Discrete Shocks Research Articles

Optimizing the Spare Unit Ordering Strategies for Replacement Under Constrained Availability From a Mathematical Perspective

This article investigates the optimal ordering policies of spare parts for preventive replacement of a single component deteriorating system in this article. The operational system suffers from a deterioration process and is also subject to random shocks during its service, where discrete shocks are categorized into fatal ones and nonfatal ones. To preventing the catastrophic losses resulting from degraded failures or shock incurred failures, a spare unit for replacement is ordered at some time between the system’s initial operation and its undesirable failure. The average cost rate with lower-limit constrained availability is minimized to seek the optimal spare unit ordering time, in which the Kuhn–Tucker necessary condition is satisfied. As a comparison strategy, the expected cost effectiveness defined as the ratio of system availability to average cost rate is maximized to dynamically adjust the optimum ordering time of the spare unit. Numerical experiments are designed to validate the existence and uniqueness of the joint optimal spare unit ordering and preventive replacement policies, as well sensitivity analysis of critical parameters are conducted.

Resilience of socially valued properties of natural systems to repeated disturbance: A framework to support value‐laden management decisions

AbstractAs global change delivers new disturbance patterns to agricultural and ecological systems, there is profound concern that many of the natural systems on which humans rely are exhibiting gradual declines or sudden regime shifts. We describe a “flow‐kick” paradigm for modeling populations subject to regular patterns of discrete shocks, and use it to develop a framework that both identifies management strategies to achieve socially valued system properties and characterizes resilience of these properties to changing disturbance patterns. We apply the framework to four examples of logistically growing species where the socially valued properties are assumed to be (i) high abundance, (ii) low abundance, (iii) fishery yield, and (iv) fishery profit. In Example 3, we describe how the flow‐kick approach generalizes the classical maximum sustainable yield. In Example 4, the flow‐kick approach surprises us by identifying management strategies that yield higher profits than the maximum admitted by the corresponding Gordon–Schaeffer model.Recommendations for Resource Managers Consider using flow‐kick modeling to: explicitly represent the dynamics of a natural resource that is shaped by discrete, recurrent disturbances (e.g., harvests of a biological population). quantify the resilience of a natural resource, and its socially valued properties, to discrete, recurrent disturbances. quantify the resilience of a managed resource to additional disturbance or change in management strategy. Instead of using management to optimize according to a single objective, consider what functional properties of a system create value for stakeholders, and identify disturbance patterns (management strategies) that achieve acceptable levels of stakeholder value.When multiple stakeholders derive different values from a resource, search for mutually acceptable management strategies by first identifying acceptable value levels, and then identifying the disturbance patterns that achieve acceptable levels for each stakeholder. Do different stakeholders' sets of acceptable disturbance patterns overlap? If not, how close are they?

Luminescence from impact- and abrasive-damaged ZnS ceramics

IR windows made of ZnS ceramics serve as protective elements for the thermal imaging systems established on mobile carriers, whereon they suffer from weathering and dust impacts. In this study, the erosion of ZnS ceramics was simulated by the abrasive damaging of polished specimens, and the response of the crystal lattice on the external forcing was investigated by the method of photoluminescence (PL). Impacts of isolated hard particles were modelled with the discrete shocks of a pointed striker, and fractoluminescence (FL) from the damaged spot was detected. The FL evidenced that the impact forcing triggers a two-stage mechanism of damage nucleation in this ductile ceramic. The dislocation motion at the stage of initial deformation followed by the interatomic bonds breakage at the stage of cracking. The PL data showed the higher stability of crystallites in chemically vapor-deposited (CVD) ZnS ceramics as compared with the same compounds obtained by the hot pressing (HP) or physical vapor-deposition (PVD) technologies. The abrasive treatment of ZnS-CVD did not affect significantly the entirety of crystallites because of plasticity of intercrystallite substance, in which the impact-induced tension dissipated. Undamaged crystallites retained their optical properties that is did not exhibit additional absorbance. Thus, the decrease of the transmissive capability under particle impacts occurs predominantly due to light scattering on the newly-formed surface irregularities.

Steady discrete shocks of 5th and 7th-order RBC schemes and shock profiles of their equivalent differential equations

An exact expression of steady discrete shocks was recently obtained by the author in [9] for a class of residual-based compact schemes (RBC) applied to the inviscid Bürgers equation in a finite domain. Following the same lines, the analysis is extended to an infinite domain for a scalar conservation law with a general convex flux. For the dissipative high-order schemes considered, discrete shocks in infinite domain or with boundary conditions at short distance (Rankine–Hugoniot relations) are found to be very close. Besides, the present analytical description of shock capturing in infinite domain is explicit and so simple that it could lead to a new approach for correcting parasitic oscillations of high order RBC schemes. In a second part of the paper, exact solutions are also derived for equivalent differential equations (EDE) approximating RBC2p−1 schemes (subscript denotes the accuracy order) at orders 2p and 2p+1. Although EDE involves Taylor expansions around steep structures, agreement between the exact EDE shock-profiles and the discrete shocks is remarkably good for RBC5 and RBC7 schemes. In addition, a strong similarity is demonstrated between the analytical expressions of discrete shocks and EDE shock profiles.

Reliability Analysis of a Filtering Reducer under the Discrete Space Environmental Shocks

Dynamic reliability analysis of a filtering reducer is performed by accounting for discrete shocks from the space environment. Gears are considered as the lumped mass and meanwhile the meshing between different gears is equivalent to a dynamic system consisting of springs and dampers during construction of the dynamic model. The Newmark method is employed to resolve differential equations, and then the additional acceleration could be obtained, caused by shocks to the filtering reducer. Dynamic reliability analysis is conducted with the help of the Simulink tool for the outputs. The results are hopefully useful for spacecraft mechanism design.

Steady discrete shocks of high-order RBC schemes

Exact expressions of steady discrete shocks are found for a class of dissipative compact schemes approximating a one-dimensional nonlinear hyperbolic problem with a 3rd, 5th and 7th order of accuracy. A discrete solution is given explicitly for the inviscid Bürgers equation and the oscillatory nature of the shock profiles is determined according to the scheme order and to the shock location with respect to the mesh.

Strategic complementarity of information in financial markets with large shocks

In a simple model of a frictionless financial market with rational agents, the value of private information increases when large discrete shocks independently affect the fundamental value of the asset and the exogenous trading. The complementarity in information gathering generates multiple equilibria.

The impacts of sociopolitical instability on construction dimension

Most existing studies focus on establishing models of interdependence between the construction sector and performance of the national economy, this issue was initiated from financial markets in this study. By adopting an autoregressive conditional jump intensity model, this study examined how various unpredictable events impact the construction sector. Dependence on the arrival process governing jump events in a discrete-time setting was explored, in addition to the behaviour of the fundamental properties of structure index during periods of distinct events. Although the market efficiency hypothesis still holds, results of this study demonstrate that acquisition announcements are perceived as discrete sudden shocks by the stock market.

A framework for decomposing shocks and measuring volatilities derived from multi-dimensional panel data of survey forecasts

This work applies previously published frameworks developed for analyzing multi-dimensional panel data of survey forecasts to IPD forecasts from the Survey of Professional Forecasters. The paper expands on these frameworks, demonstrates that the frameworks imply the existence of new and richer measures of shocks and volatilities, and shows how these measures can be extracted from multi-dimensional forecast panels. Three distinct types of economic shocks (cumulative shocks, cross-sectional shocks, and discrete shocks) and implied volatility measures based on these shocks are calculated for IPD inflation over the period 1969 through 2004. GMM tests for forecaster biases are conducted using the expanded framework.

Existence and asymptotic stability of relaxation discrete shock profiles

kIn this paper we study the asymptotic nonlinear stability of discrete shocks of the relaxing scheme for approximating the general system of nonlinear hyperbolic conservation laws. The existence of discrete shocks is established by suitable manifold construction, and it is shown that weak single discrete shocks for such a scheme are nonlinearly stable in L 2 , provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the relaxing scheme for the single shock solution of the system of hyperbolic conservation laws. These results are proved by using both a weighted norm estimate and a characteristic energy method based on the internal structures of the discrete shocks.

General equilibrium comparative statics: discrete shocks in production economies

Nachbar [Econometrica 79 (5) (2002) 2065] established minimal conditions under which, following an infinitesimal shock to endowments in an exchange economy, changes in equilibrium prices are negatively related to changes in aggregate consumption. The present paper extends Nachbar (2002) to cover discrete shocks to technologies, ownership shares, and endowments in production economies. As in Nachbar (2002), the analyst’s choice of price normalization plays a key role. The required normalization is nonstandard but has a sensible interpretation.

Stability of Discrete Shocks for Difference Approximations to Systems of Conservation Laws

The asymptotic stability of weak discrete stationary shocks for systems of conservation laws in one space dimension is proved. The difference approximation should be conservative, dissipative, and kth order accurate in space with odd k. The problem is considered in a finite interval $\vert x\vert\le\ell$ with appropriate boundary conditions, where $\ell$ is large compared with the width of the shock layer $\varepsilon^{-1}=\vert u_{_R}-u_{_L}\vert^{-1/k}$. The proof is based on the assumption that the corresponding continuous shocks for the scalar problem $u_t+uu_x=-(i\partial_x)^{k+1}u$ are stable. The latter is known to be true for k=1 and k=3.

The $l^1$ global decay to discrete shocks for scalar monotone schemes

Given a family of discrete shocks φ of a monotone scheme, we prove that the discrete shock profile with rational shock speed η is asymptotically stable with respect to the l1 topology ||.||1: if u0 - φ ∈ l1, then ||un - φnη||1→0 as n→ ∞ under no restriction conditions of the initial data to the interval [inf φ, sup φ]. The asymptotic wave profile is uniquely identified from the above family by a mass parameter.

Convergence rates to discrete shocks for nonconvex conservation laws

This paper is concerned with polynomial decay rates of perturbations to stationary discrete shocks for the Lax-Friedrichs scheme approximating non-convex scalar conservation laws. We assume that the discrete initial data tend to constant states as \(j\rightarrow \pm \infty\), respectively, and that the Riemann problem for the corresponding hyperbolic equation admits a stationary shock wave. If the summation of the initial perturbation over \((-\infty, j)\) is small and decays with an algebraic rate as \(|j|\rightarrow \infty\), then the perturbations to discrete shocks are shown to decay with the corresponding rate as \(n\rightarrow \infty\). The proof is given by applying weighted energy estimates. A discrete weight function, which depends on the space-time variables for the decay rate and the state of the discrete shocks in order to treat the non-convexity, plays a crucial role.

Discrete Shocks for Finite Difference Approximations to Scalar Conservation Laws

Numerical simulations often provide strong evidences for the existence and stability of discrete shocks for certain finite difference schemes approximating conservation laws. This paper presents a framework for converting such numerical observations to mathematical proofs. The framework is applicable to conservative schemes approximating stationary shocks of one-dimensional scalar conservation laws. The numerical flux function of the scheme is assumed to be twice differentiable but the scheme can be nonlinear and of any order of accuracy. To prove existence and stability, we show that it would suffice to verify some simple inequalities, which can usually be done using computers. As examples, we use the framework to give an unified proof of the existence of continuous discrete shock profiles for a modified first-order Lax--Friedrichs scheme and the second-order Lax--Wendroff scheme. We also show the existence and stability of discrete shocks for a third-order weighted essentially nonoscillatory (ENO) scheme.

Asymptotic stability of stationary discrete shocks of Lax-Friedrichs scheme for non-convex conservation laws

The nonlinear stability of stationary discrete shocks for the Lax-Friedrichs scheme approximating non-convex scalar conservation laws is proved without smallness restrictions on the initial perturbations provided that the summation of initial perturbation is zero. The long time behavior of the Lax-Friedrichs is also investigated for a rather broad class of initial data. The selection of the discrete weight function plays a crucial role. The detailed study of discrete error equations is a major technical involvement.

A sensory-enhanced context facilitates learning and multiple measures of unconditioned stimulus processing in the preweanling rat.

This study tested the hypothesis that increased processing or efficacy of the unconditioned stimulus (US) contributes to the facilitation of trace conditioning that occurs when preweanling rats are conditioned in a novel sensory-rich context. Experiment 1 extended previous findings (D. L. McKinzie & N. E. Spear, 1995) of facilitated acoustic trace conditioning in the 17-day-old rat in a sensory-enhanced versus a home odor context. In the enhanced or more familiar context, Experiment 2 tested rats of this age for degree of spontaneous locomotor activity and ultrasonic vocalizations, activity and ultrasounding in response to shock, and the acoustic startle reflex. The enhanced context resulted in a greater overall activity response to shock, increased ultrasounding to discrete shocks, and a sensitized latency to startle. The results suggest that enhanced US processing in a sensory-rich context is a likely contributor to its facilitative effect on infant learning.

Decay rate for perturbations of stationary discrete shocks for convex scalar conservation laws

This paper is to study the decay rate for perturbations of stationary discrete shocks for the Lax-Friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method. If the summation of the initial perturbation over (-∞,j) is small and decays at the algebraic rate as |j|→ ∞, then the solution approaches the stationary discrete shock profiles at the corresponding rate as n - ∞. This rate seems to be almost optimal compared with the rate in the continuous counterpart. Proofs are given by applying the weighted energy integration method to the integrated scheme of the original one. The selection of the time-dependent discrete weight function plays a crucial role in this procedure.

Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws

This paper is to study the asymptotic stability of stationary discrete shocks for the Lax-Friedrichs scheme approximating nonconvex scalar conservation laws, provided that the summations of the initial perturbations equal to zero. The result is proved by using a weighted energy method based on the nonconvexity. Moreover, the l 1 l^1 stability is also obtained. The key points of our proofs are to choose a suitable weight function.

Discrete shocks and fixed duration of labor contracts

This paper examines the choice between fixed and stochastic durations of labor contracts in an economy with discrete shocks. The stochastic duration expires when the consumer price index reaches a lower or upper limit. The paper proves that any contract with a stochastic duration is dominated by a contract with a fixed duration, except for the contract that expires at the first shock. This is because shocks have a cumulative effect and a fixed duration limits the time a contract can remain in force after a large number of shocks, while there is no time limit with a stochastic duration.