorithm uses the least mean square algorithm and the adaptive algorithm, and it is possible to estimate R/sub 2/ exactly. This algorithm is verified by the digital simulations and experiments.
TL;DR: The aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations, and sensitivity analysis.
Abstract: Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear inequality systems. In the latter case our constant may be computed explicitly.
TL;DR: In this paper, a low-order dynamic model for multicomponent distillation processes is presented, which makes use of well-known spatio-temporal pattern formation phenomena also termed as nonlinear wave propagation.
TL;DR: In this paper, the string-inspired technique is used for the calculation of vacuum polarisation tensors in constant electromagnetic fields, and the two-point cases are calculated explicitly, leading to compact representations for the constant field vacuum polarization tensors for both scalar and spinor QED.
TL;DR: In this paper, a two-dimensional two-component plasma model is considered and the authors present the explicit forms of the density-fugacity relationship and specific heat per particle.
Abstract: The model under consideration is a two-dimensional two-component plasma, stable against collapse for the dimensionless coupling constant β<2. The combination of a technique of renormalized Mayer expansion with the mapping onto the sine-Gordon theory provides the full thermodynamics of the plasma in the whole stability range of β. The explicit forms of the density–fugacity relationship and of the specific heat (at constant volume) per particle are presented.