Study of decagonal approximant and γ-brass-type compounds in Al-Cr-Fe thin films

This paper reports the preparation conditions and structure characteristics of Al-Cr-Fe very thin films (10-30 nm) obtained by the flash evaporation technique. The films are either amorphous or crystallized, depending on the thickness of the sample and temperature of the substrate. Annealing of amorphous films leads to crystallization of intermetallic phases that are all linked with quasicrystals. In particular, we have identified by transmission electron microscopy the following structures: body-centered-cubic (bcc) γ-brass phase, monoclinic λ-Al13(Cr,Fe)4 phase, and orthorhombic O1-phase, all of them already observed in this system, together with four new structures, i.e., a face-centered-cubic (fcc) γ-brass phase (superstructure of the bcc phase), monoclinic λ′-phase (related to the λ-phase) and two orthorhombic phases (1/1/; 1/1) and (1/0; 2/1) approximants of the decagonal phase). In this study, we point out the occurrence of twin defects of the λ-Al13(Cr,Fe)4 phase. Films prepared directly in the crystalline state comprise the O1 approximant. Electron energy loss spectroscopy measurements show that all films are not oxidized except for the presence of a native oxide layer that forms in ambient atmosphere with a thickness that cannot exceed 0.3 nm. Optical properties were investigated and show that films need to be large enough (>30 nm) to reproduce the properties of bulk alloys. Finally, contact angle wetting measurements reveal that the presence of such films on a substrate, even at very low thickness, considerably decreases the wetting behavior by wate

Coreness of Cooperative Games with Truncated Submodular Profit Functions

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game with truncated submodular profit functions. Specifically, the profit function $f(\cdot)$ is defined by a truncation of a submodular function $\sigma(\cdot)$: $f(\cdot)=\sigma(\cdot)$ if $\sigma(\cdot)\geq\eta$ and $f(\cdot)=0$ otherwise, where $\eta$ is a given threshold. In this paper, we study the core and three core-related concepts of truncated submodular profit cooperative game. We first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty. When core is empty, we show hardness results and approximation algorithms for computing other core-related concepts including relative least-core value, absolute least-core value and least average dissatisfaction value

Quantum catastrophes: a case study

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N \geq 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.Comment: 23 p

Orthonormal sequences in L2(Rd)L^2(R^d) and time frequency localization

We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.Comment: 18 page

The sequence of rice chromosomes 11 and 12, rich in disease resistance genes and recent gene duplications

Background: Rice is an important staple food and, with the smallest cereal genome, serves as a reference species for studies on the evolution of cereals and other grasses. Therefore, decoding its entire genome will be a prerequisite for applied and basic research on this species and all other cereals. Results: We have determined and analyzed the complete sequences of two of its chromosomes, 11 and 12, which total 55.9 Mb (14.3% of the entire genome length), based on a set of overlapping clones. A total of 5,993 non-transposable element related genes are present on these chromosomes. Among them are 289 disease resistance-like and 28 defense-response genes, a higher proportion of these categories than on any other rice chromosome. A three-Mb segment on both chromosomes resulted from a duplication 7.7 million years ago (mya), the most recent large-scale duplication in the rice genome. Paralogous gene copies within this segmental duplication can be aligned with genomic assemblies from sorghum and maize. Although these gene copies are preserved on both chromosomes, their expression patterns have diverged. When the gene order of rice chromosomes 11 and 12 was compared to wheat gene loci, significant synteny between these orthologous regions was detected, illustrating the presence of conserved genes alternating with recently evolved genes. Conclusion: Because the resistance and defense response genes, enriched on these chromosomes relative to the whole genome, also occur in clusters, they provide a preferred target for breeding durable disease resistance in rice and the isolation of their allelic variants. The recent duplication of a large chromosomal segment coupled with the high density of disease resistance gene clusters makes this the most recently evolved part of the rice genome. Based on syntenic alignments of these chromosomes, rice chromosome 11 and 12 do not appear to have resulted from a single whole-genome duplication event as previously suggested

An Improved Approximation Bound for Spanning Star Forest and Color Saving

Abstract. We present a simple algorithm for the maximum spanning star forest problem. We take advantage of the fact that the problem is a special case of complementary set cover and we adapt an algorithm of Duh and Fürer in order to solve it. We prove that this algorithm computes 193/240 ≈ 0.804-approximate spanning star forests; this result improves a previous lower bound of 0.71 by Chen et al. Although the algorithm is purely combinatorial, our analysis defines a linear program that uses a parameter f and which is feasible for values of the parameter f not smaller than the approximation ratio of the algorithm. The analysis is tight and, interestingly, it also applies to complementary versions of set cover such as color saving; it yields the same approximation guarantee of 193/240 that marginally improves the previously known upper bound of Duh and Fürer. We also show that, in general, a natural class of local search algorithms do not provide better than 1/2-approximate spanning star forests.

Modeling of dendrite growth from undercooled nickel melt: sharp interface model versus enthalpy method

The dendritic growth of pure materials in undercooled melts is critical to understanding the fundamentals of solidification. This work investigates two new insights, the first is an advanced definition for the two-dimensional stability criterion of dendritic growth and the second is the viability of the enthalpy method as a numerical model. In both cases, the aim is to accurately predict dendritic growth behavior over a wide range of undercooling. An adaptive cell size method is introduced into the enthalpy method to mitigate against `narrow-band features' that can introduce significant error. By using this technique an excellent agreement is found between the enthalpy method and the analytic theory for solidification of pure nickel

A stable dendritic growth with forced convection: A test of theory using enthalpy-based modeling methods

The theory of stable dendritic growth within a forced convective flow field is tested against the enthalpy method for a single-component nickel melt. The growth rate of dendritic tips and their tip diameter are plotted as functions of the melt undercooling using the theoretical model (stability criterion and undercooling balance condition) and computer simulations. The theory and computations are in good agreement for a broad range of fluid velocities. In addition, the dendrite tip diameter decreases, and its tip velocity increases with increasing fluid velocity