Majorana edge modes in the Kitaev model

We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic delta-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic d-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for a finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice.

On the Parameterized Complexity of the Maximum Edge 2-Coloring Problem

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q >= 2 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q >= 2, and has been well-studied from the point of view of approximation. Our main focus is the case when q = 2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel.

Sensitivity of polarization fluctuations to the nature of protein-water interactions: Study of biological water in four different protein-water systems

Since the time of Kirkwood, observed deviations in magnitude of the dielectric constant of aqueous protein solution from that of neat water (similar to 80) and slower decay of polarization have been subjects of enormous interest, controversy, and debate. Most of the common proteins have large permanent dipole moments (often more than 100 D) that can influence structure and dynamics of even distant water molecules, thereby affecting collective polarization fluctuation of the solution, which in turn can significantly alter solution's dielectric constant. Therefore, distance dependence of polarization fluctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different characteristics and varying sizes, chicken villin headpiece subdomain (HP-36), immunoglobulin binding domain protein G (GB1), hen-egg white lysozyme (LYS), and Myoglobin (MYO). We simulate fairly large systems consisting of single protein molecule and 20000-30000 water molecules (varied according to the protein size), providing a concentration in the range of similar to 2-3 mM. We find that the calculated dielectric constant of the system shows a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water < dM(W) (0)delta M-W (t) > is found to be sensitive to the nature of the protein. Surprisingly, dipole moment of the protein and total dipole moment of the water molecules are found to be only weakly coupled. Shellwise decomposition of water molecules around protein reveals higher density of first layer compared to the succeeding ones. We also calculate heuristic effective dielectric constant of successive layers and find that the layer adjacent to protein has much lower value (similar to 50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4-5 layers away. We also calculate shellwise orientational correlation function and tetrahedral order parameter to understand the local dynamics and structural re-arrangement of water. Theoretical analysis providing simple method for calculation of shellwise local dielectric constant and implication of these findings are elaborately discussed in the present work. (C) 2014 AIP Publishing LLC.

Zero-Crossings Based Spectrum Sensing Under Noise Uncertainties

In this work, the hypothesis testing problem of spectrum sensing in a cognitive radio is formulated as a Goodness-of-fit test against the general class of noise distributions used in most communications-related applications. A simple, general, and powerful spectrum sensing technique based on the number of weighted zero-crossings in the observations is proposed. For the cases of uniform and exponential weights, an expression for computing the near-optimal detection threshold that meets a given false alarm probability constraint is obtained. The proposed detector is shown to be robust to two commonly encountered types of noise uncertainties, namely, the noise model uncertainty, where the PDF of the noise process is not completely known, and the noise parameter uncertainty, where the parameters associated with the noise PDF are either partially or completely unknown. Simulation results validate our analysis, and illustrate the performance benefits of the proposed technique relative to existing methods, especially in the low SNR regime and in the presence of noise uncertainties.

Estimation of Parameters for Battery Storage Models

This paper presents a comprehensive and robust strategy for the estimation of battery model parameters from noise corrupted data. The deficiencies of the existing methods for parameter estimation are studied and the proposed parameter estimation strategy improves on earlier methods by working optimally for low as well as high discharge currents, providing accurate estimates even under high levels of noise, and with a wide range of initial values. Testing on different data sets confirms the performance of the proposed parameter estimation strategy.

Effects of Microstructural Heterogeneity on the Spallation Behavior of Materials

It is of utmost importance to understand the spallation behaviour of heterogeneous materials. In this paper, a driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. The spallation behavior of heterogeneity material is analyzed with this model. The heterogeniety of mesoscopic units is characterized in terms of Weibull modulus m of strength distibution and stress fluctuation parameter k. At high stress, the maximum damage increases with m; while at low stress, the maximum damage decreases. In addition, for low stress, severe stress fluctuation causes higher damage; while for high stress, causes lower damage.

Dislocation theory of the fracture criterion for anisotropic solids

A dislocation theory of fracture criterion for the mixed dislocation emission and cleavage process in an anisotropic solid is developed in this paper. The complicated cases involving mixed-mode loading are considered here. The explicit formula for dislocations interaction with a semi-infinite crack is obtained. The governing equation for the critical condition of crack cleavage in an anisotropic solid after a number dislocation emissions is established. The effects of elastic anisotropy, crack geometry and load phase angle on the critical energy release rate and the total number of the emitted dislocations at the onset of cleavage are analysed in detail. The analyses revealed that the critical energy release rates can increase to one or two magnitudes larger than the surface energy because of the dislocation emission. It is also found elastic anisotropy and crystal orientation have significant effects on the critical energy release rates. The anisotropic values can be several times the isotropic value in one crack orientation. The values may be as much as 40% less than the isotropic value in another crack orientation and another anisotropy parameter. Then the theory is applied to a fee single crystal. An edge dislocation can emit from the crack tip along the most highly shear stressed slip plane. Crack cleavage can occur along the most highly stressed slip plane after a number of dislocation emissions. Calculation is carried out step by step. Each step we should judge by which slip system is the most highly shear stressed slip system and which slip system has the largest energy release rate. The calculation clearly shows that the crack orientation and the load phase angle have significant effects on the crystal brittle-ductile behaviours.

Failure modes of doubly supported capacitive RF MEMS switches

For the design of radio frequency micro-electro-mechanical systems (RF MEMS) switches, the reliability issue becomes increasingly important. This paper represents some failure phenomena of doubly supported capacitive RF MEMS switches that include observable destruction failure and directly measurable parameter degradation obtained from the actuating-voltage testing and scanning electron microscope (SEM) observation. The relevant failure modes as well as their failure mechanisms are identified.

Effect of Work of Adhesion on Nanoindentation

Three adhesion contact models, JKR (Johnson-Kendall-Roberts), DMT (Derjaguin-Muller-Toporov) and MD (Maugis-Dugdale) are compared with the Hertz model in dealing with the nano-contact problems. It has been shown that the dimensionless load parameter, $\bar{P}=P/(\pi\Delta\gamma R)$, and the transition parameter, $\Lambda$, have significant influences on the contact stiffness (contact area) at micro/nano-scale and should not be ignored in shallow nanoindentation.

Isolation of mineralizing Nestin+ Nkx6.1+ vascular muscular cells from the adult human spinal cord

Background: The adult central nervous system (CNS) contains different populations of immature cells that could possibly be used to repair brain and spinal cord lesions. The diversity and the properties of these cells in the human adult CNS remain to be fully explored. We previously isolated Nestin(+) Sox2(+) neural multipotential cells from the adult human spinal cord using the neurosphere method (i.e. non adherent conditions and defined medium). -- Results: Here we report the isolation and long term propagation of another population of Nestin(+) cells from this tissue using adherent culture conditions and serum. QPCR and immunofluorescence indicated that these cells had mesenchymal features as evidenced by the expression of Snai2 and Twist1 and lack of expression of neural markers such as Sox2, Olig2 or GFAP. Indeed, these cells expressed markers typical of smooth muscle vascular cells such as Calponin, Caldesmone and Acta2 (Smooth muscle actin). These cells could not differentiate into chondrocytes, adipocytes, neuronal and glial cells, however they readily mineralized when placed in osteogenic conditions. Further characterization allowed us to identify the Nkx6.1 transcription factor as a marker for these cells. Nkx6.1 was expressed in vivo by CNS vascular muscular cells located in the parenchyma and the meninges. -- Conclusion: Smooth muscle cells expressing Nestin and Nkx6.1 is the main cell population derived from culturing human spinal cord cells in adherent conditions with serum. Mineralization of these cells in vitro could represent a valuable model for studying calcifications of CNS vessels which are observed in pathological situations or as part of the normal aging. In addition, long term propagation of these cells will allow the study of their interaction with other CNS cells and their implication in scar formation during spinal cord injury.

Effects of Microstructural Heterogeneity on The Spallation Behavior of Materials

It is of utmost importance to understand the spallation behaviour of heterogeneous materials. In this paper, a driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. The spallation behavior of heterogeneity material is analyzed with this model. The heterogeniety of mesoscopic units is characterized in terms of Weibull modulus m of strength distibution and stress fluctuation parameter k. At high stress, the maximum damage increases with m; while at low stress, the maximum damage decreases. In addition, for low stress, severe stress fluctuation causes higher damage; while for high stress, causes lower damage.

An egg production method for estimating spawning biomass of pelagic fish: Application to the northern anchovy, Engraulis mordax

Fishery scientists engaged in estimating the size of free-swimming populations have never had a technique available to them whereby all the parameters could be estimated from a resource survey and where no parameter values need to be assumed. Recognizing the need for a technique of this kind, the staff of the Coastal Fisheries Resources Division of the Southwest Fisheries Center (SWFC) devised an egg production method for anchovy biomass assessment. Previously, anchovy biomass was estimated by approximate methods derived from a long-time series and anchovy larval abundance, which required about 5 ma of shiptime each year to integrate the area under a seasonal spawning curve. One major assumption used in the larval abundance census method is that there is constant proportionality between larval numbers and spawning biomass. This has now proved to be erroneous. (PDF file contains 105 pages.)

Molecular neurogenetics of eye development in Drosophila

The compound eye of Drosophila melanogaster begins to differentiate during the late third larval instar in the eye-antennal imaginal disc. A wave of morphogenesis crosses the disc from posterior to anterior, leaving behind precisely patterned clusters of photoreceptor cells and accessory cells that will constitute the adult ommatidia of the retina. By the analysis of genetically mosaic eyes, it appears that any cell in the eye disc can adopt the characteristics of any one of the different cell types found in the mature eye, including photoreceptor cells and non-neuronal accessory cells such as cone cells. Therefore, cells within the prospective retinal epithelium assume different fates presumably via information present in the environment. The sevenless^+ (sev^+) gene appears to play a role in the expression of one of the possible fates, since the mutant phenotype is the lack of one of the pattern elements, namely, photoreceptor cell R7. The sev^+ gene product had been shown to be required during development of the eye, and had also been shown in genetic mosaics to be autonomous to presumptive R7. As a means of better understanding the pathway instructing the differentiation R7, the gene and its protein product were characterized.

The sev+ gene was cloned by P-element transposon tagging, and was found to encode an 8.2 kb transcript expressed in developing eye discs and adult heads. By raising monoclonal antibodies (MAbs) against a sev^+- β-galactosidase fusion protein, the expression of the protein in the eye disc was localized by immuno-electronmicroscopy. The protein localizes to the apical cell membranes and microvilli of cells in the eye disc epithelium. It appears during development at a time coincident with the initial formation of clusters, and in all the developing photoreceptors and accessory cone cells at a time prior to the overt differentiation of R7. This result is consistent with the pluripotency of cells in the eye disc. Its localization in the membranes suggests that it may receive information directing the development of R7. Its localization in the apical membranes and microvilli is away from the bulk of the cell contacts, which have been cited as a likely regions for information presentation and processing. Biochemical characterization of the sev^+ protein will be necessary to describe further its role in development.

Other mutations in Drosophila have eye phenotypes. These were analyzed to find which ones affected the initial patterning of cells in the eye disc, in order to identify other genes, like sev, whose gene products may be involved in generating the pattern. The adult eye phenotypes ranged from severe reduction of the eye, to variable numbers of photoreceptor cells per ommatidium, to sub de defects in the organization of the supporting cells. Developing eye discs from the different strains were screened using a panel of MAbs, which highlight various developmental stages. Two identified matrix elements in and anterior to the furrow, while others identified the developing ommatidia themselves, like the anti-sev MAb. Mutation phenotypes were shown to appear at many stages of development. Some mutations seem to affect the precursor cells, others, the setting up of the pattern, and still others, the maintenance of the pattern. Thus, additional genes have now been identified that may function to support the development of a complex pattern.

Seismic reflection experiments imaging the physical nature of crustal structures in southern California

Seismic reflection methods have been extensively used to probe the Earth's crust and suggest the nature of its formative processes. The analysis of multi-offset seismic reflection data extends the technique from a reconnaissance method to a powerful scientific tool that can be applied to test specific hypotheses. The treatment of reflections at multiple offsets becomes tractable if the assumptions of high-frequency rays are valid for the problem being considered. Their validity can be tested by applying the methods of analysis to full wave synthetics.

Three studies illustrate the application of these principles to investigations of the nature of the crust in southern California. A survey shot by the COCORP consortium in 1977 across the San Andreas fault near Parkfield revealed events in the record sections whose arrival time decreased with offset. The reflectors generating these events are imaged using a multi-offset three-dimensional Kirchhoff migration. Migrations of full wave acoustic synthetics having the same limitations in geometric coverage as the field survey demonstrate the utility of this back projection process for imaging. The migrated depth sections show the locations of the major physical boundaries of the San Andreas fault zone. The zone is bounded on the southwest by a near-vertical fault juxtaposing a Tertiary sedimentary section against uplifted crystalline rocks of the fault zone block. On the northeast, the fault zone is bounded by a fault dipping into the San Andreas, which includes slices of serpentinized ultramafics, intersecting it at 3 km depth. These interpretations can be made despite complications introduced by lateral heterogeneities.

In 1985 the Calcrust consortium designed a survey in the eastern Mojave desert to image structures in both the shallow and the deep crust. Preliminary field experiments showed that the major geophysical acquisition problem to be solved was the poor penetration of seismic energy through a low-velocity surface layer. Its effects could be mitigated through special acquisition and processing techniques. Data obtained from industry showed that quality data could be obtained from areas having a deeper, older sedimentary cover, causing a re-definition of the geologic objectives. Long offset stationary arrays were designed to provide reversed, wider angle coverage of the deep crust over parts of the survey. The preliminary field tests and constant monitoring of data quality and parameter adjustment allowed 108 km of excellent crustal data to be obtained.

This dataset, along with two others from the central and western Mojave, was used to constrain rock properties and the physical condition of the crust. The multi-offset analysis proceeded in two steps. First, an increase in reflection peak frequency with offset is indicative of a thinly layered reflector. The thickness and velocity contrast of the layering can be calculated from the spectral dispersion, to discriminate between structures resulting from broad scale or local effects. Second, the amplitude effects at different offsets of P-P scattering from weak elastic heterogeneities indicate whether the signs of the changes in density, rigidity, and Lame's parameter at the reflector agree or are opposed. The effects of reflection generation and propagation in a heterogeneous, anisotropic crust were contained by the design of the experiment and the simplicity of the observed amplitude and frequency trends. Multi-offset spectra and amplitude trend stacks of the three Mojave Desert datasets suggest that the most reflective structures in the middle crust are strong Poisson's ratio (σ) contrasts. Porous zones or the juxtaposition of units of mutually distant origin are indicated. Heterogeneities in σ increase towards the top of a basal crustal zone at ~22 km depth. The transition to the basal zone and to the mantle include increases in σ. The Moho itself includes ~400 m layering having a velocity higher than that of the uppermost mantle. The Moho maintains the same configuration across the Mojave despite 5 km of crustal thinning near the Colorado River. This indicates that Miocene extension there either thinned just the basal zone, or that the basal zone developed regionally after the extensional event.

Teleseismic array analysis of upper mantle compressional velocity structure

Large quantities of teleseismic short-period seismograms recorded at SCARLET provide travel time, apparent velocity and waveform data for study of upper mantle compressional velocity structure. Relative array analysis of arrival times from distant (30° < Δ < 95°) earthquakes at all azimuths constrains lateral velocity variations beneath southern California. We compare dT/dΔ back azimuth and averaged arrival time estimates from the entire network for 154 events to the same parameters derived from small subsets of SCARLET. Patterns of mislocation vectors for over 100 overlapping subarrays delimit the spatial extent of an east-west striking, high-velocity anomaly beneath the Transverse Ranges. Thin lens analysis of the averaged arrival time differences, called 'net delay' data, requires the mean depth of the corresponding lens to be more than 100 km. Our results are consistent with the PKP-delay times of Hadley and Kanamori (1977), who first proposed the high-velocity feature, but we place the anomalous material at substantially greater depths than their 40-100 km estimate.

Detailed analysis of travel time, ray parameter and waveform data from 29 events occurring in the distance range 9° to 40° reveals the upper mantle structure beneath an oceanic ridge to depths of over 900 km. More than 1400 digital seismograms from earthquakes in Mexico and Central America yield 1753 travel times and 58 dT/dΔ measurements as well as high-quality, stable waveforms for investigation of the deep structure of the Gulf of California. The result of a travel time inversion with the tau method (Bessonova et al., 1976) is adjusted to fit the p(Δ) data, then further refined by incorporation of relative amplitude information through synthetic seismogram modeling. The application of a modified wave field continuation method (Clayton and McMechan, 1981) to the data with the final model confirms that GCA is consistent with the entire data set and also provides an estimate of the data resolution in velocity-depth space. We discover that the upper mantle under this spreading center has anomalously slow velocities to depths of 350 km, and place new constraints on the shape of the 660 km discontinuity.

Seismograms from 22 earthquakes along the northeast Pacific rim recorded in southern California form the data set for a comparative investigation of the upper mantle beneath the Cascade Ranges-Juan de Fuca region, an ocean-continent transit ion. These data consist of 853 seismograms (6° < Δ < 42°) which produce 1068 travel times and 40 ray parameter estimates. We use the spreading center model initially in synthetic seismogram modeling, and perturb GCA until the Cascade Ranges data are matched. Wave field continuation of both data sets with a common reference model confirms that real differences exist between the two suites of seismograms, implying lateral variation in the upper mantle. The ocean-continent transition model, CJF, features velocities from 200 and 350 km that are intermediate between GCA and T7 (Burdick and Helmberger, 1978), a model for the inland western United States. Models of continental shield regions (e.g., King and Calcagnile, 1976) have higher velocities in this depth range, but all four model types are similar below 400 km. This variation in rate of velocity increase with tectonic regime suggests an inverse relationship between velocity gradient and lithospheric age above 400 km depth.