The logarithmic spiral, autoisoptic curve

In the Line of Investigation that in the department of “Technical Drawing” in the School of Agriculture Engineering of Madrid, we carry out on the study of The Technical Curves and his singularities, we demonstrate an interesting property of the Logarithmic Spiral. The demonstrated property consists of which the logarithmic spiral is a autoisoptic curve, that is to say that if from a point P anyone of the spiral tangent straight lines draw up to the previous arc, these form a constant angle α. This demonstration is novel and in addition we get to contribute a method to calculate the angle α given the equation of the spiral.

A 800 kW I-V curve

This paper presents the measurement of the I-V curve of an 800 kW PV generator by means of an own-made capacitive load. Along the lines of some previous works, it is shown that an I-V curve analysis can also be applied to big PV generators and that, when measuring the operating conditions with reference modules and taking some precautions (especially regarding the operating cell temperature), it is still a useful tool for characterizing them and therefore can be incorporated into maintenance procedures. As far as we know, this is the largest I-V curve measured so far.

Gini coefficient, dissimilarity index and Lorenz curve for the spanish port system by type of goods

This paper shows the Gini Coefficient, the dissimilarity Index and the Lorenz Curve for the Spanish Port System by type of goods from 1960 to the year 2010 for business units: Total traffic, Liquid bulk cargo, Solid bulk cargo, General Merchandise and Container (TEUs) with the aim of carcaterizar the Spanish port systems in these periods and propose future strategies.

A 500-kW pv generator I-V curve

This paper presents the measurement of the I-V curve of a 500-kW PV generator by means of an own-made capacitive load. It is shown that I-V curve analysis can also be applied to big PV generators and that when measuring the operation conditions with reference modules and taking some precautions (especially regarding the operation cell temperature), it is still a useful tool for characterizing them and therefore can be incorporated into maintenance procedures. As far as we know, this is the largest I-V curve measured so far.

On the free-boundary for an elliptic inverse nonlocal problem arising in the nuclear fusion. A numerical approach

We consider a mathematical model related to the stationary regime of a plasma magnetically confined in a Stellarator device in the nuclear fusion. The mathematical problem may be reduced to an nonlinear elliptic inverse nonlocal two dimensional free{boundary problem. The nonlinear terms involving the unknown functions of the problem and its rearrangement. Our main goal is to determinate the existence and the estimate on the location and size of region where the solution is nonnegative almost everywhere (corresponding to the plasma region in the physical model)

Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented

Accurate Parabolic Navier-Stokes solutions of the supersonic flow around and elliptic cone

Flows of relevance to new generation aerospace vehicles exist, which are weakly dependent on the streamwise direction and strongly dependent on the other two spatial directions, such as the flow around the (flattened) nose of the vehicle and the associated elliptic cone model. Exploiting these characteristics, a parabolic integration of the Navier-Stokes equations is more appropriate than solution of the full equations, resulting in the so-called Parabolic Navier-Stokes (PNS). This approach not only is the best candidate, in terms of computational efficiency and accuracy, for the computation of steady base flows with the appointed properties, but also permits performing instability analysis and laminar-turbulent transition studies a-posteriori to the base flow computation. This is to be contrasted with the alternative approach of using order-of-magnitude more expensive spatial Direct Numerical Simulations (DNS) for the description of the transition process. The PNS equations used here have been formulated for an arbitrary coordinate transformation and the spatial discretization is performed using a novel stable high-order finite-difference-based numerical scheme, ensuring the recovery of highly accurate solutions using modest computing resources. For verification purposes, the boundary layer solution around a circular cone at zero angle of attack is compared in the incompressible limit with theoretical profiles. Also, the recovered shock wave angle at supersonic conditions is compared with theoretical predictions in the same circular-base cone geometry. Finally, the entire flow field, including shock position and compressible boundary layer around a 2:1 elliptic cone is recovered at Mach numbers 3 and 4

An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.

Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality

Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality

The elliptic model for communication fluxes

In this paper, a model (called the elliptic model) is proposed to estimate the number of social ties between two locations using population data in a similar manner to how transportation research deals with trips. To overcome the asymmetry of transportation models, the new model considers that the number of relationships between two locations is inversely proportional to the population in the ellipse whose foci are in these two locations. The elliptic model is evaluated by considering the anonymous communications patterns of 25 million users from three different countries, where a location has been assigned to each user based on their most used phone tower or billing zip code. With this information, spatial social networks are built at three levels of resolution: tower, city and region for each of the three countries. The elliptic model achieves a similar performance when predicting communication fluxes as transportation models do when predicting trips. This shows that human relationships are influenced at least as much by geography as is human mobility.

The elliptic rendezvous problem in DROMO formulation

The extension of DROMO formulation to relative motion is evaluated. The orbit of the follower spacecraft can be constructed through differences on the elements defining the orbit of the leader spacecraft. Assuming that the differences are small, the problemis linearized. Typical linearized solutions to relativemotion determine the relative state of the follower spacecraft at a certain time step. Because of the form of DROMO formulation, the performance of a frozen-anomaly transformation is explored. In this case, the relative state is computed for a certain value of the anomaly, equal for leader and follower. Since the time for leader and follower do not coincide, the implicit time delay needs to be corrected to recover the physical sense of the solution. When determining the relative orbit, numerical testing shows significant error reductions compared to previous linearized solutions.