Multicomponent superconducting order parameter in UTe2

An unconventional superconducting state was recently discovered in UTe2, where spin-triplet superconductivity emerges from the paramagnetic normal state of a heavy fermion material. The coexistence of magnetic fluctuations and superconductivity, together with the crystal structure of this material, suggest that a unique set of symmetries, magnetic properties, and topology underlie the superconducting state. Here, we report observations of a non-zero polar Kerr effect and of two transitions in the specific heat upon entering the superconducting state, which together suggest that the superconductivity in UTe2 is characterized by a two-component order parameter that breaks time reversal symmetry. These data place constraints on the symmetries of the order parameter and inform the discussion on the presence of topological superconductivity in UTe2.

Diffusion in multicomponent aqueous alcoholic mixtures

The Fick diffusion coefficient matrix of the highly associating quaternary mixture water + methanol + ethanol + 2-propanol as well as its ternary and binary subsystems is analyzed with molecular dynamics simulation techniques. Three of the ternary subsystems are studied in this sense for the first time. The predictive capability of the employed force fields, which were sampled with the Green–Kubo formalism and Kirkwood–Buff integration, is confirmed by comparison with experimental literature data on vapor-liquid equilibrium, shear viscosity and Fick diffusion coefficient, wherever possible. A thorough analysis of the finite size effects on the simulative calculation of diffusion coefficients of multicomponent systems is carried out. Moreover, the dependence of the Fick diffusion coefficient matrix on the velocity reference frame and component order is analyzed. Their influence is found to be less significant for the main matrix elements, reaching a maximum variation of 19%. The large differences found for the cross elements upon variation of the reference frame hinder a straightforward interpretation of the Fick diffusion coefficient matrix with respect to the presence of diffusive coupling effects.

On the k -Component Independence Number of a Tree

Let G be a graph and k ≥ 1 be an integer. A subset S of vertices in a graph G is called a k -component independent set of G if each component of G S has order at most k . The k -component independence number, denoted by α c k G , is the maximum order of a vertex subset that induces a subgraph with maximum component order at most k . We prove that if a tree T is of order n , then α k T ≥ k / k + 1 n . The bound is sharp. In addition, we give a linear-time algorithm for finding a maximum k -component independent set of a tree.

An investigation of reliability optimization in standby systems

Due to the limitations of space or extra costs incurred, the reliability optimization problem of a spare system is of great interest and importance. In this article, we devote our efforts into the investigation of reliability optimization problem of the warm spare gate and cold spare gate. For a spare gate with fixed components, we first examine the relationship between the component order and the corresponding reliability; then, the equivalence of a cascaded model with a multiple-input spare gate is further presented. We find that for a warm spare gate, the corresponding reliability value is anticipated to be affected by the adopted component replacing order; nevertheless, the reliability is a fixed value once the components are provided for a cold spare gate. This finding indicates that reliability is irrespective of the component order for a cold spare gate. Therefore, for the warm spare gate, the component order can be varied to improve the corresponding system reliability, whereas for the cold spare gate, we should attempt to improve the reliabilities of the spare components aiming to obtain a higher reliability. These findings are potentially useful in the design process of a system consisting of spare gates.

Supplier Replacement Model in a One-Level Assembly System under Lead-Time Uncertainty

Supplier selection/replacement strategies and optimized purchasing policies play a key role in efficient supply chain management in today’s dynamic market. Here we study supplier replacement in a one-level assembly system (OLAS) producing one type of finished product. To assemble the product, we need to provide multi-type components, but assembly will be interrupted if any single component is missing, and incoming units will get hoarded until the missing component arrives. The assembly process can be interrupted by various sources of uncertainty, including delays in component deliveries. There is consequently a non-negligible risk that the assembly process may get stopped any moment. This brings inventory-related costs, which should be minimized. Here we consider discrete lead-time distributions to mimic industry-world reality. We present a model that takes into account not only optimal assignment of component order release dates but also replacement of a critical supplier. For a given unit, we model several alternative suppliers with alternative pricing and lead-time uncertainties, and we evaluate the impact on the total assembly system. For a more general case where several suppliers may be replaced, we propose a genetic algorithm.

One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning

The unusual correlated state that emerges in URu2Si2 below THO = 17.5 K is known as “hidden order” because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are “hidden.” We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across THO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

Multiple Precast Component Orders Acceptance and Scheduling

Precast components manufacturer generally operates under limited production capacity and produces products of one order which may delay another. This paper develops a precast component order acceptance and scheduling model that aims to maximize the total profit in a stochastic multiple orders environment. In that model, the increasing of the overall profit of the precast component manufacturer is achieved by using a heuristic algorithm and a dynamic order acceptance heuristic. Results of numerical examples indicate the proposed model realizes the increasing total profit in most cases comparing to accept all of the orders. Besides, this study tested three order acceptance criteria and found that the profit-based criterion is to be more stable in terms of maximum total profit. This approach is anticipated to provide support to precast component manufacturers when faced with multiple orders in long-term production.

Methods of catastrophe theory in the phenomenology of phase transitions

The monograph is devoted to describing the methods of catastrophe theory and building on the basis of these methods, phenomenological models of phase transitions in solids. Methods of constructing structurally stable normal forms of functions, including functions that are imposed on the symmetry conditions. The classification of phenomenological models of phase transitions for two interacting one-component order parameter, two-component and three-component order parameters the number of control parameters varied in the experiment. Theoretical dependence of the anomalies of the physical properties of the models are compared with experimental data in ferroelectrics, magnetic materials, solid solutions of rare earth metals, multiferroics and other solids that are experiencing phase transitions. For professionals in the field of solid state physics and phase transitions.

On the elusive grammatical status of da-construction in Macedonian and Serbian (independent type)

The da-construction in Macedonian and Serbian languages combines the modal conjunctive particle da with the finite form of the verb to express a wide range of modal meanings. Being a Balkan Sprachbund novelty, the da-constructions in dependent clauses take on the functions of the infinitive in a complex predicate (in all cases in Macedonian, partly in Serbian). The da-construction in independent simple sentences has a complete conjugation paradigm with the imperative meaning and competes with the synthetic imperative forms in both languages, expressing also optative meanings. The article offers an analytical review on the status of these forms based on data gathered from Macedonian, Bulgarian (being closely related to Macedonian) and Serbian languages. There are two salient extremes in it: 1) the da-construction is not an analytical form of the verb and does not have an independent status in the verb system, instead it functions as a syntactic construction; 2) it is indeed an analytical form of the subjunctive mood, with da being a grammatical indicator of modality with the general non-factual meaning. The article concludes that the first view should be regarded as definitive in determining the status of the da- constructions in the Serbian language. To support this conclusion, we are putting forward the following arguments: a) the verb form is non-adjacent to the da particle in the form; b) there is a competition between the infinitive and the da- constructions as complex predicates as well as in some tenses (future tense: ja ću ići / ja ću da idem) and negative structures (nemoj ići / nemoj da ideš); c) The conjunctive particle da does not always have the non-factual meaning, and in most cases the following verb form can take on any tense or mood. In Macedonian the da-construction should be regarded as an analytical form of the subjunctive mood on account of the following characteristics: а) the da-construction has a syntactically fixed component order, which means that it is a semantically bound or fused chain of components which lost their individual meanings; b) the da-construction has a complete conjugation paradigm, one for da+praes and another for da+imperf, on which stems a wide range of modal meanings: imperative, optative and some others; c) the particle da has an invariant meaning of non-factuality, and it marks the verb form in this construction as non-indicative.

The Mechanisms of Proversion and Reversion in Producing the Compounds of the English Language

The subject-matter of this paper is the structural mechanism of the proverse and reverse word-compounding as a word-building process in modern English while having the model of word-combination as a starting basis for such transformations. The mechanism of proversion represents the process transforming a word-combination into a compound word while preserving the initial order of components coinciding with that of a word-combination (A + B → AB). When the reverse process of compounding takes place, the components of a resulting compound word change their places as to each other in comparison with a component-order in an initial word-combination (A + B → BA). The hypothesis of the investigation is that the compounding by proversion occurs if words of an initial word-combination are tied with the syntactic relation of agreement, while the reverse compounding usually tends to provide compounding on the basis of the syntactic relation of control. The proversive model is mostly the basis for creating nominative parts of speech, and the result of the reverse intergration of a word-combination into a compound word is manifested mainly by a verb or a verbal. The article describes the general and certain specific models of proverse and reverse compounding with the indication of their functional and stylistic peculiar features. The conclusion indicates the perspectives of working out the problem on the basis of other languages and on the comparative ground.