DFT Calculations of Vibrational Frequencies of Carbon–Nitrogen Clusters: Raman Spectra of Carbon Nitrides

We have performed the calculation of structures of clusters containing carbon and nitrogen atoms. We determine the bond lengths in each case. We also calculate the vibrational frequencies of all of the clusters. We compare the calculated values of the vibrational frequencies with those measured by the Raman spectra of amorphous carbon nitrides. Some of the calculated frequencies are in agreement with those measured. We identity that linear structures and hence “back bones” are present in the glassy state.     

Alignment of molecules in pulsed resonant laser fields

We investigate by numerical simulations the dynamics of alignment of linear molecules in resonant pulsed laser fields and its dependence on pulse length, field strength, and molecular parameters. We propose an analytical short-time approximation for the time-dependent wave packets. We provide a theoretical basis for the occurrence of saturation in the rotational pumping. We present a formula to predict the time at which the maximum alignment occurs. We discuss the magnitude of the laser-induced alignment and we relate it to a theoretical upper limit.     

The eigenvalue problem in phase space

We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c‐function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi‐representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc.     

Alkaline erosion of CR 39 polymer surfaces

We have investigated the mechanism of erosion of CR 39 polymer in alkaline environments. We observed the kinetics of absorption of water and methanol into both unirradiated and γ-irradiated samples. We use a capillary model to interpret our results.We etched our samples in both KOH solutions, and KOH solutions doped with methanol. Etch rate was desensitizing to γ-irradiation when KOH concentration approached saturation, but KOH solutions doped with methanol were not desensitizing, unlike with nuclear tracks. We account for this difference.     

High-sensitivity detection using isotachophoresis with variable cross-section geometry

We present a theoretical and experimental study on increasing the sensitivity of ITP assays by varying channel cross-section. We present a simple, unsteady, diffusion-free model for plateau mode ITP in channels with axially varying cross-section. Our model takes into account detailed chemical equilibrium calculations and handles arbitrary variations in channel cross-section. We have validated our model with numerical simulations of a more comprehensive model of ITP. We show that using strongly convergent channels can lead to a large increase in sensitivity and simultaneous reduction in assay time, compared to uniform cross-section channels. We have validated our theoretical predictions with detailed experiments by varying channel geometry and analyte concentrations. We show the effectiveness of using strongly convergent channels by demonstrating indirect fluorescence detection with a sensitivity of 100 nM. We also present simple analytical relations for dependence of zone length and assay time on geometric parameters of strongly convergent channels. Our theoretical analysis and experimental validations provide useful guidelines on optimizing chip geometry for maximum sensitivity under constraints of required assay time, chip area and power supply.     

Limit cycles in the presence of convection: a first-order analysis

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads pattern outwards from the source. Convection adds instability to the reaction–diffusion system. We see the result of the instability in a readiness to create pattern. In the case of strong convection, we consider that the first-order approximation may be valid for some aspects of the solution behaviour. We employ the method of Riemann invariants and rescaling to transform the reduced system into one invariant under parameter change. We carry out numerical experiments to test our analysis. We find that most aspects of the solution do not comply with this, but we find one significant characteristic which is approximately first order. We consider the correspondence of the Partial Differential Equation with the Ordinary Differential Equation along rays from the initiation point in the transformed system. This yields an understanding of the behaviour.     

The potential and flux landscape theory of evolution

We established the potential and flux landscape theory for evolution. We found explicitly the conventional Wright's gradient adaptive landscape based on the mean fitness is inadequate to describe the general evolutionary dynamics. We show the intrinsic potential as being Lyapunov function(monotonically decreasing in time) does exist and can define the adaptive landscape for general evolution dynamics for studying global stability. The driving force determining the dynamics can be decomposed into gradient of potential landscape and curl probability flux. Non-zero flux causes detailed balance breaking and measures how far the evolution from equilibrium state. The gradient of intrinsic potential and curl flux are perpendicular to each other in zero fluctuation limit resembling electric and magnetic forces on electrons. We quantified intrinsic energy, entropy and free energy of evolution and constructed non-equilibrium thermodynamics. The intrinsic non-equilibrium free energy is a Lyapunov function. Both intrinsic potential and free energy can be used to quantify the global stability and robustness of evolution. We investigated an example of three allele evolutionary dynamics with frequency dependent selection (detailed balance broken). We uncovered the underlying single, triple, and limit cycle attractor landscapes. We found quantitative criterions for stability through landscape topography. We also quantified evolution pathways and found paths do not follow potential gradient and are irreversible due to non-zero flux. We generalized the original Fisher's fundamental theorem to the general (i.e., frequency dependent selection) regime of evolution by linking the adaptive rate with not only genetic variance related to the potential but also the flux. We show there is an optimum potential where curl flux resulting from biotic interactions of individuals within a species or between species can sustain an endless evolution even if the physical environment is unchanged. We offer a theoretical basis for explaining the corresponding Red Queen hypothesis proposed by Van Valen. Our work provides a theoretical foundation for evolutionary dynamics.     

Proton transference in hydrogen bonded systems. I. Uracil tautomerism

We have made a detailed analysis of the adequacy of different theoretical approaches to the study of uracil tautomerism. We have considered the effect of molecular relaxation and the ability of several methods to reproduce it. We have also considered their performance in predicting the tautomerization energy barrier. We found that semiempirical methods are not adequate for predicting the energy value but that they can be used for obtaining geometry optimizations. We also found a strong discrepancy between the energy values predicted by a minimal basis set and a 2ζ basis set, the last one being 24.9 kcal/mol. The implications of these findings are discussed and the results compared with experimental evidence.     

Complete set of Hopf bifurcation in an autocatalytic ring network

We investigate the Hopf bifurcation for a five species chemical ring network with an autocatalytic reaction. We show that the bifurcation hypersurface in the rate constants space is the boundary of a simply connected set. We use a numerical method to calculate this hypersurface.     

Coarse-grained simulations of ABA amphiphilic triblock copolymer solutions in thin films

We study a coarse-grained model of A(10)-B(20)-A(10) amphiphilic triblock copolymers in aqueous solution under confinement. We focus on the influence of the wall interaction on the morphology of the ensuing self-assembled structures. We also study the dynamics of the polymers. All our simulations are confined between two walls. We study three different combinations of walls: hydrophobic and hydrophobic, hydrophobic and hydrophilic, hydrophilic and hydrophilic. We moreover elucidate the concentration influence. The conformation and behavior of the copolymer in strongly confined systems depend on the type of wall interaction and concentration.     

Low-temperature structural behaviour of LaCoO3 – A high-resolution neutron study

We present the temperature evolution of the crystallographic structure of LaCoO₃ in the range 4–300 K. We observe no anomalies in the rhombohedral unit cell parameters at temperatures where electronic transitions are expected to occur. We also find no evidence of the monoclinic distortion of the unit cell proposed others. We parameterise the octahedral tilt and distortion as a function of temperature which show a linear evolution towards a more symmetric form.     

Fabrication of flexible light shutter using liquid crystals with polymer structure

We fabricated a light shutter using plastic substrates for high visibility of a flexible see-through display. To achieve a flexible light shutter using liquid crystals (LC), it is essential to maintain the cell gap when the light shutter is bent. We studied methods to fabricate flexible LC light shutters using plastic substrates. We demonstrated light shutters that are initially transparent and flexible with or without polymer walls. We have elucidated that polymer walls and networks provide mechanical stability against the bending of an LC light shutter without any degradation in the electro-optic characteristics. We predict that a flexible light shutter provides not only high visibility but also mechanical stability to a flexible see-through display by positioning it at the back of a flexible see-through display panel.     

Ab initio calculation of vibrational frequencies and Raman spectra of barium peroxide glass including comparison of tetrahedral BaO4 with GeO4 and SiO4

We have calculated the vibrational frequencies of clusters of atoms from the first principles by using the density-functional theory in the local density approximation (LDA). We are also able to calculate the electronic binding energy for all of the clusters of atoms from the optimized structure. We have made clusters of BanOm (n, m=1-6) and have determined the bond lengths, vibrational frequencies as well as intensities in each case. We find that the peroxide cluster BaO2 occurs with the O-O vibrational frequency of 836.3 cm(-1). We also find that a glass network occurs in the material which explains the vibrational frequency of 67 cm(-1). The calculated values agree with those measured from the Raman spectra of barium peroxide and Ba-B-oxide glass. We have calculated the vibrational frequencies of BaO4, GeO4 and SiO4 each in tetrahedral configuration and find that the vibrational frequencies in these systems depend on the inverse square root of the atomic mass.     

Average band structure of smectic C* type random materials

We consider a Smectic C* type structure which exhibits alignment fluctuations which can be described by noise associated with both director angles. We take the propagation of axially incident electromagnetic waves, and from Maxwell equations, we establish the stochastic governing set of equations corresponding to optical phenomena. We note that this set of equations can be expressed as a linear vector stochastic system of differential equations with multiplicative noise. We use a procedure to calculate from the stochastic differential set of equations, the governing equations for the expected value of the electromagnetic transverse magnetic and electric fields for a certain autocorrelation function, and calculate explicitly their corresponding band structure for a particular spectral noise density. We have shown that the average resulting electromagnetic fields exhibit a biased decaying exponential dependence which impedes to propagate the waves in one sense while it permits them in the other sense. We have also found a remarkable widening of the band gap and the appearance of new local maxima for the modes without band gap.     

Electrostatics of DNA complexes with cationic lipid membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.     

Interplay between shear flow and elastic deformations in liquid crystals

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.     

Power-law intermittency of single emitters

We summarize experimental observations of fluorescence intermittency of single semiconductor nanocrystals and single molecules. We review the main models proposed earlier to explain the broad power-law distributions of on- and off-blinking times. We argue that a self-trapping model with a distribution of trapping distances can account for most, if not all, observations to date. We propose possible scenarios for photo-ionization, the switching to states with long on-times and the influence of disorder and surfaces on the trapping dynamics.     

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.