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A standard experimental setup for Inelastic Electron Tunneling Spectroscopy (IETS) performs the measurement of the second derivative of the current with respect to the voltage ( d 2 I / d V 2 ) using a small AC signal and a lock-in based second harmonic detection. This avoids noise arising from direct differentiation of the current-voltage characteristics (I–V) by standard numerical methods. Here we demonstrate a noise-filtering algorithm based on Tikhonov Regularization to obtain IET spectra (i.e. d 2 I / d V 2 vs. V) from measured DC I–V curves. This leads to a simple and effective numerical method for IETS extraction. We apply the algorithm to I–V data from a molecular junction and a metal-insulator-semiconductor tunneling device, demonstrating that the computed first/second derivatives have a workable match with those obtained from our lock-in measurements; the computed IET spectral peaks also correlate well with reported experimental ones. Finally, we present a scheme for automated tuning of the algorithm parameters well-suited for the use of this numerical protocol in real applications. [ABSTRACT FROM AUTHOR]

Supply chain networks are representation of interaction among different entities. Usually these entities are facilities which can be represented as nodes in a network and the flow of material between them can be represented as flow on arcs (paths) connecting them. These flows can be facilitated via multiple modes available to transport material from one facility to another. We discuss a multi-modal supply chain distribution problem where the aim is to minimize sum of transportation cost on various modes between facilities, inventory, backlog and lost sales costs over a time-horizon. The problem can be represented as a time-space network of nodes and arcs. Each node defines the state of a facility at a given time-period and the arcs between these nodes are either transportation, inventory or backlog carrying arcs. The time-horizon consists of discrete time-periods and the flows on transportation arcs are required to be an integer multiple of predefined lot sizes as in vehicle capacities, batch sizes, etc. Apart from this, there are certain business rules which are posed on transportation modes incoming to a facility or posed on the suppliers of a facility are to be followed. The problem stated above is first modeled as a Mixed Integer Linear Program (MILP) and solved using a MILP solver. We propose integer rounding heuristics to get a feasible solution to the problem. We report in our results that these heuristics can be used to generate an integer feasible solution quickly. Using this feasible solution as an MIP start in solver helps us in reaching optimal solution in lesser time. [ABSTRACT FROM AUTHOR]

We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and some at the other branch-and-bound nodes. Two of the techniques are specifically applicable to commonly found univariate nonlinear functions and are more effective than other general approaches. These techniques have been implemented in the Minotaur toolkit. Tests on benchmark instances show up to 12% improvement in the average time to solve the instances. Shared-memory parallel versions of NLP based branch-and-bound and LP/NLP based branch-and-bound algorithms have also been developed in the toolkit. These implementations solve different nodes of branch-and-bound concurrently. About 44% improvement in the speed and an increase in the number of instances solved within the time limit are observed when the two schemes are used together on a computer with 16 cores. These parallelization methods are compared to alternate approaches that exploit parallelism in existing commercial MILP solvers. The latter approaches are seen to perform better thus highlighting the importance of MILP techniques. [ABSTRACT FROM AUTHOR]

Gate-all-around field-effect transistors deliver the best inversion layer control among the family of multi-gate transistors and are proving to be the promising architecture for logic nodes beyond 10 nm. Sub-10 nm devices typically have effective oxide thickness below 1 nm and a higher mobility channel for faster switching. However, the thinner oxide barrier and lower effective mass of the channel material both aid gate leakage, which is one of the metrics for the scaling limit. This paper presents a 2D finite element method (FEM)-based model that accurately calculates gate leakage current from the quasi-bound states (QBS) that exist in the inversion layer of the nanowire. The lifetime of QBS is calculated considering the scattered cylindrical waves in the open system by solving Schrödinger's equation using the FEM. The impact of channel and oxide material, channel diameter, strain in the nanowire, and oxide thickness on gate leakage current density is investigated. [ABSTRACT FROM AUTHOR]

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting extensions that we implement in our framework and demonstrate their impact on solution times. Without a flexible framework that enables structure exploitation, finding global solutions to difficult nonconvex MINLP problems will remain out of reach for many applications. [ABSTRACT FROM AUTHOR]

We study the facet defining inequalities of the convex hull of a mixed-integer bilinear covering arising in trim-loss (or cutting stock) problem under the framework of disjunctive cuts. We show that all of them can be derived using a disjunctive procedure. Some of these are split cuts of rank one for a convex mixed-integer relaxation of the covering set, while others have rank at least two. For certain linear objective functions, the rank-one split cuts are shown to be sufficient for finding the optimal value over the convex hull of the covering set. A relaxation of the trim-loss problem has this property, and our computational results show that these rank-one inequalities find the lower bound quickly. [ABSTRACT FROM AUTHOR]

The design of rural drinking water schemes consists of optimization of several network components like pipes, tanks, pumps and valves. The sizing and configuration of these network configurations need to be such that the water requirements are met while at the same time being cost efficient so as to be within government norms. We developed the JalTantra system to design such water distribution networks. The Integer Linear Program (ILP) model used in JalTantra and described in our previous work solved the problem optimally, but took a significant amount of time for larger networks—an hour for a network with 100 nodes. In this current work, we describe a series of three improvements of the model. We prove that these improvements result in tighter models, i.e. the set of points of linear relaxation is strictly smaller than the linear relaxation for the initial model. We test the series of three improved models along with the initial model over eight networks of various sizes and show a distinct improvement in performance. The 100-node network now takes only 49 s to solve. These changes have been implemented in JalTantra, resulting in a system that can solve the optimization of real world rural drinking water networks in a matter of seconds. The JalTantra system is free for use, and is available at https://www.cse.iitb.ac.in/jaltantra/. [ABSTRACT FROM AUTHOR]

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness of the new inequalities and the extended formulation using some examples. [ABSTRACT FROM AUTHOR]