Vector Dependence Research Articles

Thermal fluctuations and bending rigidity of bilayer membranes

We present a new scheme to estimate the elastic properties of biological membranes in computer simulations. The method analyzes the thermal fluctuations in terms of a coupled undulatory mode, which disentangle the mixing of the mesoscopic undulations and the high-q protrusions. This approach makes possible the accurate estimation of the bending modulus both for membranes under stress and in tensionless conditions; it also extends the applicability of the fluctuation analysis to the small membrane areas normally used in atomistic simulations. Also we clarify the difference between the surface tension imposed in simulations through a pressure coupling barostat, and the surface tension that can be extracted from the analysis of the low wave vector dependence of the coupled undulatory fluctuation spectrum. The physical analysis of the peristaltic mode is also refined, by separating the bulk and protrusions contributions. We illustrate the procedure by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayers. The bending moduli obtained from our analysis, shows good agreement with available experiments.

Hall thruster plasma fluctuations identified as the E×B electron drift instability: Modeling and fitting on experimental data

Microturbulence has been implicated in anomalous transport at the exit of the Hall thruster, and recent simulations have shown the presence of an azimuthal wave which is believed to contribute to the electron axial mobility. In this paper, the 3D dispersion relation of this E×B electron drift instability is numerically solved. The mode is found to resemble an ion acoustic mode for low values of the magnetic field, as long as a non-vanishing component of the wave vector along the magnetic field is considered, and as long as the drift velocity is small compared to the electron thermal velocity. In these conditions, an analytical model of the dispersion relation for the instability is obtained and is shown to adequately describe the mode obtained numerically. This model is then fitted on the experimental dispersion relation obtained from the plasma of a Hall thruster by the collective light scattering diagnostic. The observed frequency-wave vector dependences are found to be similar to the dispersion relation of linear theory, and the fit provides a non-invasive measurement of the electron temperature and density.

Theory of Nano-Carbon Based Materials: Cyclotron Resonance, Kohn's Theorem and Hubbard Model

A monolayer of carbon is called graphene. It exhibits unusual properties in the Hall effect and in the cyclotron resonance. It is found that it exhibits fractional charge in the Hall effect. The interactions amongst electrons almost become constant at low temperatures. Hence, the Kohn's theorem, which shows that the interactions do not play much role in determining the cyclotron resonance, becomes operative at low temperatures. The experiments on graphene do not depend on the wave vector dependence of the frequency. Hence whether the dispersion depends on k2 or on k does not matter. The Hubbard model has been very successful in explaining the ground state of several electron systems. We consider a triangle with three vortices. Each vortex can be occupied by two electrons. By using the spin in a particular way, we can obtain new features in the Hubbard model. There is a doubling in the Peierls-Luttinger phase factor and eigen values acquire higher multiplicities than are known for the usual treatment of spin. The flux is distributed on the area of the triangle. The graphene consists of hexagons of carbon atoms but the Hall effect shows that there are defects on which electrons form clusters so that there is spin wave type behaviour. A cluster of electrons shows spin-waves leading to "spin deviation" of several per cent.

Plasmonic excitations in Coulomb-coupledN-layer graphene structures

We study Dirac plasmons and their damping in spatially separated $N$-layer graphene structures at finite doping and temperatures. The plasmon spectrum consists of one optical excitation with a square-root dispersion and $N-1$ acoustical excitations with linear dispersions, which are undamped at zero temperature within a triangular energy region outside the electron-hole continuum. For any finite number of graphene layers we have found that the energy and weight of the optical plasmon increase in the long wavelength limit, respectively, as square-root and linear functions of $N$. This is in agreement with recent experimental findings. With an increase of the number of multilayer acoustical plasmon modes, the energy and weight of the upper lying branches also exhibit an enhancement with $N$. This increase is strongest for the uppermost acoustical mode so that its energy can exceed at some value of momentum the plasmon energy in an individual graphene sheet. Meanwhile, the energy of the low lying acoustical branches decreases weakly with $N$ as compared with the single acoustical mode in double-layer graphene structures. Our numerical calculations provide a detailed understanding of the overall behavior of the wave vector dependence of the optical and acoustical multilayer plasmon modes and show how their dispersion and damping are modified as a function of temperature, interlayer spacing, and inlayer carrier density in (un)balanced graphene multilayer structures.

Vector-based Attribute Reduction Method for Formal Contexts

Attribute reduction is one basic issue in knowledge discovery of information systems. In this paper, based on the object oriented concept lattice and classical concept lattice, the approach of attribute reduction for formal contexts is investigated. We consider attribute reduction and attribute characteristics from the perspective of linear dependence of vectors. We first introduce the notion of context matrix and the operations of corresponding column vectors, then present some judgment theorems of attribute reduction for formal contexts. Furthermore, we propose a new method to reducing formal context and show corresponding reduction algorithms. Compared with previous reduction approaches which employ discernibility matrix and discernibility function to determine all reducts, the proposed approach is more simpler and easier to implement.

Two-Dimensional Incommensurate Magnetic Fluctuations in Sr2(Ru0.99Ti0.01)O4

We investigate the imaginary part of the wave vector dependent dynamic spin susceptibility in Sr$_2$(Ru$_{0.99}$Ti$_{0.01}$)O$_4$ as a function of temperature using neutron scattering. At T=5 K, two-dimensional incommensurate (IC) magnetic fluctuations are clearly observed around $\mathbf{Q}_\text{c}=(0.3,0.3,L)$ up to approximately 60 meV energy transfer. We find that the IC excitations disperse to ridges around the $(\pi,\pi)$ point. Below 50 K, the energy and temperature dependent excitations are well described by the phenomenological response function for a Fermi liquid system with a characteristic energy of 4.0(1) meV. Although the wave vector dependence of the IC magnetic fluctuations in Sr$_2$(Ru$_{0.99}$Ti$_{0.01}$)O$_4$ is similar to that in the Fermi liquid state of the parent compound, Sr$_2$RuO$_4$, the magnetic fluctuations are clearly suppressed by the Ti-doping.

Acoustic excitations in glassy sorbitol and their relation with the fragility and the boson peak

We report a detailed analysis of the dynamic structure factor of glassy sorbitol by using inelastic X-ray scattering and previously measured light scattering data [B. Ruta, G. Monaco, F. Scarponi, and D. Fioretto, Philos. Mag. 88, 3939 (2008)]. The thus obtained knowledge on the density-density fluctuations at both the mesoscopic and macroscopic length scale has been used to address two debated topics concerning the vibrational properties of glasses. The relation between the acoustic modes and the universal boson peak (BP) appearing in the vibrational density of states of glasses has been investigated, also in relation with some recent theoretical models. Moreover, the connection between the elastic properties of glasses and the slowing down of the structural relaxation process in supercooled liquids has been scrutinized. For what concerns the first issue, it is here shown that the wave vector dependence of the acoustic excitations can be used, in sorbitol, to quantitatively reproduce the shape of the boson peak, supporting the relation between BP and acoustic modes. For what concerns the second issue, a proper study of elasticity over a wide spatial range is shown to be fundamental in order to investigate the relation between elastic properties and the slowing down of the dynamics in the corresponding supercooled liquid phase.

Exchange interactions in Cd1−xMnxTe wide quantum wells

The exchange interactions between excitons and manganese ions in wide (80 nm) quantum wells of Cd${}_{1\ensuremath{-}x}$Mn${}_{x}$Te ($x\ensuremath{\approx}0.0015$ and $x\ensuremath{\approx}0.00027$) have been measured for states with center of mass quantum numbers up to 10. The corresponding translational wave vectors are in the range up to $4\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{2.84526pt}{0ex}}$cm${}^{\ensuremath{-}1}$ and in this range we detect no systematic variation of the exchange parameter ${N}_{0}(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})$, which remains constant to within $\ifmmode\pm\else\textpm\fi{}3%$. The result is consistent with previous studies of the wave vector dependence of the electron contribution ${N}_{0}\ensuremath{\alpha}$ but differs from previous observations of the wave vector dependence of exciton exchange interaction in quantum wells with much higher concentrations of manganese.

Indirect optical absorption in silicon via thin-film surface plasmon

Optical excitations in semiconductors have been extensively studied in the dipole limit, neglecting the spatial variation of the exciting field. This is a very good approximation in most cases. However, when approaching the regime of nano optics and plasmonics, optical fields of extreme spatial confinement is found, e.g., surface plasmon polaritons (SPPs). Here we investigate the optical absorption of a SPP bound to an Ag thin-film embedded in Si at photon energies below the direct band gap of Si. In this regime, all absorbtion processes in Si must be assisted by a source of crystal momentum to overcome the momentum mismatch of the indirect transition. While phonon-assisted processes are the obvious example, the optical wave vector can also supply the needed momentum, provided the optical field displays sufficient spatial variation. We apply a simple model for the electric field and a band theoretical model response function for Si, including both frequency and wave vector dependence, and find that absorption in the Si medium relative to the Ag film may be increased significantly due to indirect transitions facilitated by the optical wave vector.

Counterion adsorption theory of dilute polyelectrolyte solutions: Apparent molecular weight, second virial coefficient, and intermolecular structure factor

Polyelectrolyte chains are well known to be strongly correlated even in extremely dilute solutions in the absence of additional strong electrolytes. Such correlations result in severe difficulties in interpreting light scattering measurements in the determination of the molecular weight, radius of gyration, and the second virial coefficient of charged macromolecules at lower ionic strengths from added strong electrolytes. By accounting for charge-regularization of the polyelectrolyte by the counterions, we present a theory of the apparent molecular weight, second virial coefficient, and the intermolecular structure factor in dilute polyelectrolyte solutions in terms of concentrations of the polymer and the added strong electrolyte. The counterion adsorption of the polyelectrolyte chains to differing levels at different concentrations of the strong electrolyte can lead to even an order of magnitude discrepancy in the molecular weight inferred from light scattering measurements. Based on counterion-mediated charge regularization, the second virial coefficient of the polyelectrolyte and the interchain structure factor are derived self-consistently. The effect of the interchain correlations, dominating at lower salt concentrations, on the inference of the radius of gyration and on molecular weight is derived. Conditions for the onset of nonmonotonic scattering wave vector dependence of scattered intensity upon lowering the electrolyte concentration and interpretation of the apparent radius of gyration are derived in terms of the counterion adsorption mechanism.

Directional dependence of random vectors

In this paper we define and study several properties of the concept of (multivariate) directional dependence and study the new concept in terms of copulas, and provide new measures of multivariate association based on directional dependence. Finally, we show the relationships of directional dependence with other dependence concepts such as association and conditional dependence.

Approaching an organic semimetal: Electron pockets at the Fermi level for a p-benzoquinonemonoimine zwitterion.

There is compelling evidence of electron pockets, at the Fermi level, in the band structure for an organic zwitterion molecule of the p-benzoquinonemonoimine type. The electronic structure of the zwitterion molecular film has a definite, although small, density of states evident at the Fermi level as well as a nonzero inner potential and thus is very different from a true insulator. In spite of a small Brillouin zone, significant band width is observed in the intermolecular band dispersion. The results demonstrate that Bloch's theorem applies to the wave vector dependence of the electronic band structure formed from the molecular orbitals of adjacent molecules in a molecular thin film of a p-benzoquinonemonoimine type zwitterion.

Extended Phonon Collapse and the Origin of the Charge-Density Wave in2H−NbSe2

We report inelastic x-ray scattering measurements of the temperature dependence of phonon dispersion in the prototypical charge-density-wave (CDW) compound 2H-NbSe2. Surprisingly, acoustic phonons soften to zero frequency and become overdamped over an extended region around the CDW wave vector. This extended phonon collapse is dramatically different from the sharp cusp in the phonon dispersion expected from Fermi surface nesting. Instead, our experiments, combined with ab initio calculations, show that it is the wave vector dependence of the electron-phonon coupling that drives the CDW formation in 2H-NbSe2 and determines its periodicity. This mechanism explains the so far enigmatic behavior of CDW in 2H-NbSe2 and may provide a new approach to other strongly correlated systems where electron-phonon coupling is important.

Surface phonon propagation in topological insulators

The effect of helical Dirac states on surface phonons in a topological insulators is investigated. Their coupling is derived in the continuum limit by assuming displacement-dependent Dirac cones. The resulting renormalization of sound velocity and attenuation and its dependence on the chemical potential and wave vector is calculated. At finite wave vectors a Kohn anomaly in the renormalized phonon frequency is caused by intraband transitions. It appears at wave vectors $q<2{k}_{F}$ due to a lack of backscattering for helical Dirac electrons. The wave vector and chemical potential dependence of this anomaly is calculated.

Extreme residual dependence for random vectors and processes

A two-dimensional random vector in the domain of attraction of an extreme value distributionGis said to be asymptotically independent (i.e. in the tail) ifGis the product of its marginal distribution functions. Ledford and Tawn (1996) discussed a form of residual dependence in this case. In this paper we give a characterization of this phenomenon (see also Ramos and Ledford (2009)), and offer extensions to higher-dimensional spaces and stochastic processes. Systemic risk in the banking system is treated in a similar framework.

Extreme residual dependence for random vectors and processes

A two-dimensional random vector in the domain of attraction of an extreme value distribution G is said to be asymptotically independent (i.e. in the tail) if G is the product of its marginal distribution functions. Ledford and Tawn (1996) discussed a form of residual dependence in this case. In this paper we give a characterization of this phenomenon (see also Ramos and Ledford (2009)), and offer extensions to higher-dimensional spaces and stochastic processes. Systemic risk in the banking system is treated in a similar framework.

Aspects of the reproductive biology of Brassavola cebolleta Rchb.f. (Orchidaceae)

This survey assessed some aspects of the reproductive biology of Brassavola cebolleta Rchb. f. (Orchidaceae) in the Municipality of Dourados, Mato Grosso do Sul State, Brazil. Floral biology, breeding systems, floral visitors and seed germination were analyzed. Differential success and fruit production rate were calculated. Pollination system indicated the pollen vector dependence and absence of pre-zygotic barriers related to self-incompatibility. Pollination occurred at night, being the potential pollen vector a Lepidoptera-Notodontidae of the genus Hemiceras. Differential success of male was 19%, female 9%, and the rate of effective fructification was 6.3%. Fruits produced after pollinator visits were larger than those generated by manual cross pollination, and despite the lower number of potentially viable seeds produced by the first, they presented a higher germination rate in asymbiotic media. This study warns to the vulnerability of the studied species, since the habitat fragmentation associated with pollinator scarcity and seed predation may significantly decrease new recruitment into populations.

Acoustic vibrations in free‐standing single‐, bi‐layer nanomembranes and patterned wires

AbstractBrillouin light scattering investigations of acoustic vibrations in freestanding membranes, soft‐hard bi‐layers and patterned wires are described. Studies of longitudinal and transverse standing wave resonances, the wave vector dependence of surface and guided waves as well as their hybridization with flexural and dilational waves are presented. Size effects and the role of reduced dimensions on the acoustic behavior are investigated in soft rectangular polymeric wires on freestanding silicon nitride membranes. The mode frequencies and amplitudes are analyzed in terms of surface Green's functions and the xyz algorithm.

Structure Determination of the Top‐Loop of the Conserved 3′‐Terminal Secondary Structure in the Genome of Flaviviruses

To what extent small differences in RNA sequences (mutations) can have a profound impact on biology remains an intriguing question. This effect can be studied by using untranslated RNA regions as a model. We have studied the influence of mutations on the structure of an RNA hairpin that occurs in the 3'-untranslated region (UTR) of Flaviviridae, and is known to have a large impact on the vector dependency of flaviviruses. Three related RNA sequences were studied by NMR spectroscopy. The selected sequences represent each one of the three clusters in the flavivirus genes (mosquito-borne, tick-borne, and no-known-vector viruses). A new strategy was used to obtain chemical shift signatures of carbonyl atoms in unlabeled uridine nucleobases to characterize their involvement in hydrogen bonding. Clear differences occur in the structures and stacking pattern of the three RNA hairpins. The observed differences cannot be predicted based on sequence analysis. A different biology can be correlated with a different RNA tertiary structure. The underlying biological mechanism, however, remains to be studied.

Concentration fluctuations in a binary glass former investigated by x-ray photon correlation spectroscopy

We investigate structure and dynamics of concentration fluctuations in the binary glass former methyl-tetrahydrofuran and oligomeric methyl metacrylate by photon correlation spectroscopy with partially coherent x-rays from a synchrotron source. Although the system is macroscopically well miscible and optically clear in the full temperature range, calorimetric and dielectric measurements reveal two distinct glass transition temperatures. The relaxation of long range concentration fluctuations turns out to be diffusive and exponential only well above the upper glass transition temperature. As the characteristic time tau(cf) for concentration fluctuations shows a much weaker temperature dependence than the alpha-relaxation both traces finally intersect upon lowering the temperature. Thus, close to T(g), the concentration fluctuations show pronounced features of out-of-equilibrium dynamics such as compressed relaxation functions and a crossover to a ballistic wave vector dependence of tau(cf), like previously observed in various soft matter systems. Moreover, the analysis of time-resolved correlation functions reveals that the relaxation of concentration fluctuations around T(g) involves pronounced dynamic heterogeneities.