One-dimensional Interface Research Articles

Photovoltaic Effect and Evidence of Carrier Multiplication in Graphene Vertical Homojunctions with Asymmetrical Metal Contacts.

Graphene exhibits exciting potentials for high-speed wideband photodetection and high quantum efficiency solar energy harvest because of its broad spectral absorption, fast photoelectric response, and potential carrier multiplication. Although photocurrent can be generated near a metal-graphene interface in lateral devices, the photoactive area is usually limited to a tiny one-dimensional line-like interface region. Here, we report photoelectric devices based on vertical graphene two-dimensional homojunction, which is fabricated via vertically stacking four graphene monolayers with asymmetric metal contacts. The devices show excellent photovoltaic output with excitation wavelength ranging from visible light to mid-infrared. The wavelength dependence of the internal quantum efficiency gives direct evidence of the carrier multiplication effect in graphene. The simple fabrication process, easy scale-up, large photoresponsive active area, and broadband response of the vertical graphene device are very promising for practical applications in optoelectronics and photovoltaics.

Interface-capturing lattice Boltzmann equation model for two-phase flows.

In this work, an interface-capturing lattice Boltzmann equation (LBE) model is proposed for two-phase flows. In the model, a Lax-Wendroff propagation scheme and a properly chosen equilibrium distribution function are employed. The Lax-Wendroff scheme is used to provide an adjustable Courant-Friedrichs-Lewy (CFL) number, and the equilibrium distribution is presented to remove the dependence of the relaxation time on the CFL number. As a result, the interface can be captured accurately by decreasing the CFL number. A theoretical expression is derived for the chemical potential gradient by solving the LBE directly for a two-phase system with a flat interface. The result shows that the gradient of the chemical potential is proportional to the square of the CFL number, which explains why the proposed model is able to capture the interface naturally with a small CFL number, and why large interface error exists in the standard LBE model. Numerical tests, including a one-dimensional flat interface problem, a two-dimensional circular droplet problem, and a three-dimensional spherical droplet problem, demonstrate that the proposed LBE model performs well and can capture a sharp interface with a suitable CFL number.

Spatially resolved one-dimensional boundary states in graphene-hexagonal boron nitride planar heterostructures.

Two-dimensional interfaces between crystalline materials have been shown to generate unusual interfacial electronic states in complex oxides. Recently, a one-dimensional interface has been realized in hexagonal boron nitride and graphene planar heterostructures, where a polar-on-nonpolar one-dimensional boundary is expected to possess peculiar electronic states associated with edge states of graphene and the polarity of boron nitride. Here we present a combined scanning tunnelling microscopy and first-principles theory study of the graphene-boron nitride boundary to provide a first glimpse into the spatial and energetic distributions of the one-dimensional boundary states down to atomic resolution. The revealed boundary states are about 0.6 eV below or above the Fermi level depending on the termination of the boron nitride at the boundary, and are extended along but localized at the boundary. These results suggest that unconventional physical effects similar to those observed at two-dimensional interfaces can also exist in lower dimensions.

THE MATHEMATICAL ANALYSIS OF COLUMN ORIENTED DATABASE

There are two obvious ways to map a two-dimension relational database table onto a one-dimensional storage interface: store the table row-by-row, or store the table column-by-column. Historically, database system implementations and research have focused on the row-by row data layout, since it performs best on the most common application for database systems: business transactional data processing. However, there are a set of emerging applications for database systems for which the row-by-row layout performs poorly. These applications are more analytical in nature, whose goal is to read through the data to gain new insight and use it to drive decision making and planning. In this paper, we study about the facts responsible for making Column Oriented database when traditional Row-oriented databases are already present, analysis of generation of Column Oriented databases, etc. Finally It will be conclude by giving a probabilistic analysis of Column Oriented database.

Creep dynamics of viscoelastic interfaces

The movement of a purely elastic interface driven on a disordered energy potential is characterized by a depinning transition: when the pulling force σ is larger than some critical value the system is in a flowing regime and moves at a finite velocity. On the other hand, if the interface remains pinned and its velocity is zero. We show that in the case of a one-dimensional interface, the inclusion of viscoelastic relaxation produces the appearance of an intervening regime between the pinned and the flowing phases in a well-defined stress interval , in which the interface evolves through a sequence of avalanches that give rise to a creep process. As the creep velocity vanishes as a power law. As the creep velocity increases as a power law due to the increase of the typical size of the avalanches. The present observations may serve to improve the understanding of fatigue failure mechanisms.

Electronic and magnetic properties of nitrogen-doped graphene nanoribbons with grain boundary

Grain boundary (GB) is a one-dimensional interface between two domains of materials with different crystallographic orientations. We investigate the effect of N-doping on the electronic and magnetic properties for hybrid graphene nanoribbon (GNR) with GB, using density functional theory. We find that substituted N atom energetically prefers to distribute at the GB as well as at the ribbon edges. The substituted N atom can induce a variable total magnetic moment depending on the doping sites. After N doping, the translational GB can be spin polarized with ferromagnetic order, and then several spin configurations are generated considering the magnetic couplings between the magnetic moments localized at the ribbon edges and linear translational GB. However, for N-doped GNR with tilt GB, the magnetic moment is extended and denser at the ribbon edges and linear GB. Moreover, small splits of some peaks at the Fermi level are also observed due to partial polarization of GB.

Uniqueness of the thermodynamic limit for driven disordered elastic interfaces

We study the finite-size fluctuations at the depinning transition for a one-dimensional elastic interface of size L displacing in a disordered medium of transverse size M = kLζ with periodic boundary conditions, where ζ is the depinning roughness exponent and k is a finite aspect-ratio parameter. We focus on the crossover from the infinitely narrow (k → 0) to the infinitely wide (k → ∞) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behaviour of the velocity–force characteristics are unique and k-independent. We also show that the finite-size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of k. Our results are relevant for understanding anisotropic size effects in force-driven and velocity-driven interfaces.

Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation: Numerical study

We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length ξ>0 and at finite temperature T. Using the exact mapping from the static 1D interface to the 1+1 directed polymer (DP) growing in a continuous space, we focus our analysis on the disorder free energy of the DP end point, a quantity which is strictly zero in the absence of disorder and whose sample-to-sample fluctuations at a fixed growing time t inherit the statistical translation invariance of the microscopic disorder explored by the DP. Constructing a new numerical scheme for the integration of the Kardar-Parisi-Zhang evolution equation obeyed by the free energy, we address numerically the time and temperature dependence of the disorder free-energy fluctuations at fixed finite ξ. We examine, on one hand, the amplitude D[over ̃](t) and effective correlation length ξ[over ̃](t) of the free-energy fluctuations and, on the other hand, the imprint of the specific microscopic disorder correlator on the large-time shape of the free-energy two-point correlator. We observe numerically the crossover to a low-temperature regime below a finite characteristic temperature T(c)(ξ), as previously predicted by Gaussian variational method computations and scaling arguments and extensively investigated analytically in [Phys. Rev. E 87, 042406 (2013)]. Finally, we address numerically the time and temperature dependence of the roughness B(t), which quantifies the DP end point transverse fluctuations, and we show how the amplitude D[over ̃](∞)(T,ξ) controls the different regimes experienced by B(t)-in agreement with the analytical predictions of a DP toy model approach.

Variational characterization of the critical curve for pinning of random polymers

In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges. There are two phases, localized and delocalized, depending on the inverse temperature and on the disorder bias. Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process [Birkner, Greven and den Hollander, Probab. Theory Related Fields 148 (2010) 403-456], we derive variational formulas for the quenched, respectively, annealed critical curve separating the two phases. These variational formulas are used to obtain a necessary and sufficient criterion, stated in terms of relative entropies, for the two critical curves to be different at a given inverse temperature, a property referred to as relevance of the disorder. This criterion in turn is used to show that the regimes of relevant and irrelevant disorder are separated by a unique inverse critical temperature. Subsequently, upper and lower bounds are derived for the inverse critical temperature, from which sufficient conditions under which it is strictly positive, respectively, finite are obtained. The former condition is believed to be necessary as well, a problem that we will address in a forthcoming paper. Random pinning has been studied extensively in the literature. The present paper opens up a window with a variational view. Our variational formulas for the quenched and the annealed critical curve are new and provide valuable insight into the nature of the phase transition. Our results on the inverse critical temperature drawn from these variational formulas are not new, but they offer an alternative approach, that is, flexible enough to be extended to other models of random polymers with disorder.

Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation

Experimental realizations of a one-dimensional (1D) interface always exhibit a finite microscopic width ξ>0; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description of the interface fluctuations below a characteristic temperature T(c)(ξ). Exploiting the exact mapping between the static 1D interface and a 1+1 directed polymer (DP) growing in a continuous space, we study analytically both the free-energy and geometrical fluctuations of a DP, at finite temperature T, with a short-range elasticity and submitted to a quenched random-bond Gaussian disorder of finite correlation length ξ. We derive the exact time-evolution equations of the disorder free energy F[over ¯](t,y), which encodes the microscopic disorder integrated by the DP up to a growing time t and an endpoint position y, its derivative η(t,y), and their respective two-point correlators C[over ¯](t,y) and R[over ¯](t,y). We compute the exact solution of its linearized evolution R[over ¯](lin)(t,y) and we combine its qualitative behavior and the asymptotic properties known for an uncorrelated disorder (ξ=0) to justify the construction of a "toy model" leading to a simple description of the DP properties. This model is characterized by Gaussian Brownian-type free-energy fluctuations, correlated at small |y|</~ξ, and of amplitude D̃(∞)(T,ξ). We present an extended scaling analysis of the roughness, supported by saddle-point arguments on its path-integral representation, which predicts D̃(∞)~1/T at high temperatures and D̃(∞)~1/T(c)(ξ) at low temperatures. We identify the connection between the temperature-induced crossover of D̃(∞)(T,ξ) and the full replica symmetry breaking in previous Gaussian variational method (GVM) computations. In order to refine our toy model with respect to finite-time geometrical fluctuations, we propose an effective time-dependent amplitude D̃(t). Finally, we discuss the consequences of the low-temperature regime for two experimental realizations of Kardar-Parisi-Zhang interfaces, namely, the static and quasistatic behavior of magnetic domain walls and the high-velocity steady-state dynamics of interfaces in liquid crystals.

Nonsteady relaxation and critical exponents at the depinning transition

We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime. This "mesoscopic" time-regime is robust under changes of the microscopic disorder including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L~2^{25}) simulations for the non-steady dynamics of the continuum displacement quenched Edwards Wilkinson equation, getting accurate and consistent depinning exponents for this class: \beta = 0.245 \pm 0.006, z = 1.433 \pm 0.007, \zeta=1.250 \pm 0.005 and \nu=1.333 \pm 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent \beta) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.

Strategy for simulating supercritical cryogenic jets using high-order schemes

This study presents a strategy for simulations of cryogenic single-species jets under supercritical pressure conditions. In this strategy, a pressure evolution equation is introduced and numerical diffusion terms are consistently constructed in order to maintain the pressure and velocity equilibriums at fluid interfaces. By taking the idea of the equilibrium, the interfaces with high density and temperature ratio are robustly captured without the generation of spurious oscillations, while a high-order central differencing scheme resolves the flow fields. The present method preserves the mass and momentum conservation properties, while the poor energy conservation property is recognized. The one-dimensional interface advection and two-dimensional cryogenic jet mixing problems demonstrate the superiority and robustness of the present method over a conventional fully conservative approach.

Generalized Caroli formula for the transmission coefficient with lead-lead coupling

We present a generalized transmission coefficient formula for the lead-junction-lead system, in which interaction between the leads has been taken into account. Based on this formula, the Caroli formula could be easily recovered and a transmission coefficient formula for interface problem in the ballistic system can be obtained. The condition of validity for the formula is carefully explored. We mainly focus on heat transport. However, the corresponding electrical transport could be similarly dealt with. Also, an illustrative example is given to clarify the precise meaning of the quantities used in the formula, such as the concept of the reduced interacting matrix in different situations. In addition, an explicit transmission coefficient formula for a general one-dimensional interface setup is obtained based on the derived interface formula.

Performance Analysis of Column Oriented Database Vs Row Oriented Database

There are two obvious methods to map a two-dimension relational database table onto a one-dimensional storage interface: store the table row-by-row, or store the table column-by-column. Traditionally, database system implementations and research have focused on the row-by row data layout, since it performs best on the most common application for database systems: business transactional data processing. However, there are a set of emerging applications for database systems for which the row-by-row layout performs poorly. These applications are more analytical in nature, whose goal is to read through the data to gain new insight and use it to drive decision making and planning. In this paper, we study the poor performance of row-by-row data layout for these emerging applications, and evaluate the column-by-column data layout opportunity as a solution to this problem. The solution will be analyzed and represented by graph. At the end of the paper we will see the comparative performance of Oracle 10g and MSSQLServer database.

Simulating binary fluid-surfactant dynamics by a phase field model

In this paper, the dynamics of a binary fluid-surfactant systemdescribed by a phenomenological phase field model is investigatedthrough analytical and numerical computations. We first considerthe case of one-dimensional planar interface and prove theexistence of the equilibrium solution. Then we derive theanalytical equilibrium solution for the order parameter and thesurfactant concentration in a particular case. The results showthat the present phase field formulation qualitatively mimics thesurfactant adsorption on the binary fluid interfaces. We furtherstudy the time-dependent solutions of the system by numericalcomputations based on the pseudospectral Fourier computationalframework. The present numerical results are in a good agreementwith the previous theoretical study in the way that the surfactantfavors the creation of interfaces and also stabilizes theformation of phase regions.

THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past 25 years a new universality class has emerged to describe a host of important physical and probabilistic models (including one-dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar–Parisi–Zhang (KPZ) universality class and underlying it is, again, a continuum object — a non-linear stochastic partial differential equation — known as the KPZ equation.The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media.As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.

Spectral collocation and radial basis function methods for one-dimensional interface problems

Differential equations with singular sources or discontinuous coefficients yield non-smooth or even discontinuous solutions. This problem is known as the interface problem. High-order numerical solutions suffer from the Gibbs phenomenon in that the accuracy deteriorates if the discontinuity is not properly treated. In this work, we use the spectral and radial basis function methods and present a least squares collocation method to solve the interface problem for one-dimensional elliptic equations. The domain is decomposed into multiple sub-domains; in each sub-domain, the collocation solution is sought. The solution should satisfy more conditions than the given conditions associated with the differential equations, which makes the problem over-determined. To solve the over-determined system, the least squares method is adopted. For the spectral method, the weighted norm method with different scaling factors and the mixed formulation are used. For the radial basis function method, the weighted shape parameter method is presented. Numerical results show that the least squares collocation method provides an accurate solution with high efficacy and that better accuracy is obtained with the spectral method.

One-dimensional Voter Model Interface Revisited

We consider the voter model on $\mathbb{Z}$, starting with all 1's to the left of the origin and all $0$'s to the right of the origin. It is known that if the associated random walk kernel $p$ has zero mean and a finite r-th moment for any $r>3$, then the evolution of the boundaries of the interface region between 1's and 0's converge in distribution to a standard Brownian motion $(B_t)_{t>0}$ under diffusive scaling of space and time. This convergence fails when $p$ has an infinite $r$-th moment for any $r<3$, due to the loss of tightness caused by a few isolated $1$'s appearing deep within the regions of all $0$'s (and vice versa) at exceptional times. In this note, we show that as long as $p$ has a finite second moment, the measure-valued process induced by the rescaled voter model configuration is tight, and converges weakly to the measure-valued process $1_{x< B_t} dx$, $t>0$.

Temperature-induced crossovers in the static roughness of a one-dimensional interface

At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian variational method (GVM), we explore the consequences of a finite interface width $\ensuremath{\xi}$ on the small-lengthscale fluctuations. We compute analytically the static roughness $B(r)$ of the interface as a function of the distance $r$ between two points on the interface. We focus on the case of short-range elasticity and random-bond disorder. We show that for a finite width $\ensuremath{\xi}$ two temperature regimes exist. At low temperature, the expected thermal and random-manifold regimes, respectively, for small and large scales, connect via an intermediate ``modified'' Larkin regime, that we determine. This regime ends at a temperature-independent characteristic ``Larkin'' length. Above a certain characteristic temperature that we identify, this intermediate regime disappears. The thermal and random-manifold regimes connect at a single crossover lengthscale, that we compute. This is also the expected behavior for zero width. Using a directed polymer description, we also study via a second GVM procedure and generic scaling arguments, a modified toy model that provides further insights on this crossover. We discuss the relevance of the two GVM procedures for the roughness at large lengthscale in those regimes. In particular, we analyze the scaling of the temperature-dependent prefactor in the roughness $B(r)\ensuremath{\sim}{T}^{2\th{}}{r}^{2\ensuremath{\zeta}}$ and its corresponding thorn exponent $\th{}$. We briefly discuss the consequences of those results for the quasistatic creep law of a driven interface, in connection with previous experimental and numerical studies.

Theoretical evaluation of influence of convective heat transfer and original sample size on shell melting time during Ti dissolution in secondary steelmaking

The dissolution of Ti additions in liquid steel during secondary steelmaking occurs in a two step process. In the first step, a steel shell solidifies around the initial cold addition, whereas in the second step, after this shell has remelted, the Ti dissolves directly in the steel bath. The initial presence of this steel shell modifies the position of dissolution and influences the local concentration and thus the inclusion formation. Further complications arise from the fact that part of the Ti will dissolve while enclosed by the steel shell, altering the alloy composition first released in the ladle and effectively shortening the subsequent free dissolution period. The duration of the steel shell period and the fraction of predissolved Ti have been investigated using a conservative one-dimensional sharp interface model solving the coupled heat and mass transfer in a cylindrical shell/addition composite. The influence of the convection conditions and the original Ti radius was evaluated in a parametric study. A pronounced effect of the convective heat transfer on the shell melting time was found. It is thus concluded that the dissolution behaviour is strongly dependent on the local flow conditions, which is determined by factors such as stirring conditions and addition characteristics.