Infinite Periodic Model Research Articles

Diverse coherence-resonance chimeras in coupled type-I excitable systems.

Coherence-resonance chimera was discovered in [Phys. Rev. Lett. 117, 014102 (2016)10.1103/PhysRevLett.117.014102], which combines the effect of coherence-resonance and classical chimeras in the presence of noise in a network of type-II excitable systems. However, the same in a network of type-I excitable units has not been observed yet. In this paper we report the occurrence of coherence-resonance chimera in coupled type-I excitable systems. We consider a paradigmatic model of type-I excitability, namely, the saddle-node infinite period model, and show that the coherence-resonance chimera appears over an optimum range of noise intensity. Moreover, we discover a unique chimera pattern that is a mixture of classical chimera and the coherence-resonance chimera. We support our results using quantitative measures and map them in parameter space. This study reveals that the coherence-resonance chimera is a general chimera pattern and thus it deepens our understanding of role of noise in coupled excitable systems.

Modelling Multiperiod Carbon Markets Using Singular Forward-Backward SDEs

We introduce a model for the evolution of emissions and the price of emissions allowances in a carbon market, such as the European Union Emissions Trading System (EU ETS). The model accounts for multiple trading periods, or phases, with multiple times at which compliance can occur. At the end of each trading period, the participating firms must surrender allowances for their emissions made during that period, and additional allowances can be used for compliance in the following periods. We show that the multiperiod allowance pricing problem is well-posed for various mechanisms (such as banking, borrowing, and withdrawal of allowances) linking the trading periods. The results are based on the analysis of a forward-backward stochastic differential equation with coupled forward and backward components, a discontinuous terminal condition, and a forward component that is degenerate. We also introduce an infinite-period model for a carbon market with a sequence of compliance times and with no end date. We show that, under appropriate conditions, the value function for the multiperiod pricing problem converges, as the number of periods increases, to a value function for this infinite-period model and that such functions are unique. Finally, we present a numerical example that demonstrates empirically the convergence of the multiperiod pricing problem. Funding: The Engineering and Physical Sciences Research Council and Climate-KIC funded all parts of H. Chotai’s PhD programme in the centre for doctoral training and provided many opportunities for travel to conferences and events during the programme. D. Crisan received financial support from École Polytechnique and Université Paris Diderot through visitor grants.

Subcontracting and lot-sizing with constant capacities

In this paper, we consider the subcontracting and single-item lot-sizing problem with constant capacities, which is uncapacitated in subcontracting but capacitated in production. For a holistic understanding of the problem, an infinite-period model is proposed. Such a model provides a unified view of a capacitated lot-sizing problem. The usefulness of the infinite-period model is shown by the principle that the firm’s production schedule drives the subcontractor’s supply schedule. For efficient construction of the production schedule, an innovative technique–coined using the concept of the shadow period–is presented to designate the optimal marginal supply cost. The success of the infinite-period model is finally proved with the concept of the effective period, indicating the supply coverage over periods. This fills the gap between the uncapacitated techniques and the capacitated techniques, making it possible to apply the best techniques from the lot-sizing literature. With this novel approach, we improve existing algorithms and provide new ones for concave production and supply cost structures involving setups.

A lattice model for transition zones in ballasted railway tracks

The procedure presented in this work aims at providing a framework for studying settlement of ballast in zones with stiffness variation of the railway track support. The proposed procedure results from expanding an existing infinite periodic model of a railway track to account for variations in the stiffness of the foundation. Ballast is simulated via a linear lattice, whose dynamic response differs from that of a continuum. The expanded model is composed of three regions: a left region, which is semi-infinite and periodic; a mid-region, of finite length and where the properties of the foundation can change; and a right region, which is also semi-infinite and periodic and whose properties can differ from those of the left region. The equations of motion of the mid-region are written directly in the time domain, with the rail being described by finite elements. On the other hand, the left and right semi-infinite regions are treated semi-analytically in the frequency domain, and afterwards their responses are converted to the time domain, resulting in convolution integrals prescribed at the boundaries of the mid-region that simulate non-reflective boundaries. The final model only contains the degrees of freedom corresponding to the mid-region (which can be as short as the region where the stiffness variation is present), and that leads to faster calculations than if the boundaries were placed further away to dissipate undesired reflections. The method is cast in the time domain, and all elements are assumed to behave linearly. In the future, the model will be expanded to incorporate non-linear behaviour of the ballast. The presented method is validated by means of simple examples, and afterwards applied to a real scenario in which a culvert crosses a railway track. As presented, the method can be used to study the linear dynamics of transitions zones, study mitigation measures, and infer about indicators like force transmitted and energy dissipated, which might be useful to assess the development of settlement of the ballast.

Self-Fulfilling Risk Panics: An Expected Utility Framework

Even if an asset has no fundamental uncertainty with a constant dividend process, a stochastic sentiment-driven equilibrium for the asset price exists besides the well-known fundamental equilibrium. Our paper constructs such sentiment-driven equilibria under general utility functions within an OLG structure. Our paper further shows that the existence of sentiment-driven equilibria is robust in a standard infinite-period model as long as the pricing kernel is affected by the asset price.

Divestment options under tacit and incomplete information

While the literature has mainly focused on why a firm decides to divest a subsidiary, we investigate theoretically what the best divestment option is for a firm to divest a subsidiary. The firm chooses among the four most popular divestment options in practice: sell-offs, spin-offs, carve-outs, and management buyouts. In an infinite-period model, where divestiture is completed in the first two periods, the owners of a parent firm divest a subsidiary for the best value. The information possessed by the owners, subsidiary managers and outside buyers about the subsidiary's profitability may be complete or incomplete (the knowledge of information) and this information may be explicit or tacit (the nature of information). We investigate how the nature of information, the knowledge of information, risk aversion and discount on future performance determine the best divestment option.

Wave dispersion analysis of multi-story frame building structures using the periodic structure theory

Introducing the periodic structure theory in the field of solid-state-physics into the field of civil engineering, this paper conducts a comprehensive theoretical and numerical study on the wave dispersion properties of multi-story frame building structures. At first, the theoretical infinite periodic model for the multi-story frame building structure is developed. Combining the Bloch-Floquet theorem and the State-Space-Transfer-Matrix-Method (SSTMM), the dispersion equation of the infinite periodic system is solved, from which dispersion curves and group/phase velocity curves of a practical multi-story reinforced concrete frame building structure are investigated. Second, a parametric study is performed to investigate the influences of the typical material parameters (density, strength grade of concrete), geometrical parameters (span length, floor height), theoretical simplified parameters as well as the damping parameter of frame building structures on the dispersion relations. Then, harmonic analysis and time history analysis are conducted to analyze the dynamic properties of the finite periodic frame structure in the frequency domain. Numerical results show that, when the main frequency region of the external excitations (like seismic waves) falls into the passing bands, dynamic responses of the multi-story frame building structure are very large; while the main frequency region of the external excitations falls into the attenuation zones, seismic responses of the multi-story frame building structure are very small.

Aftermarket power and foremarket competition

I revisit the issue of aftermarkets by developing an infinite period model with overlapping consumers. If the aftermarket is characterized by constant returns to scale, then social surplus and consumer surplus are invariant with respect to aftermarket power. Under increasing returns to scale, however, greater aftermarket power leads to: greater concentration in the foremarket; higher barriers to entry; higher social surplus; and possibly higher consumer surplus.

Friction Paths for Cubic Boron Nitride: An Ab Initio Study

Friction coefficients for cubic boron nitride were determined with the use of hybrid density functional B3LYP calculations. Two cluster models and an infinite periodic model were applied. Various contacts between duplicated surfaces and different sliding paths of the surfaces with respect to each other were taken into consideration, and friction coefficients were derived. The calculations suggest that three different sliding paths contribute to the friction, the friction coefficient for the periodic model being 0.21 at its lowest. This value is in agreement with previous experimental studies, where a friction coefficient of 0.1–0.2 has been measured for cubic boron nitride.

Infinite periodic model of human lung

As described in a companion abstract, an investigation is underway to develop a bioacoustic model of human lung. In parallel with the numerical model described in the companion abstract, a semianalytic model is being developed. The basic unit cell, a truncated octahedron, is the same. In contrast here, the medium is assumed to be infinite in extent. The resulting lattice possesses cubic symmetry, and, for homogeneous deformation, all material properties are determined by a single unit cell. Deformation of the unit cell is determined by the 24 vertices of the polyhedron, only 6 of which are independent. In this presentation we discuss quasistatic deformation of the discretized medium, and thus ignore inertia and energy dissipation. An analytic model for the nonlinear elasticity of collagen and elastin is used to determine the stiffnesses of the springs connecting vertices of the polyhedra. Minimization of the potential energy for a given macroscopic deformation permits calculation of microscopic deformation within the unit cell, which in turn determines the stresses and therefore the elastic constants. Sample calculations will be presented, including the longitudinal and transverse wave speeds in the medium as functions of direction and orientation. [Work supported by ONR and ARL IR&D.]

Computer simulation of Alfven resonance in a cylindrical, axially bounded flux tube

The resonant absorption of Alfven waves in an axially bounded cylindrical flux tube is investigated in a dissipative MHD simulation. It is found that in an axially bounded flux tube, in contrast to an infinite periodic model, the resonant frequency is nearly independent of the poloidal component of the magnetic field. This is a consequence of the 'ballooning' structure of the resonant Alfven waves. The scaling with resistivity and viscosity of the width of the resonance layer, the dissipation rate, and the time for steady state absorption to occur, are all in agreement with theory.

The optimality of (s,S) inventory policies in the infinite period model*

Summary The infinite period stationary inventory model is considered. There is a constant lead time, a nonnegative set‐up cost, a linear purchase cost, a holding and shortage cost function, a fixed discount factor β, 0 < β < 1, and total backlogging of unfilled demand. Both the total discounted cost (β < 1) and the average cost (β= 1) criteria are considered. Under the assumption that the negatives of the one period holding and shortage costs are unimodal, a unified proof of the existence of an optimal (s.S) policy is given. As a by‐product of the proof upper and lower bounds on the optimal values of s and S are found. New results simplify the algorithm of Veinott and Wagner for finding an optimal (s, S) policy for the case β< 1. Further it is shown that the conditions imposed on the one period holding and shortage costs can be weakened slightly.