Morse Theory And Invariant Concepts of Convexity

In optimization, the literature on invariant definitions of convexity has largely centered on the notion of invexity. However, the connection with Morse theory and related geometric trends has not been recognized and results do not appear to be as impressive as those in topology. Our purpose is to improve the situation in optimization, and to clarify the relationship between these two trends. The main result is that the problem can be reduced to the case of functions of one variable.     

Influence of the mode of deformation on recrystallisation kinetics in Nickel through experiments,theory and phase field model

Abstract

In this paper, we report the influence of the mode of deformation on recrystallisation kinetics through experiments, theory and a phase field model. Ni samples of 99.6% purity are subjected to torsion and rolling at two equivalent plastic strains and the recrystallisation kinetics and microstructure are compared experimentally. Due to significant differences in the distributions of the nuclei and stored energy for the same equivalent strain, large differences are observed in the recrystallisation kinetics of rolled and torsion-tested samples. Next, a multi-phase field model is developed in order to understand and predict the kinetics and microstructural evolution. The coarse-grained free energy parameters of the phase field model are taken to be a function of the stored energy. In order to account for the observed differences in recrystallisation kinetics, the phase field mobility parameter is a required constitutive input. The mobility is calculated by developing a mean field model of the recrystallisation process assuming that the strain free nuclei grow in a uniform stored energy field. The activation energy calculated from the mobilities obtained from the mean field calculation compares very well with the activation energy obtained from the kinetics of recrystallisation. The recrystallisation kinetics and microstructure as characterised by grain size distribution obtained from the phase field simulations match the experimental results to good accord. The novel combination of experiments, phase field simulations and mean field model facilitates a quantitative prediction of the microstructural evolution and kinetics.     

Early transition metal dopants in cuprous oxide: To spin or not to spin

We present a trend study of a large variety of dopants at the cation site in Cu₂O (i.e. substituting Cu), focussing largely on the early 3d-, 4d-, and 5d-transition metals (TMs) in which many of them are known to be non-magnetic. We also include s-, sp- and d¹⁰-metals for comparison. We find that doping with sp-elements results in zero spin moment while dopants with a partially filled d-band show a stronger tendency to magnetize and 3d-TM dopants exhibit a larger magnetic moment than most of the 4d- and 5d-TM dopants. From this trend study, we also find a correlation between their substitution enthalpy and associated interatomic relaxations. In particular, Ti-doped Cu₂O appears to be an interesting system, given its “peculiar” ability to exhibit a spin moment when doped with a non-magnetic substituent like Ti. We also find that the interaction between two doped Ti atoms in Ti₂:Cu₂O is predominantly antiferromagnetic, and interestingly (and unexpectedly), this interaction rapidly declines as a function of inter-dopant distance, as in the case for the magnetic late-TM dopants like Co₂:Cu₂O.     

Crime and punishment: Does it pay to punish?

Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension.     

Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies

We review some of the techniques that lead to the effective medium representation of a three-dimensional (3D) periodic metamaterial. We consider a 3D lattice of lead telluride cubic resonators at mid-infrared (MIR) frequencies. Each cubic resonator is modeled with both an electric and a magnetic dipole, through a method called the dual dipole approximation. The electric and magnetic polarizabilities of a cubic resonator are computed via full-wave simulations by mapping the resonator's scattered field under electric/magnetic excitation only to the field radiated by an equivalent electric/magnetic dipole. We then analyze the allowed modes in the lattice, with transverse polarization and complex wavenumber, highlighting the attenuation that each mode experiences after one free space wavelength. We observe the presence of two modes with low attenuation constant, dominant in different frequency ranges, able to propagate inside the lattice: this allows the treatment of the metamaterial as a homogeneous material with effective parameters, evaluated by using various techniques. We then show that the metamaterial under analysis allows for the generation of artificial magnetism (i.e., relative effective permeability different than unity, including negative permeability with low losses) at MIR frequencies.     

Multiple Keys for a Single Lock: The Unusual Structural Plasticity of the Nucleotidyltransferase (4′)/Kanamycin Complex

The most common mode of bacterial resistance to aminoglycoside antibiotics is the enzyme‐catalysed chemical modification of the drug. Over the last two decades, significant efforts in medicinal chemistry have been focused on the design of non‐ inactivable antibiotics. Unfortunately, this strategy has met with limited success on account of the remarkably wide substrate specificity of aminoglycoside‐modifying enzymes. To understand the mechanisms behind substrate promiscuity, we have performed a comprehensive experimental and theoretical analysis of the molecular‐recognition processes that lead to antibiotic inactivation by Staphylococcus aureus nucleotidyltransferase 4′(ANT(4′)), a clinically relevant protein. According to our results, the ability of this enzyme to inactivate structurally diverse polycationic molecules relies on three specific features of the catalytic region. First, the dominant role of electrostatics in aminoglycoside recognition, in combination with the significant extension of the enzyme anionic regions, confers to the protein/antibiotic complex a highly dynamic character. The motion deduced for the bound antibiotic seem to be essential for the enzyme action and probably provide a mechanism to explore alternative drug inactivation modes. Second, the nucleotide recognition is exclusively mediated by the inorganic fragment. In fact, even inorganic triphosphate can be employed as a substrate. Third, ANT(4′) seems to be equipped with a duplicated basic catalyst that is able to promote drug inactivation through different reactive geometries. This particular combination of features explains the enzyme versatility and renders the design of non‐inactivable derivatives a challenging task.     

Reprint of : Connection between wave transport through disordered 1D waveguides and energy density inside the sample: A maximum-entropy approach

We study the average energy – or particle – density of waves inside disordered 1D multiply-scattering media. We extend the transfer-matrix technique that was used in the past for the calculation of the intensity beyond the sample to study the intensity in the interior of the sample by considering the transfer matrices of the two segments that form the entire waveguide. The statistical properties of the two disordered segments are found using a maximum-entropy ansatz subject to appropriate constraints. The theoretical expressions are shown to be in excellent agreement with 1D transfer-matrix simulations.     

Synthesis of poly(ethylene glycol)‐based hydrogels and their swelling/shrinking response to molecular recognition

To synthesize the novel molecular‐ and pH‐stimulus‐responsive hydrogel, we prepared poly(ethylene glycol)‐based hydrogel containing ionic groups. We evaluated the fundamental swelling/shrinking properties of the hydrogels synthesized by various conditions. Decreasing the molecular weight of a crosslinker provided the increasing of the equilibrium swelling ratio. Also, the equilibrium swelling ratio was changed by the introduction of functional ionic monomers and its compositions. Furthermore, the swelling/shrinking behaviors of the hydrogels were affected by the environmental condition of aqueous solution, in fact the hydrogels were considerably shrunk (to one‐fifth volume) using a di‐ionic solute in the aqueous solution through the ionic interactions between the hydrogel and the solutes. Additionally, the specific shrinking to diamine compounds was also observed in response to pH change. These results clearly show the swelling/shrinking responsibility of the hydrogels toward the molecular recognitions and its pH conditions. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3153–3158