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At least 1,693 records · Page 94

On Bellman’s and Knuth’s Problems and their Generalizations

Various generalizations of the classical problem of the fastest raising to a power (or the so-called problem on addition chains) are studied in the asymptotic sense. Under weak restrictions, we demonstrate asymptotically tight solutions of the two best known generalizations, namely, Bellman’s problem on the computational complexity (on the minimal number of multiplication operations) of a normed monomial of several variables and Knuth’s problem on the computational complexity of a power system of one variable. We also briefly review some results on the computational complexity for three problems, namely, the computation of p-element systems of normed monomials in q variables, additive computations for systems of p integer linear forms over q variables, and the computation of p-element systems of the free Abelian group with q generators.

97 MATHEMATICS AND COMPUTING↗

Once More on the Lattice of Subvarieties of the Wreath Product of the Variety of Semilattices and the Variety of Semigroups with Zero Multiplication

It is known that the monoid wreath product of any two semigroup varieties that are atoms in the lattice of all semigroup varieties may have a finite as well as an infinite lattice of subvarieties. If this lattice is finite, then as a rule it has at most eleven elements. This was proved in a paper of the author in 2007. The exclusion is the monoid wreath product Sl w N{sub 2} of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice L(Sl w N{sub 2}) of subvarieties of Sl w N{sub 2} is still unknown. In a previous paper, we have shown that the lattice L(Sl w N{sub 2}) contains a sublattice having 33 elements. In the present paper, it is proved that the lattice under consideration has exactly three maximal subvarieties. As a first application of the obtained results we calculate the finite basis of the lattice union of the variety of all semilattices and the largest variety among subvarieties of our lattice having at least one heterotypic identity. As a second application we show that the considered lattice of subvarieties has at least 39 elements.

97 MATHEMATICS AND COMPUTING↗

To the Calculations of Scattering Amplitudes in Diffraction Problems for Elongated Bodies of Revolution

This paper is a complement to the article “Scattering amplitudes in a neighborhood of limit rays in short-wave diffraction by elongated bodies of revolution”. It contains discussions of some points of the article, which worth of more detailed considerations, such as the influence of the integration limits on the computation result of scattering amplitudes and the estimation of permissible values of scattering angle intervals as functions of parameters of the problems.

97 MATHEMATICS AND COMPUTING↗

Analyzing honeycomb photonic crystal waveguides by Dirichlet-to-Neumann maps

As an analog to graphene, honeycomb photonic crystals (PhCs) have attracted a great deal of interest in recent years. The additional degrees of freedom in a honeycomb PhC are useful in designing and optimizing waveguides, can be used to control the symmetry of the system and to realize novel optical devices. In this paper, we present an efficient numerical method for analyzing two-dimensional honeycomb PhC waveguides. Our method is based on a special supercell that covers one period of the honeycomb PhC waveguide and the so-called Dirichlet-to-Neumann map of the supercell. The method gives rise to a linear eigenvalue value problem with relatively small matrices, and it is validated by comparing with previous works. As an application of the method, we calculate edge modes for a few different PhCs. For a honeycomb PhC with dielectric rods in air, we found an edge mode at the zigzag edge, without using special modified rods at the edge. For a honeycomb PhC with air holes, we found a new edge mode when the PhC is bounded by a perfectly electric conductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

An elementary optical logic circuit for quantum computing: a review

The classical computing has already done wonders with computation, however limitations on speed and security of transmitted information is endorsing novel computation techniques. Quantum computing is expected to resolve complex problems especially for unachievable speed with best possible secure communication. The logic gates for two Quantum bits (qubits) are one of the most important part of information processing in Quantum computing. Although photons are the best candidates for the processing of qubit but they need lots of nonlinear coupling to perform logic operations. Recent developments in the field of integrated optics showing promising signs for the development of Quantum networks and Quantum computation. In this article we have reviewed the technology of handling polarization encoded Qubit to perform logic operations and interconnections of logic circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Generation of spiraling Bessel beams from dark/antidark Gaussian beams diffracted by a curved fork-shaped hologram

In this paper, we present a theoretical study on the generation of spiraling Bessel beams by illuminating a curved fork-shaped hologram (CFH) by spatially coherent dark/antidark Gaussian beams. The amplitude expression of the generated spiraling Bessel beam is obtained by using the framework of the Fresnel diffraction approach and by means of the stationary phase method. Numerical calculations show that upon propagating, the longitudinal intensity of the generated field reaches a threshold maximum value at a distance z{sub max}. It is demonstrated that z{sub max} increases with the increasing of the topological charge p and the order m. The result corresponding to the incident Gaussian beam diffracted by CFH is obtained as a particular case of this study.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stopping of Fast Structural Ions in a Substance by Means of Excitation of Their Own Electrons

The paper considers the theory of stopping of fast structural ions in a substance. Within the eikonal approximation, it develops a non-perturbative method for calculation of effective stopping of fast structural ions by means of excitation of their own electrons during collision with atoms. It shows that taking into account the interaction of atoms with the ion nucleus can make a considerable contribution into the value of the abovementioned effective stopping. It also examines the dependence of this contribution on the charge of the ion nucleus.

74 ATOMIC AND MOLECULAR PHYSICS↗

Radial Inertia Effect on Dynamic Compressive Response of Polymeric Foam Materials

Polymeric foams have been extensively used in shock isolation applications because of their superior shock or impact energy absorption capability. However, as a type of soft condensed matter, the highly nonlinear, heterogeneous, and dissipative behavior of polymeric foams may result in an ineffective mitigation or isolation to shock/blast loading. To meet certain desired shock mitigation or isolation requirements, the polymeric foams need to be experimentally characterized to obtain their intrinsic material response. However, radial inertia during dynamic compression has become a severe issue and needs to be fully understood. In this study, we developed an analytical method to calculate the additional stress induced by radial inertia in a polymeric foam specimen. The radial inertia is generally caused by Poisson’s effect and associated with three different mechanisms – axial strain acceleration, large deformation, and Poisson’s ratio change. In conclusion, the effect of Poisson’s ratio change during deformation on radial inertia was specifically investigated for hyperelastic foam materials, and verified with experimental results obtained from Kolsky compression bar tests on a silicone foam.

36 MATERIALS SCIENCE↗

Static Thermochemical Model of COREX Melter Gasifier

COREX is one of the commercial smelting reduction processes. It uses the finer size ore and semi-soft coal instead of metallurgical coke to produce hot metal from iron ore. The use of top gas with high calorific value as a by-product export gas makes the process economical and green. The predictive thermochemical model of the COREX process presented here enables rapid computation of process parameters such as (1) required amount of ore, coal, and flux; (2) amount of slag and gas generated; and (3) gas compositions (based on the raw material and desired hot metal quality). The model helps in predicting the variations in process parameters with respect to the (1) degree of metallization and (2) post-combustion ratio for given raw material conditions. In general reduction in coal, flux, and oxygen, the requirement is concomitant with an increase in the degree of metallization and post-combustion ratio. The model reported here has been benchmarked using industrial data obtained from the JSW Steel Plant, India.

01 COAL, LIGNITE, AND PEAT↗

Synergistic Effect of Nitrogen and Refractory Material on TiN Formation and Equiaxed Grain Structure of Ferritic Stainless Steel

The effect of nitrogen content on the formation of an equiaxed solidification structure of Fe-16Cr steel was investigated. Moreover, two different kinds of refractory materials, i.e., alumina and magnesia, were employed to control the type of oxide inclusion. The characteristics of TiN(-oxide) inclusions were quantitatively analyzed in both molten steel and solidified samples. When the melting was carried out in the alumina refractory, the grain size continuously decreased with increasing nitrogen content. However, a minimum grain size was observed at a specific nitrogen content (approx. 150 ppm) when the steel was melted in the magnesia refractory. Most of the single TiN particles had a cuboidal shape and fine irregularly shaped particles were located along the grain boundary due to the microsegregation of Ti at the grain boundary during solidification. The type of TiN-oxide hybrid inclusion was strongly affected by the refractory material where Al{sub 2}O{sub 3}-TiN and MgAl{sub 2}O{sub 4}-TiN hybrid-type inclusions were obtained in the alumina and magnesia refractory experiments, respectively. The formation of oxide inclusions was well predicted by thermochemical computations and it was commonly found that oxide particles were initially formed, followed by the nucleation and growth of TiN. When the nitrogen content increased, the number density of TiN linearly increased in the alumina refractory experiments. However, the number of TiN exhibits a maximum at about [N] = 150 ppm, at which a minimum grain size was obtained in the magnesia refractory experiments. Therefore, the larger the number density of TiN, the smaller the primary grain size after solidification. The number density of TiN in the steel melted in the magnesia refractory was greater than that in the steel melted in the alumina refractory at given Ti and N contents, which was due to the lower planar lattice disregistry of MgAl{sub 2}O{sub 4}-TiN interface rather than that of Al{sub 2}O{sub 3}-TiN interface. When ∆T{sub TiN} (= difference between the TiN precipitation temperature and the liquidus of the steel) was 20 K to 40 K, the number density of effective TiN was maximized and thus, the grain size was minimized after solidification. Finally, although most of the TiN particles were smaller than 1 μm in the molten steel samples irrespective of the nitrogen content, TiN particles larger than 10 μm were observed in the solidified samples when the nitrogen content was greater than 150 ppm. The growth of TiN particles during melting and solidification was well predicted by the combinatorial simulation of the ‘Ostwald ripening model’ based on the Lifshitz–Slyozov–Wagner theory in conjunction with the ‘Diffusion controlled model’ using Ohnaka’s microsegregation equation.

36 MATERIALS SCIENCE↗

Influence of Aluminum-Carbon Composite Pellets on FeO Reduction and Iron Recovery from Electric Arc Furnace Slag

We investigated the effect of Al-C composite pellets (ACCP) on the reduction behavior of FeO in electric arc furnace (EAF) slag and the iron recovery at different n{sub Al}/(n{sub Al} + n{sub C}) at 1823 K (1550 °C). A carbothermic reaction was the dominant process at n{sub Al}/(n{sub Al} + n{sub C}) < 0.4, whereas aluminothermic reduction was the major process at n{sub Al}/(n{sub Al} + n{sub C}) > 0.6; these observations are based on the final content of FeO and Al{sub 2}O{sub 3} in the molten slag. The aluminum and carbon present in the ACCP competitively affected the reaction stoichiometry (i.e., the material balance) between the production of CO + Al{sub 2}O{sub 3} and the consumption of FeO. Iron recovery increased up to a yield of approx. 90 pct as the n{sub Al}/(n{sub Al} + n{sub C}) ratio increased. Because Al in the ACCP readily reacts to reduce FeO in the molten slag, iron recovery is proportional to the n{sub Al}/(n{sub Al} + n{sub C}) ratio. The precipitation of solid compounds in the slag phase, such as monoxide ([Mg,Fe]·O) and spinel (MgO·Al{sub 2}O{sub 3}), occurred during FeO reduction; this was experimentally confirmed as well as by thermochemical computation. Furthermore, we proposed a schematic reaction mechanism in the present study.

36 MATERIALS SCIENCE↗

Sensitivity of Viscosity on Molten Ti Infusion into a B{sub 4}C-Packed Bed at the Microscale

The effect of the surface tension–viscosity dissipation driving liquid Ti flow into a B{sub 4}C packed bed was analyzed at 1941 K and 2573 K. The model consisted of randomized size distributions of pores (1 to 10 µm) mimicking a packed bed to determine the depth of infusion. Statistical uncertainty was determined as a function of viscosity and pore geometry. The computations were performed with our in-house software, which incorporates a directed acyclic graph and modified nodal analysis algorithms.

36 MATERIALS SCIENCE↗

Evolutionary computation algorithms to coordinating order acceptance and batch delivery for an integrated supply chain scheduling

This paper proposes a novel approach of coordinating decisions in an integrated supply chain (ISC): coordinating order acceptance (OA) and batch delivery (BD) due to round trip transportation (RTT) and using third-party logistics (3PL) vehicles. The paper aims at trading off among accepted orders revenue, delivery costs as well as any penalties incurred in the ISC to maximize the total benefit. A novel mixed-integer programming is proposed for the problem. In addition, the paper provides a heuristic to form batches and develops a hybrid evolutionary computation algorithms based on particle swarm optimization (PSO) and genetic algorithm (GA) to solve the problem. An information sharing mechanism is improved and applied. To explore and to locate the proposed PSO in a better neighborhood, a local search is proposed. Taguchi experimental design is utilized to set the appropriate values of the algorithms’ parameters and random instances are generated to evaluate the performance of the algorithms. The paper investigates the profitability sensitivity of the problem to parameters and analyzes the effect of the changes in the parameters on the performance of our proposed algorithms. The attained results show the appropriate performance of our algorithms.

97 MATHEMATICS AND COMPUTING↗

RFB Side Effects - Shunt Currents

The various models related to fluid flow, electrochemistry and shunt current, and their interactions are reviewed, and gaps identified in the development of flow battery holistic models. In a flow battery stack, the cells are electrically connected through the manifolds via the electrolyte. This results in shunt current through the electrolyte, which is a source of loss in the battery stack. This issue is examined in depth with a mathematical method of calculating shunt current distribution, the associated losses, and strategies to mitigate shunt current losses, along with the trade-offs.

Crawford, Aladsair J.↗

Hybrid machine learning/physics-based approach for predicting oxide glass-forming ability

Predicting the liquid compositions that will vitrify at experimentally accessible quench rates remains one of the grand challenges in the field of condensed matter physics. This glass-forming ability can be quantified as the critical quench rate needed to suppress crystallization. Knowledge of this critical quench rate also informs which glass composition could be used for new applications. There have been several physical and empirical models presented in the literature to predict the critical quench rate/glass forming ability. These models range from those theoretically derived to those quantified only through experimental characterization. In this work, we instead propose a new method to calculate the critical quench rate using the recently developed toy landscape model combined with machine learning. The toy landscape model accesses the underlying physics that control the vitrification behavior by directly simulating the liquid thermodynamics and kinetics. In conclusion, the results are discussed in terms of industrial impact, physical insights, and how the glass science community can develop improved predictions of glass-forming ability.

Crystallization↗

Electron impact excitation of N-like ions from the ICFT R-matrix calculation

We carried out intermediate coupling frame transformation (ICFT) R-matrix calculations on N-like ions (11≤Z≤20), which included a total of 272 fine structure levels in both the configuration interaction (CI) and close-coupling (CC) collision expansions. Comparisons with previous theoretical values were made in terms of energy levels, radiative transition rates, and oscillator strengths. The effective collision strengths (ϒ) were estimated in the temperature range of 10{sup 4}–10{sup 7} K. An excellent agreement with available computations was reached for dipole-allowed transitions, while differences in ϒ were found for non-dipole allowed and forbidden transitions. This discrepancy is mainly attributed to the difference in CC expansions. Our calculations provide a good supplement to the electron impact excitation data on N-like ions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

The ground-state properties of nuclei with 8 $\leqslant$ Z $\leqslant$ 120 from the proton drip line to the neutron drip line have been investigated using the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. Here, it is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the α-decay energies and proton emitters based on the RCHB calculations are investigated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: II. Fully vibrationally-resolved electronic excitation of the isotopologues of H 2 (X 1 $Σ^{+}_{g}$)

Here, we present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of the isotopologues of molecular hydrogen (D 2 , T 2 , HD, HT, and DT) initially in the ground electronic state. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 500 eV for excitation of all bound vibrational levels and dissociative excitation of the B 1 $Σ^{+}_{g}$, C 1 Π u , EF 1 $Σ^{+}_{g}$, B' 1 $Σ^{+}_{g}$, GK 1 $Σ^{+}_{g}$, I 1 Π g , J 1 Δ g , D 1 Π u , H 1 $Σ^{+}_{g}$, b 1 $Σ^{+}_{g}$, c 3 Π u , a 3 $Σ^{+}_{g}$, e 3 $Σ^{+}_{u}$, d 3 Π u , h 3 $Σ^{+}_{g}$, g 3 $Σ^{+}_{g}$, i 3 Π g , and j 3 Δ g electronic states from all bound vibrational levels of the ground electronic (X 1 $Σ^{+}_{g}$) state. Including the previously-published MCCC e-H2 cross sections the data set contains cross sections for over 60,000 electronic and vibrational transitions. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org.

74 ATOMIC AND MOLECULAR PHYSICS↗