Neural-network-powered pulse reconstruction from one-dimensional interferometric correlation traces.

Discontinuity solutions to plate and beam problems

In this paper, we will give a p-version finite element method for the one-dimensional nonlinear elastoplasticity problem. A family of admissible constitutive laws based on the so-called gauge function method is introduced first, and then a p-version semi-discretization scheme is presented. We show that the existence and uniqueness of the solution for the semi-discrete problem can be guaranteed by using some special properties of the constitutive law. Finally, we show that as the polynomial degree of the elements ${\bf p} \to \infty $ oo the solution of the semi-discrete problem will converge to the solution of the continuous problem. The p-version convergence analysis given here is only for one-dimensional problems with a linear hardening constitutive law hypothesis. However, it also gives us a very useful idea for the study of the hp-version finite element method for the one-dimensional problem with more general constitutive laws or even two-dimensional problems.

This research is focused on solving the Cutting Stock with Limited Open Stacks Problem (CS-LOSP). The CS-LOSP is an optimization problem which consists of the classical Cutting Stock Problem (CSP) paired with the additional constraint that the maximum number of open stacks from the sequencing of the cutting patterns obtained from the CSP solution is equal or lower than a preset limit. Despite being a problem with great practical importance, the literature lacks models for this problem, and only one-dimensional problems are addressed. In this paper, we propose two integer linear programming formulations for the CS-LOSP that are valid for solving instances of the CSP of any dimension. In order to eliminate symmetrical solutions to the problem, the proposed formulations sequence sets of cutting patterns instead of sequencing the cutting patterns individually, thus, the search space for solutions is reduced. A set of randomly generated instances for the two-dimensional problem is used to perform computational experiments in order to validate the proposed mathematical formulations.

A universal approach for continuous or discrete nonlinear programmings with multiple variables and constraints

This paper examines the sensitivity to gridding of first-contact miscible and three-component multicontact miscible condensing-gas drive predictions made with an upstream differenced simulator. These cross-section simulations are made for various reservoir descriptions and for models of increasing numbers of grid blocks. The largest models range from 5000 to 24,000 grid blocks. The paper examines gridding sensitivity when the coefficients of convective terms are evaluated by the single-point upstream method, and it also examines the utility of two-point upstream weighting and selectively refined initial gridding for moderating gridding sensitivity. These simulations show the following behavior. For some problems with single-point upstream weighting, ultimate recovery changes monotonically with an increasing number of grid blocks. The change in recovery with increasing grid blocks can either be a decrease or an increase depending on the particular reservoir description, although decreasing recovery was the most common behavior for the reservoir descriptions examined here. Two-point upstream weighting and selectively refined initial gridding reduced, but didn't eliminate, this sensitivity. Some predictions appear to converge almost linearly with grid size to approximately the same answer in the limit of zero grid block size (i.e., infinite grid blocks) when the problem is worked in different ways, e.g., single-point weighting, two-point weighting, selectively refined initial gridding. Other problems, however, do not appear to be converging for the largest models that were feasible. Addition of physical diffusion/dispersion of a magnitude that might occur in reservoirs didn't affect the gridding sensitivity for two of the three reservoir descriptions examined, at least not for grid sizes that were feasible. However, for one reservoir description, recoveries computed with and without physical diffusion/dispersion appear to be diverging with grid refinement.

This paper proposes the usage of an adaptive meshless method – radial point interpolation method (RPIM) for the analysis of armchair graphene nano ribbon (GNR) to be used for interconnect applications. The validity and efficiency of the proposed method are demonstrated using the following three examples: one-dimensional problem, two-dimensional problem and the cantilever beams under various forces and boundary conditions. Electrostatic analysis of the GNR is performed using RPIM. The delay of the GNR is calculated using the quasi-static capacitance. It is found that the delay is reduced compared to the RKPM analysis, making it as a suitable candidate for RF interconnects.

The Hamiltonian describing fermion pair production from an arbitrarily time-varying electric field in two dimensions is studied using a group-theoretic approach. We show that this Hamiltonian can be encompassed by two, commuting SU(2) algebras, and that the two-dimensional problem can therefore be reduced to two one-dimensional problems. We compare the group structure for the two-dimensional problem with that previously derived for the one-dimensional problem, and verify that the Schwinger result is obtained under the appropriate conditions.

Plane Poiseuille flow of a rarefied gas, which flows horizontally in the presence of strong gravitation, is studied based on the Boltzmann equation. Applying the asymptotic analysis for a small variation in the flow direction [Y. Sone, Molecular Gas Dynamics (Birkhäuser, 2007)], the two-dimensional problem is reduced to a one-dimensional problem, as in the case of a Poiseuille flow in the absence of gravitation, and the solution is obtained in a semianalytical form. The reduced one-dimensional problem is solved numerically for a hard sphere molecular gas over a wide range of the gas-rarefaction degree and the gravitational strength. The presence of gravitation reduces the mass flow rate, and the effect of gravitation is significant for large Knudsen numbers. To verify the validity of the asymptotic solution, a two-dimensional problem of a flow through a long channel is directly solved numerically, and the validity of the asymptotic solution is confirmed.

A new efficient and accurate procedure for solving heat condution problems

The properties of SF-NFS sandwiches composed of two superconducting (S) electrodes separated by a weak-link region formed by a normal-metal (N) step with the thickness d N situated on the top of a lower S electrode and a ferromagnetic (F) layer with the thickness d F deposited onto the step and the remaining free surface of the lower electrode have been studied theoretically. It has been shown in the approximation of linearized semiclassical Usadel equations that the two-dimensional problem in the weak-link region can be reduced to two one-dimensional problems in its SFS and SNFS segments. The spatial distributions of the critical current density Jc in the segments as a function of the layer thickness d F have been calculated. The dependences of the critical current Ic of the structure on the magnitude of the magnetization vector M of the ferromagnetic layer have been found for various directions of the magnetization within the junction plane. It has been shown that these dependences are affected considerably by both the orientation of M and the spatial distribution of Jc.

This thesis treats different aspects of the class of Mixed-Integer Optimal Control Problems (MIOCPs). These are optimization problems that combine the difficulties of underlying dynamic processes with combinatorial decisions. Typically, these combinatorial decisions are realized as switching decisions between the system’s different operations modes. During the last decades, direct methods emerged as the state-of-the-art solvers for MIOCPs. The formulation of a valid, tight and dependable integral relaxation, i.e., the formulation of a model for fractional values, plays an important role for these direct solution methods. We give detailed insight into several relaxation approaches for MIOCPs and compare them with regard to their respective structures. In particular, these are the typical solution’s structures and properties as convexity, problem size and numerical behavior. From these structural properties, we deduce some required specifications of a solver. Additionally, the modeling and subsequent limitation of the switching process directly tackle the class-specific typical issue of chattering solutions. One of the relaxation methods for MIOCPs is the outer convexification, where the binary variables only enter affinely. For the approximation of this relaxation’s solution, we took up on the control approximation problem in integral sense derived by Sager as part of a decomposition approach for MIOCPs with affine binary controls. This problem describes the optimal approximation of fractional controls with binary controls such that the corresponding dynamic process is changed as little as possible. For the multi-dimensional problem, we developed a new heuristic, which for the first time gives a bound that only depends on the control grid and not anymore on the number of the system’s controls. For the generalization of the control approximation problem with additional constraints, we derived a tailored branch-and-bound algorithm, which is based on the properties of the Lagrangian relaxation of the one-dimensional problem. This algorithm beats state-of-the-art commercial solvers for Mixed-Integer Linear Programs (MILPs) for this special approximation problem by several orders of magnitude. Overall, we present several, partially new modeling approaches for MIOCPs together with the accompanying structural properties. On this basis, we develop new theories for the approximation of certain relaxed solutions. We discuss the efficient implementation of the resulting structure exploiting algorithms. This leads to a deeper and better understanding of MIOCPs. We show the practicability of the theoretical observations with the help of four prototypical problems. The presented methods and algorithms allow on their basis the direct development of decision support and analysis tools in practice.

A modified sequential gradient-based method for the inverse estimation of transient heat transfer coefficients in non-linear one-dimensional heat conduction problems

The finite volume method is a more recent method than both finite difference and finite element methods. It is widely used in practice for example in fluid dynamics computations. We present the method in the simplest possible settings, first for one-dimensional elliptic problems, then for the transport equation in one and two dimensions. For the latter, we return to the method of characteristics already introduced in Chap. 1, to solve one-dimensional nonlinear problems as well as two-dimensional linear problems.

Non-stationary two-dimensional problems of thermal conductivity for plates and panels with plane-parallel boundaries in the presence of volume-distributed non-stationary heat sources are formulated. A method of constructing a solution to the formulated heat conduction problems for the considered bodies is proposed. The technique uses the approximation of the temperature distribution in both elements by the thickness variable by a cubic polynomial. The coefficients of the approximation polynomial are given through the integral over the thickness variable temperature characteristics and the conditions for the boundary values of the temperature on the outer surfaces of the plate and panel. As a result, the initial two-dimensional initial boundary value problems for the temperature for the plate and panel are reduced to one-dimensional initial boundary value problems for the integral temperature characteristics. To construct the solution of the initial-boundary value problem for the integral characteristics of the temperature in the case of a plate infinite in longitudinal and transverse coordinates, the integral Laplace transform in time and the integral Fourier transform in the longitudinal coordinate were used. The solution of the problem on the integral temperature characteristics in the case of the panel is found using the integral Laplace transform in time and the finite integral transform in the transverse coordinate. Expressions of integral temperature characteristics for the plate and panel are obtained in the form of convolutions of functions corresponding to homogeneous solutions of initial-boundary value problems for integral temperature characteristics and functions describing the available non-stationary heat sources in these bodies and given surface temperature values. The general solutions of the two-dimensional initial boundary value problems of thermal conductivity for slabs and panels are recorded for the presence of arbitrarily variable spatial coordinates of non-stationary heat sources and the conditions of convective heat exchange with the external environment on the surfaces of the considered bodies.

The acoustic environment can serve as a niche axis, structuring animal behaviour by providing or obscuring salient information. Meadow katydid choruses occupy the ultrasonic, less studied, realm of this acoustic milieu, form dense populations in some habitats and present a potential sensory challenge to co‐occurring ultrasonic‐hearing animals. Aerial‐hawking insectivorous bats foraging immediately over vegetation must listen for echoes of their prey and other cues amidst the chorus din. We experimentally created the cacophony of a katydid chorus in a katydid‐free rice paddy using an aggregation of 100 ultrasonic speakers in a 25 × 25 m grid to test the hypothesis that aerially hawking bats are averse to this noise source. We alternated between chorus‐on and chorus‐off hourly, and acoustically monitored bat activity and arthropod prey abundance. We found that our phantom katydid chorus reduced bat activity nearest the sound source by 39.3% (95% CI: 7.8%–60.0%) for species whose call spectrum fully overlapped with the chorus, and elicited marginal reductions in activity in species with only partial spectral overlap. Our study suggests that ultrasonic insect choruses degrade foraging habitat, potentially suppressing bats’ ecosystem services as consumers of pests; and, given the global distribution of meadow katydids, may provide an underappreciated force modifying animal behaviour in other grassland habitats. A free Plain Language Summary can be found within the Supporting Information of this article.