Dressed emitters as impurities

Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular nonradiating effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. Moreover, it allows us to formulate and settle – independently of the bath Hamiltonian – a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the case of more than one emitter, which is used to derive a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states.

Formulation and Evaluation of Liquisolid Compacts of BCS Class II Drug Ketoprofen

Aims: The main objective of the current research work is to develop liquisolid compacts of BCS Class II drug ketoprofen with an intention to enhance the solubility of drug by applying liquisolid technique. Place and Duration of Study: Smriti College of Pharmaceutical Education between June 2018 June 2019. Methodology: Initially liquid medication was obtained by dissolving drug in suitable solvent. Saturation solubility studies were performed in various hydrophilic non-volatile solvents to select the solvent showing highest solubility for drug. This liquid medication was admixed with calculated amounts of carrier material (Avicel PH 102) and coating material (Cab-O-Sil) using Spireas mathematical model in order to obtain liquisolid formulations. Further, this powder mass of liquisolid system was compressed to form Ketoprofen liquisolid compact formulations ranging from TK1 to TK9. They were further subjected to post compression evaluation tests such as weight variation, hardness, friability, content uniformity, disintegration and in vitro dissolution studies. Results: Based on the solubility studies, PEG 400 was selected as solvent for ketoprofen drug. Rheological properties for the prepared liquisolid powder system were performed for all the formulations and they showed acceptable flow properties. The results obtained for the post compression evaluation tests of all the prepared liquisolid compacts were present within the acceptable limits. The disintegration time observed for all formulations were within 5 minutes. The results of in vitro release of all the liquisolid compacts showed enhanced release rates compared to that of directly compressed tablet. Lquisolid compact formulation TK7 showed maximum release of 97.62% of drug within 12 minutes in pH 7.4 phosphate buffer which was much higher when compared to that of directly compressed tablet. The SEM and PXRD studies for TK7 revealed conversion of crystalline to molecularly dispersed form of drug in the obtained liquisolid formulation. DSC and FTIR studies also revealed that there was no presence of any significant interaction between drug and excipients involved in the formulation. Conclusion: Finally, it could be concluded that Liquisolid technique was successful in enhancing the solubility and further dissolution profile of BCS Class II drug Ketoprofen.

The Balanced Connected k-Partition Problem: Polyhedra and Algorithms

The balanced connected k-partition (BCPk) problem consists in partitioning a connected graph into connected subgraphs with similar weights. This problem arises in multiple practical applications, such as police patrolling, image processing, data base and operating systems. In this work, we address the BCPk using mathematical programming. We propose a compact formulation based on flows and a formulation based on separators. We introduce classes of valid inequalities and design polynomial-time separation routines. Moreover, to the best of our knowledge, we present the first polyhedral study for BCPk in the literature. Finally, we report on computational experiments showing that the proposed algorithms significantly outperform the state of the art for BCPk.

Modeling Single-Picker Routing Problems in Classical and Modern Warehouses

The standard single-picker routing problem (SPRP) seeks the cost-minimal tour to collect a set of given articles in a rectangular single-block warehouse with parallel picking aisles and a dedicated storage policy, that is, each stock-keeping unit is only available from one storage location in the warehouse. We present a compact formulation that forgoes classical subtour elimination constraints by directly exploiting two of the properties of an optimal picking tour used in the dynamic programming algorithm published in the seminal paper of Ratliff and Rosenthal. We extend the formulation to three important settings prevalent in modern e-commerce warehouses: scattered storage, decoupling of picker and cart, and multiple end depots. In numerical studies, our formulation outperforms existing standard SPRP formulations from the literature and proves able to solve large instances within short runtimes. Realistically sized instances of the three problem extensions can also be solved with low computational effort. For scattered storage, we note a rough tendency that runtimes increase with longer pick lists or a higher degree of duplication. In addition, we find that decoupling of picker and cart can lead to substantial cost savings depending on the speed and capacity of the picker when traveling alone, whereas additional end depots have rather limited benefits in a single-block warehouse. Summary of Contribution: Efficiently routing order pickers is of great practical interest because picking costs make up a substantial part of operational warehouse costs. For the prevalent case of a rectangular warehouse with parallel picking aisles, we present a highly effective modeling approach that covers—in addition to the standard setting—several important storage and order-picking strategies employed in modern e-commerce warehouses: scattered storage, decoupling of picker and cart, and multiple end depots. In this way, we provide practitioners as well as scientists with an easy and quick way of implementing a high-quality solution approach for routing pickers in the described settings. In addition, we shed some light on the cost benefits of the different storage and picking strategies in numerical experiments.

Extension of Boley’s continuum mechanics-based successive approximation method to two-layer rectangular beams

An extension of Boley’s continuum mechanics-based successive approximation method is presented for rectangular beams composed of two isotropic linear elastic layers. The solution is cast into the form of tables, in complete analogy to the tables originally presented by Boley and Tolins for single-layer strips. The first column in these tables corresponds to the classical Bernoulli–Euler theory of beams. The further columns represent comparatively fast converging correction terms of an increasing refinement. Our two-layer formulation automatically satisfies the stress continuity conditions at the interface of the two layers. Enforcing displacement continuity at the interface between the layers, we derive results that do satisfy the equilibrium field equations, the stress continuity conditions at the interface and the stress boundary conditions at the upper and lower edges. When converged, the field constitutive relations and the displacement continuity at the interface between the two layers are also satisfied. We present a compact formulation, which allows writing down the results for more than the three successive steps considered by Boley and Tolins. The elasticity solutions presented subsequently can be used as novel analytic benchmarks for comparison with refined structural mechanics beam theories. Interior solutions for beams with a finite axial extent can be obtained by assigning approximate boundary conditions at the lateral ends. Comparisons to finite element computations for a clamped–clamped beam give strong evidence for the correctness of our analytic results.

Compact gauge fields on Causal Dynamical Triangulations: a 2D case study

We discuss the discretization of Yang-Mills theories on Dynamical Triangulations in the compact formulation, with gauge fields living on the links of the dual graph associated with the triangulation, and the numerical investigation of the minimally coupled system by Monte Carlo simulations. We provide, in particular, an explicit construction and implementation of the Markov chain moves for 2D Causal Dynamical Triangulations coupled to either U(1) or SU(2) gauge fields; the results of exploratory numerical simulations on a toroidal geometry are also presented for both cases. We study the critical behavior of gravity-related observables, determining the associated critical indices, which turn out to be independent of the bare gauge coupling: we obtain in particular ν = 0.496(7) for the critical index regulating the divergence of the correlation length of the volume profiles. Gauge observables are also investigated, including holonomies (torelons) and, for the U(1) gauge theory, the winding number and the topological susceptibility. An interesting result is that the critical slowing down of the topological charge, which affects various lattice field theories in the continuum limit, seems to be strongly suppressed (i.e. by orders of magnitude) by the presence of a locally variable geometry: that may suggest possible ways for improvement also in other contexts.

A Compact Arc-Based ILP Formulation for the Pickup and Delivery Problem with Divisible Pickups and Deliveries

We consider the capacitated single vehicle one-to-one pickup and delivery problem with divisible pickups and deliveries (PDPDPD). In this problem, we do not make the standard assumption of one-to-one pickup and delivery problems (PDPs) that each location has only one transportation request. Instead we assume there are multiple requests per location that may be performed individually. This may result in multiple visits to a location. We provide a new compact arc-based integer linear programming (ILP) formulation for the PDPDPD by deriving time-consistency constraints that identify the order in which selected outgoing arcs from a node are actually traversed. The formulation can also easily be applied to the one-to-one PDP by restricting the number of times that a node can be visited. Numerical results on standard one-to-one PDP test instances from the literature show that our compact formulation is almost competitive with tailor-made solution methods for the one-to-one PDP. Moreover, we observe that significant cost savings of up to 15% on average may be obtained by allowing divisible pickups and deliveries in one-to-one PDPs. It turns out that divisible pickups and deliveries are not only beneficial when the vehicle capacity is small, but also when this capacity is unrestrictive.

Compact Trap-Assisted-Tunneling Model for Line Tunneling Field-Effect-Transistor Devices

Trap-assisted-tunneling (TAT) is a well-documented source of severe subthreshold degradation in tunneling field-effect-transistors (TFET). However, the literature lacks in numerical or compact TAT models applied to TFET devices. This work presents a compact formulation of the Schenk TAT model that is used to fit experimental drain-source current (Ids) versus gate-source voltage (Vgs) data of an L-shaped and line tunneling type TFET. The Schenk model incorporates material-dependent fundamental physical constants that play an important role in influencing the TAT generation (GTAT) including the lattice relaxation energy, Huang–Rhys factor, and the electro-optical frequency. This makes fitting any experimental data using the Schenk model physically relevant. The compact formulation of the Schenk TAT model involved solving the potential profile in the TFET and using that potential profile to calculate GTAT using the standard Schenk model. The GTAT was then approximated by the Gaussian distribution function for compact implementation. The model was compared against technology computer-aided design (TCAD) results and was found in reasonable agreement. The model was also used to fit an experimental device’s Ids–Vgs characteristics. The results, while not exactly fitting the experimental data, follow the general experimental Ids–Vgs trend reasonably well; the subthreshold slope was loosely similar to the experimental device. Additionally, the ON-current, especially to make a high drain-source bias model accurate, can be further improved by including effects such as electrostatic degradation and series resistance.