Less memory and high accuracy logarithmic number system architecture for arithmetic operations

<p>Interpolation is another important procedure for logarithmic number system (LNS) addition and subtraction. As a medium of approximation, the interpolation procedure has an urgent need to be enhanced to increase the accuracy of the operation results. Previously, most of the interpolation procedures utilized the first degree interpolators with special error correction procedure which aim to eliminate additional embedded multiplications. However, the interpolation procedure for this research was elevated up to a second degree interpolation. Proper design process, investigation, and analysis were done for these interpolation configurations in positive region by standardizing the same co-transformation procedure, which is the extended range, second order co-transformation. Newton divided differences turned out to be the best interpolator for second degree implementation of LNS addition and subtraction, with the best-achieved BTFP rate of +0.4514 and reduction of memory consumption compared to the same arithmetic used in european logarithmic microprocessor (ELM) up to 51%.</p>

Long-term trends of precipitation in Europe in different datasets

&lt;p&gt;It is already a well known fact that different types of climate datasets (station, gridded, reanalyses) and even individual datasets differ in how they describe statistical properties of climate variables. Here we compare precipitation trends in Europe between station data (taken from the ECA&amp;D database), gridded data (E-OBS and CRU TS), and reanalyses (JRA-55 and NCEP/NCAR) for period 1961-2011, both annually and for individual seasons. Theil-Sen non-parametric trend estimator is used for the quantification of the trend magnitude; Mann-Kendall test is used to evaluate the significance of trends.&lt;/p&gt;&lt;p&gt;On the annual basis, station data indicate precipitation increases in northern Europe and decreases in southern and southeastern Europe. Whereas trends in the gridded datasets roughly agree with station data, reanalyses provide much more negative trends with a different geographical distribution. There is a tendency for reanalyses to overestimate precipitation in the beginning of the period at some places, whereas they underestimate precipitation near the end of the period elsewhere. The disagreement among different data types and datasets is larger in all seasonal analyses except winter. Particularly notable is an excessive drying trend in central, southwestern, and southeastern Europe in NCEP/NCAR in most seasons. Reanalyses thus do not appear to be suitable data sources for estimation of precipitation trends. &amp;#160;&lt;/p&gt;&lt;p&gt;Reasons for the disagreement are varied and are conjectured by a detailed examination of station / point or regional time series: station series may suffer from inhomogeneities; gridded data may be affected by different sets of stations entering the interpolation procedure at different times; while reanalyses may be affected by different kinds of data being assimilated into them in different periods.&lt;/p&gt;

Plate Structural Analysis Based on a Double Interpolation Element with Arbitrary Meshing

This paper presents the plate structural analysis based on the finite element method (FEM) using a double interpolation element with arbitrary meshing. This element used in this research is related to the first-order shear deformation theory (FSDT) and the double interpolation procedure. The first stage of the procedure is the same with the standard FEM for the quadrilateral element, but the averaged nodal gradients must be computed for the second stage of this interpolation. Shape functions established by the double interpolation procedure exhibit more continuous nodal gradients and higher-order polynomial contrast compared to the standard FEM when analysing the same mesh. Note that the total degrees of freedom (DOFs) do not increase in this procedure, and the trial solution and its derivatives are continuous across inter-element boundaries. Besides, with controlling distortion factors, the interior nodes of a plate domain are derived from a set of regular nodes. Four practical examples with good results and small errors are considered in this study for showing excellent efficiency for this element. Last but not least, this element allows us to implement the procedure in an existing FEM computer code as well as can be used for nonlinear analysis in the near future.

Temporal Transitions of Demographic Dot Maps

Dot maps are often used to display the distributions of populations over space. This paper details a method for extending dot maps in order to visualize changes in spatial patterns over time. Specifically, we outline a selective linear interpolation procedure to encode the time range in which dots are visible on a map, which then allows for temporal queries and animation. This methodology is exemplified first by animating population growth across the United States, and second, through an interactive application showing changing poverty distributions in Toronto, Canada.

Analysis of Linear Elastic Fracture Mechanics for Cracked Functionally Graded Composite Plate by Enhanced Local Enriched Consecutive-interpolation Elements

This paper reports the application of consecutive-interpolation procedure into four-node quadrilateral elements for analysis of two-dimensional cracked solids made of functionally graded composite plate. Compared to standard finite element method, the recent developed consecutive-interpolation has been shown to possess many desirable features, such as higher accuracy and smooth nodal gradients it still satisfies the Kronecker-delta property and keeps the total number of degrees of freedom unchanged. The discontinuity in displacement fields along the crack faces and stress singularity around the crack tips are mathematically modeled using enrichment functions. The Heaviside function is employed to describe displacement jump, while four branch functions being developed from asymptotic stress fields are taken as basis functions to capture singularities. The interesting characteristic of functionall graded composite plate is the spatial variation of material properties which are intentionally designed to be served for particular purposes. Such variation has to be taken into account during the computation of Stress Intensity Factors (SIFs). Performance of the proposed approach is demonstrated and verified through various numerical examples, in which SIFs are compared with reference solutions derived from other methods available in literatures.

Interpolation and Model Checking for Nonlinear Arithmetic

We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model into a full model for a set of assertions or returns an explanation (a model interpolant) when no solution exists. This mode of interaction fits well into the model-constructing satisfiability (MCSAT) framework of SMT. We use it to develop an interpolation procedure for any MCSAT-supported theory. In particular, this method leads to an effective interpolation procedure for nonlinear real arithmetic. We evaluate the new procedure by integrating it into a model checker and comparing it with state-of-art model-checking tools for nonlinear arithmetic.

Application of Nonhydraulic Delineation Method of Flood Hazard Areas Using LiDAR-Based Data

Fluvial dynamics are an important aspect of land-use planning as well as ecosystem conservation. Lack of floodplain and flood inundation maps can cause severe implication on land-use planning and development as well as in disaster management. However, flood hazard delineation traditionally involves hydrologic models and uses hydraulic data or historical flooding frequency. This entails intensive data gathering, which leads to extensive amount of cost, time, and complex models, while typically only covers a small portion of the landscape. Therefore, alternative approaches had to be explored. This study explores an alternative approach in delineating flood hazard areas through a straightforward interpolation process while using high-resolution LiDAR-based datasets. The objectives of this study are: (1) to delineate flood hazard areas through a straightforward, nonhydraulic, and interpolation procedure using high-resolution (LiDAR-based) datasets and (2) to determine whether using high-resolution data, coupled with a straightforward interpolation procedure, will yield reliable potential flood hazard maps. Results showed that a straightforward interpolation method using LiDAR-based data produces a reliable potential flood zone map. The resulting map can be used as supplementary information for rapid analysis of the topography which could have implications in area development planning and ecological management and best practices.

Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.