Inconsistent Initial Conditions Research Articles

Study on curing characteristics of cold-mixed and cold-laid asphalt mixture based on electrical properties

Determination of the rolling time of cold-mixed and cold-laid asphalt mixture is crucial to the operational process and performance of the road. The moisture content of the cold-mixed and cold-laid asphalt mixture is directly related to its curing performance. The research purpose of this paper includes the development of a device for stably testing the electrical properties of cold mixed and cold paving asphalt mixture, the monitoring of water content, and electrical properties of cold mixed and cold paving asphalt mixture at different curing times. The electrical properties of cold-mixed and cold-laid asphalt mixture were tested by a digital bridge instrument (LCR). The relationship model between moisture content and electrical properties was established. The normalization method is used to deal with the electrical performance parameters to avoid the influence of inconsistent initial conditions. The results show that the absolute values of resistance, impedance and inductance of all kinds of emulsified asphalt and their mixtures increase with the decrease of moisture content, and the absolute value of capacitance decreases with the decrease of moisture content. Normalized resistance value, inductance value and impedance value can accurately judge whether the cold-mixed and cold-laid asphalt mixture has been fully cured. The cement absorbs water for hydration, which also increases the mixture's temperature and speeds up the curing rate. When the normalized resistance value is 10 at any A.C. frequency(100 Hz ∼ 100 kHz), it can be considered that the cold-mixed and cold-laid asphalt mixture can be rolled. When the normalized inductance value reaches 100 at a high frequency(100 kHz, 40 kHz), it can also be used as the evaluation index. From the aspects of electrical properties, this paper provided an experimental basis for the construction quality control of cold-mixed and cold-laid asphalt mixture.

Biochemically Tracked Variability of Blood Plasma Thawed-State Exposure Times in a Multisite Collection Study.

The integrity of blood plasma/serum (P/S) specimens can be impacted by preanalytical handling and storage conditions that result in thawed-state exposures (> -30°C). We recently reported a simple dilute-and-shoot, intact-protein liquid chromatography/mass spectrometry (LC/MS) assay called ΔS-Cys-Albumin that quantifies cumulative exposure of P/S to thawed conditions based on the change in relative abundance of the oxidized (S-cysteinylated) proteoform of albumin (S-Cys-Albumin) in the native sample to that of an aliquot of the sample intentionally driven to its maximum oxidation state. Herein, we evaluated the effect of prestorage delay and initial storage temperature on sample integrity by applying the ΔS-Cys-Albumin assay to a set of plasma samples (n = 413) collected under a single clinical study but from 12 different collection sites. Major differences (p < 0.0001) were observed between different groups of samples with modestly inconsistent initial handling conditions (i.e., initial processing of whole blood to plasma and placement at -80°C completed in under 3 hours, 3-13 hours, and over 17 hours). ΔS-Cys-Albumin was significantly inversely correlated with delay time at 4°C before centrifugation and total delay before final storage at -80°C (p < 0.0001). Samples from two collection sites had much lower ΔS-Cys-Albumin values relative to samples from other sites, in accordance with the fact that they were stored at -20°C for an average of 7.6 months before shipment to the central repository for final storage at -80°C. Based on the rate law for S-Cys-Albumin formation in plasma ex vivo, the average time that each plasma specimen had been exposed to the equivalent of room temperature (23°C) was back calculated from the measured ΔS-Cys-Albumin values. A survey of clinical analytes in P/S whose measured concentrations are sensitive to the initial handling/storage conditions documented in this study is provided and the ramifications of the plasma integrity findings from this multisite clinical study are discussed.

Model of grout filtration in a porous soil

To strengthen the foundations and protect them from ground water, liquid grout is pumped under pressure into a loose porous soil. Modern construction techniques use colloids or suspensions which form a waterproof layer upon solidification. Calculation of grout distribution in a porous soil is an important part of designing buildings and structures. The distribution of suspended particulates in unconsolidated soil is described by mathematical equations of particles filtration in the porous media. The aim of this work is modelling of suspended particles transport and deposit formation in a porous soil for different filtration modes. The distributions of solid particles of different sizes transported by the carrier fluid and retained on the frame of the porous medium at different kinetic rates of deposit growth are examined. Model of one-dimensional filtration with size-exclusion particle retention mechanism includes a hyperbolic system of the first order differential equations with inconsistent initial and boundary conditions that leads to discontinuous solutions. A modified mathematical model for polydisperse media with the competition between particles of different sizes for small pores is considered. The computational scheme for numerical solutions is constructed by finite difference method. Optimization methods to improve convergence and reduce computation time are used. A multi-particle model of grout filtration in a porous soil is constructed, considering the variety of sizes of suspended particles. A numerical calculation of the problem is performed for various blocking filtration coefficient. Solutions are obtained with a discontinuity on the concentration front. Approbation of the obtained numerical solutions is carried out. Plots of the suspended and retained particles concentrations depending on time and coordinates are constructed. A new model of multi-particle transport in a porous medium widely extends the design capabilities of waterproof underground walls. The solution of the filtration problem for solid particles of different sizes makes it possible to calculate the optimal composition of grout for constructing a waterproof layer in a porous soil. The developed computing finite-difference methods allow to obtain the numerical solution of complex systems of equations with good accuracy and a moderate amount of computation.

Conditional Events and Quantum Logic

This paper begins with an overview of quantum mechanics, and then recounts a relatively recent algebraic extension of the Boolean algebra of probabilistic events to “conditional events” (order pairs of events). The main point is to show that a so-called “superposition” of two (or more) quantum events (usually with mutually inconsistent initial conditions) can be represented in this algebra of conditional events and assigned a consistent conditional probability. There is no need to imagine that a quantum particle can simultaneously straddle two inconsistent possibilities.

General mapping discrete-time models of a descriptor system with an arbitrary initial condition

The definition of discretization proposed previously by the authors for continuous-time signals is extended to include an impulse and its derivatives, and then applied to descriptor systems that produce such signals. This definition provides bases for the continuous-time impulses to have their discrete-time counterparts, by taking values at multiple sampling points into account, rather than a single point that has traditionally been used for ordinary functions. Theorems are developed based on the definition, one of which provides a useful formula for choosing a sufficient initial-condition for a discrete-time descriptor system such that its initial response corresponds, in the sense of the proposed discretization definition, to the continuous-time original. This solves the long-standing issue of ambiguity surrounding discontinuous initial responses and that of inconsistent initial conditions that have obscured the validity of discrete-time descriptor models and of their numerical computations.

Consistent initial conditions for the Saint-Venant equations in river network modeling

Abstract. Initial conditions for flows and depths (cross-sectional areas) throughout a river network are required for any time-marching (unsteady) solution of the one-dimensional (1-D) hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths). These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1) the pseudo time-marching method (PTM) that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2) the steady-solution method (SSM) that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

Closed form solution for the equations of motion for constrained linear mechanical systems and generalizations: An algebraic approach

In this paper, a mathematical methodology is presented for the determination of the solution of motion for linear constrained mechanical systems applicable also to systems with singular coefficients. For mathematical completeness and also to incorporate some other interesting cases, the methodology is formulated for a general class of higher order matrix differential equations. Thus, describing the system in an autoregressive moving average (ARMA) form, the closed form solution is derived in terms of the finite and infinite Jordan pairs of the system׳s polynomial matrix. The notion of inconsistent initial conditions is considered and an explicit formula for the homogeneous system is given. In this respect, the methodology discussed in the present note provides an alternative view to the problem of computation of the response of complex multi-body systems. Two interesting examples are provided and applications of the equation to such systems are illustrated.

MAPPING DISCRETE-TIME MODELS FOR DESCRIPTOR-SYSTEMS WITH CONSISTENT INITIAL CONDITIONS

Discretization of a regular continuous-time descriptor-system, whose initial condition is consistent with its input, is considered using a general mapping method presented in our previous paper. The proposed mapping discrete-time model is shown to be a proper discretization under the definition explained in the paper. This assures that the response of the mapping model approaches that of the continuous-time descriptor system as the sampling period approaches zero. The consistency of initial conditions for the discrete-time model is also studied and the long-standing issue of ambiguities surrounding irregularities of discrete-time responses at the initial time are clarified with a simple solution. A proper range of design parameters are investigated and their suitable choices suggested. To illustrate the use of the proposed method, a simple circuit that cannot be expressed in the ordinary state-space form is considered. Its responses to a sinusoidal input when started from the consistent and inconsistent initial conditions are simulated to show that the irregularities at the initial time can be overcome easily. The proposed technique provides a convenient simulation and design environment for handling discrete-time systems in a unified manner with consistency and ease.

-Stable Derivative-Free Error-Corrected Trapezoidal Rule for Burgers' Equation with Inconsistent Initial and Boundary Conditions

We combine suitable arithmetic average approximations, with explicit backward Euler formula, and derive a third-order -stable derivative-free error-corrected trapezoidal rule (LSDFECT). Then, we apply LSDFECT rule to the linearized Burgers' equation with inconsistent initial and boundary conditions and test its stability and exactness. We use Mathematica 7.0 for computation.

A perturbation approach for consistent initialization of index-1 explicit differential–algebraic equations arising from battery model simulations

Estimation of consistent initial conditions is very crucial for the successful solution of differential–algebraic equation (DAE) systems that arise in many fields of science and engineering. In this paper, an efficient perturbation approach for initialization of DAE systems of index-1 is proposed and implemented for DAE models governing batteries. In addition, different existing solvers are compared for consistent initialization of DAE systems. The proposed approach does not necessarily require a nonlinear solver for initialization and builds on the applicability and usability of robust and efficient explicit, linearly implicit and semi-implicit integrators in time. Three different problems are presented wherein the proposed approach is observed to work for a wider range of inconsistent initial conditions compared to other existing generally used routines. It is also observed that the present approach is computationally efficient compared to the other existing approaches in a given environment.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventional simulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter.

Are symmetric tidal streams possible with long-range dark-matter forces?

The unique dynamics of the tidal disruption of satellite galaxies is an extremely sensitive probe of long-range interactions between dark-matter particles. Dark-matter forces that are several percent the strength of gravity will lead to order unity changes in the ratio of the number of stars in the leading and trailing tidal streams of a satellite galaxy. The approximate symmetry of the stellar tidal streams of the Sagittarius dwarf galaxy would thus exclude attractive dark-matter forces greater than 10% the strength of gravity which would entirely eliminate the leading stream. However, recent simulations suggest that dark-matter forces 100% the strength of gravity could completely strip the stellar component of Sagittarius of its dark matter, allowing for the subsequent development of symmetric tidal streams. Here we argue that these simulations use inconsistent initial conditions corresponding to separate pure stellar and pure dark-matter satellites moving independently in the host galaxy's halo, rather than a single disrupting composite satellite as had been intended. A new simulation with different initial conditions, in particular a much more massive satellite galaxy, might demonstrate a scenario in which symmetric tidal streams develop in the presence of large dark-matter forces. This scenario must satisfy several highly restrictive criteria described in this paper.

Eliminating constraint drift in the numerical simulation of constrained dynamical systems

By means of the Udwadia–Kalaba approach we propose an explicit equation of constrained motion developed to simulate constrained dynamical systems without error accumulation due to constraint drift. The basic idea is to embed a small virtual force and a small virtual impulse to the equation of motion, in order to avoid the drift typically experienced in constrained multibody simulations. The embedded correction terms are selected to minimally alter the dynamics in an acceleration and kinetic energy norm sense. The formulation allows one to use a standard ODE solver, avoiding the need for iterative constraint stabilization. The equation is based on the pseudoinverse of a constraint matrix such that it can be used under redundant constraints and kinematic singularities. The proposed method takes into account the finite word-length of the computational environment, and also accommodates possibly inconsistent initial conditions.

A New Perspective for Modeling Power Electronics Converters: Complementarity Framework

The switching behavior of power converters with ldquoidealrdquo electronic devices (EDs) makes it difficult to define a switched model that describes the dynamics of the converter in all possible operating conditions, i.e., a ldquocompleterdquo model. Indeed, simplifying assumptions on the sequences of modes are usually adopted, also in order to obtain averaged models and discrete-time maps. In this paper, we show how the complementarity framework can be used to represent complete switched models of a wide class of power converters, with EDs having characteristics represented by piecewise-affine (even complicated) relations. The model equations can be written in an easy and compact way without the enumeration of all converter modes, eventually formalizing the procedure to an algorithm. The complementarity model can be used to perform transient simulations and time-domain analysis. Mathematical tools coming from nonlinear programming allow to simulate numerically the transient behavior of even complex power converters. Also rigorous time-domain analysis is possible without excluding pathological situations like, for instance, inconsistent initial conditions and simultaneous switchings. Basic converter topologies are used as examples to show the construction procedure for the complementarity models and their usefulness for simulating the dynamic evolution also for nontrivial operating conditions.

Soil organic carbon dynamics at the regional scale as influenced by land use history: a case study in forest soils from southern Belgium

AbstractLand use change (LUC) is known to have a large impact on soil organic carbon (SOC) stocks. However, at a regional scale, our ability to explain SOC dynamics is limited due to the variability generated by inconsistent initial conditions between sample points, poor spatial information on previous land use/land management history and scarce SOC inventories. This study combines the resampling in 2003–2006 of an extensive soil survey in 1950–1960 with exhaustive historical data on LUC (1868–2006) to explain observed changes in the SOC stocks of temperate forest soils in the Belgian Ardennes. Results from resampling showed a significant loss of SOC between the two surveys, associated with a decrease in variability. The mean carbon content decreased from 40.4 to 34.5 g C kg−1 (10.6 to 9.6 kg C m−2), with a mean rate of C change (ΔSOC) of −0.15 g C kg−1 year−1 (−0.023 kg C m−2 year−1). Soils with high SOC content tended to loose carbon while conversely soils with low SOC tended to gain carbon. Land use change history explained a significant part of past and current SOC stocks as well as ΔSOC during the last 50 years. We show that the use of spatially explicit historical data can help to quantitatively explain changes in SOC content at the regional scale.

Viscous boundary layers in flows through a domain with permeable boundary

The effect of small viscosity on nearly inviscid flows of an incompressible fluid through a given domain with permeable boundary is studied. The Vishik–Lyusternik method is applied to construct a boundary layer asymptotic at the outlet in the limit of vanishing viscosity. Mathematical problems with both consistent and inconsistent initial and boundary conditions at the outlet are considered. It is shown that in the former case, the viscosity leads to a boundary layer only at the outlet. In the latter case, in the leading term of the expansion there is a boundary layer at the outlet and there is no boundary layer at the inlet, but in higher order terms another boundary layer appears at the inlet. To verify the validity of the expansion, a number of simple examples are presented. The examples demonstrate that asymptotic solutions are in quite good agreement with exact or numerical solutions.

Remark on the solution of linear time‐invariant descriptor systems

AbstractFor linear time‐invariant descriptor systems the correct solution in the sense of distributions is discussed for inconsistent initial conditions. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Time-domain response and sensitivity of periodically switched nonlinear circuits

This paper presents a new sampled-data simulation method for analysis of the response and sensitivity of periodically switched circuits with mildly nonlinear elements at time points of an equal interval. Using the Volterra functional series and interpolating the Fourier series, the method extends the sampled-data simulation algorithm of linear circuits to periodically switched nonlinear circuits. In addition, it extends the two-step algorithm for periodically switched linear circuits to periodically switched nonlinear circuits to handle inconsistent initial conditions encountered at switching instants. The method is a general computer-oriented formulation method. It does not require costly Newton-Raphson iterations. Instead, it performs preprocessing computation of a set of constant matrices and vectors that are used in subsequent simulation steps. The response and sensitivity at time points of an equal space are obtained using elementary matrix algebra. The method is most effective if the nonlinear characteristics of circuits is mild and computationally efficient if the response and sensitivity over a long period of time are needed. The method has been implemented in a computer program. Simulation results on example circuits are compared with those from PSPICE, brute-force (BF), charge conservation, and linear multistep predictor-corrector methods to show the speed and accuracy of the method. The normalized difference between the response and sensitivity of example circuits obtained from the proposed method and those from PSPICE and BF at nonswitching time points is below 0.5%. The accuracy of the method at switching time points is verified using charge conservation.

Computer methods for switched circuits

This paper presents a state-of-the-art review of the recent advances in computer methods for analysis and design of switched circuits in both time and frequency domains. It also presents new research results on time-domain analysis and sensitivity of switched nonlinear circuits, time- and frequency-domain statistical analysis of switched linear and nonlinear circuits, and efficient modeling and analysis of clock feedthrough and charge injection in switched linear circuits. In time-domain analysis, the modeling of switches and its effect on the simulation of switched circuits are investigated. Formulation methods for these circuits are examined. Inconsistent initial conditions arising from ideal switching are investigated and numerical methods that derive the consistent initial conditions are examined. Sampled-data simulation (SDSIM) of switched linear circuits including clocked sigma-delta modulators is investigated. SDSIM is extended to switched nonlinear circuits. Time-domain sensitivity of switched linear and nonlinear circuits is analyzed using SDSIM. Efficient time-domain statistical analysis of switched linear and nonlinear circuits is introduced, and their effectiveness is assessed using Monte Carlo simulation. Methods that compute the effect of the clock jitter of periodically switched linear (PSL) circuits are examined. Time-domain noise analysis of PSL circuits is investigated. In frequency-domain analysis, exact frequency analysis of multiphase PSL circuits is reviewed. Sensitivity analysis of these circuits is examined in detail. Adjoint network theory and its usefulness in noise and sensitivity analysis of switched linear circuits are studied. Group delay of PSL circuits is investigated briefly. Efficient modeling and analysis of clock feed-though and charge injection of PSL circuits are introduced. Distortion and sensitivity of periodically switched nonlinear circuits with mild nonlinearities are investigated. Finally, frequency-domain noise analysis of PSL circuits is examined.

On inconsistent initial conditions for linear time-invariant differential-algebraic equations

Given an arbitrary initial value x/sub 0//sup -/ for the differential-algebraic equation Ax/spl dot/(t)+Bx(t)=f(t), an initial value x/sub 0//sup +/ can be selected from among all consistent initial values by means of the Laplace transform. We show that this choice is the only one that fulfills some simple, physically reasonable assumptions on linear systems' behavior. Our derivation is elementary compared to previous justifications of the above Laplace transform based method. We also characterize x/sub 0//sup +/ by means of a system of linear equations involving A, B, derivatives of f, and x/sub 0//sup -/, which gives a new method to numerically calculate x/sub 0//sup +/.