Provenance analysis using Raman spectroscopy of carbonaceous material: A case study in the Southern Alps of New Zealand

Detrital provenance analyses in orogenic settings, in which sediments are collected at the outlet of a catchment, have become an important tool to estimate how erosion varies in space and time. Here we present how Raman Spectroscopy on Carbonaceous Material (RSCM) can be used for provenance analysis. RSCM provides an estimate of the peak temperature (RSCM-T) experienced during metamorphism. We show that we can infer modern erosion patterns in a catchment by combining new measurements on detrital sands with previously acquired bedrock data. We focus on the Whataroa catchment in the Southern Alps of New Zealand and exploit the metamorphic gradient that runs parallel to the main drainage direction. To account for potential sampling biases, we also quantify abrasion properties using flume experiments and measure the total organic carbon content in the bedrock that produced the collected sands. Finally, we integrate these parameters into a mass-conservative model. Our results first demonstrate that RSCM-T can be used for detrital studies. Second, we find that spatial variations in tracer concentration and erosion have a first-order control on the RSCM-T distributions, even though our flume experiments reveal that weak lithologies produce substantially more fine particles than do more durable lithologies. This result implies that sand specimens are good proxies for mapping spatial variations in erosion when the bedrock concentration of the target mineral is quantified. The modeling suggests that highest present-day erosion rates (in Whataroa catchment) are not situated at the range front but around 10 km into the mountain belt.

Statistical model of OFDMA cellular networks uplink interference using lognormal distribution

In this letter, we propose an analytical approach to model uplink intercell interference (ICI) in hexagonal grid based orthogonal frequency division multiple access (OFMDA) cellular networks. The key idea is that the uplink ICI from individual cells is approximated with a lognormal distribution with statistical parameters being determined analytically. Accordingly, the aggregated uplink ICI is approximated with another lognormal distribution and its statistical parameters can be determined from those of individual cells using Fenton-Wilkson method. Analytic expressions of uplink ICI are derived with two traditional frequency reuse schemes, namely integer frequency reuse schemes with factor 1 (IFR-1) and factor 3 (IFR-3). Uplink fractional power control and lognormal shadowing are modeled. System performances in terms of signal to interference plus noise ratio (SINR) and spectrum efficiency are also derived. The proposed model has been validated by simulations. © 2013 IEEE.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

Climate seasonality limits leaf carbon assimilation and wood productivity in tropical forests.

The seasonal climate drivers of the carbon cy- cle in tropical forests remain poorly known, although these forests account for more carbon assimilation and storage than any other terrestrial ecosystem. Based on a unique combina- tion of seasonal pan-tropical data sets from 89 experimental sites (68 include aboveground wood productivity measure- ments and 35 litter productivity measurements), their asso- ciated canopy photosynthetic capacity (enhanced vegetation index, EVI) and climate, we ask how carbon assimilation and aboveground allocation are related to climate seasonal- ity in tropical forests and how they interact in the seasonal carbon cycle. We found that canopy photosynthetic capacity seasonality responds positively to precipitation when rain- fall is < 2000 mm yr-1 (water-limited forests) and to radia- tion otherwise (light-limited forests). On the other hand, in- dependent of climate limitations, wood productivity and lit- terfall are driven by seasonal variation in precipitation and evapotranspiration, respectively. Consequently, light-limited forests present an asynchronism between canopy photosyn- thetic capacity and wood productivity. First-order control by precipitation likely indicates a decrease in tropical forest pro- ductivity in a drier climate in water-limited forest, and in cur- rent light-limited forest with future rainfall < 2000 mm yr-1.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.