Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Spatial distribution of the soil carbon pool in a Holm oak dehesa in Spain

Aims Dehesas are agroforestry systems characterized by scattered trees among pastures, crops and/or fallows. A study at a Spanish dehesa has been carried out to estimate the spatial distribution of the soil organic carbon stock and to assess the influence of the tree cover. Methods The soil organic carbon stock was estimated from the five uppermost cm of themineral soil with high spatial resolution at two plots with different grazing intensities. The Universal Kriging technique was used to assess the spatial distribution of the soil organic carbon stocks, using tree coverage within a buffering area as an auxiliary variable. Results A significant positive correlation between tree presence and soil organic carbon stocks up to distances of around 8 m from the trees was found. The tree crown cover within a buffer up to a distance similar to the crown radius around the point absorbed 30 % of the variance in the model for both grazing intensities, but residual variance showed stronger spatial autocorrelation under regular grazing conditions. Conclusions Tree cover increases soil organic carbon stocks, and can be satisfactorily estimated by means of crown parameters. However, other factors are involved in the spatial pattern of the soil organic carbon distribution. Livestock plays an interactive role together with tree presence in soil organic carbon distribution.

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

Extension of the characteristic equation to absorption chillers with adiabatic absorbers

Various researchers have developed models of conventional H2O–LiBr absorption machines with the aim of predicting their performance. In this paper, the methodology of characteristic equations developed by Hellmann et al. (1998) is applied. This model is able to represent the capacity of single effect absorption chillers and heat pumps by means of simple algebraic equations. An extended characteristic equation based on a characteristic temperature difference has been obtained, considering the facility features. As a result, it is concluded that for adiabatic absorbers a subcooling temperature must be specified. The effect of evaporator overflow has been characterized. Its influence on cooling capacity has been included in the extended characteristic equation. Taking into account the particular design and operation features, a good agreement between experimental performance data and those obtained through the extended characteristic equation has been achieved at off-design operation. This allows its use for simulation and control purposes.

Non-destructive measurement techniques for taper equation development: a study case in the Spanish Northern Iberian Range

In recent years, the technology for measuring the diameter and height of standing trees has improved significantly. These enhancements allow estimation of the volume of standing trees using stem taper equations, which traditionally have been constructed with data from felled trees, in an accurate and economically feasible way. A nondestructive method was evaluated with data from 38 pines and was validated with data from another 38 pines, both in the Northern Iberian Range (Spain). The electronic dendrometer Criterion RD1000 (Laser Technology Inc.) and the laser hypsometer TruPulse (Laser Technology Inc.) were used due to their accuracy and interoperability. The methodology was valid (unbiased and precise) measuring from a distance similar to the height of the tree. In this distance, statistical criteria and plots based on the residuals showed no clear advantage in volume estimation with models fitted with data from destructive methods against models fitted with data from the proposed non-destructive technique. This methodology can be considered useful for individual volume estimation and for developing taper equations.

Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrodinger equation

The effective mass Schrodinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band which are similar to those originated in quantum wires and quantum wells coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.

FTCS finite difference scheme GPGPU parallel computing for the heat conduction equation = Programación en paralelo GPGPU del método en diferencias finitas FTCS para la ecuación del calor

En el presente artículo se muestran las ventajas de la programación en paralelo resolviendo numéricamente la ecuación del calor en dos dimensiones a través del método de diferencias finitas explícito centrado en el espacio FTCS. De las conclusiones de este trabajo se pone de manifiesto la importancia de la programación en paralelo para tratar problemas grandes, en los que se requiere un elevado número de cálculos, para los cuales la programación secuencial resulta impracticable por el elevado tiempo de ejecución. En la primera sección se describe brevemente los conceptos básicos de programación en paralelo. Seguidamente se resume el método de diferencias finitas explícito centrado en el espacio FTCS aplicado a la ecuación parabólica del calor. Seguidamente se describe el problema de condiciones de contorno y valores iniciales específico al que se va a aplicar el método de diferencias finitas FTCS, proporcionando pseudocódigos de una implementación secuencial y dos implementaciones en paralelo. Finalmente tras la discusión de los resultados se presentan algunas conclusiones. In this paper the advantages of parallel computing are shown by solving the heat conduction equation in two dimensions with the forward in time central in space (FTCS) finite difference method. Two different levels of parallelization are consider and compared with traditional serial procedures. We show in this work the importance of parallel computing when dealing with large problems that are impractical or impossible to solve them with a serial computing procedure. In the first section a summary of parallel computing approach is presented. Subsequently, the forward in time central in space (FTCS) finite difference method for the heat conduction equation is outline, describing how the heat flow equation is derived in two dimensions and the particularities of the finite difference numerical technique considered. Then, a specific initial boundary value problem is solved by the FTCS finite difference method and serial and parallel pseudo codes are provided. Finally after results are discussed some conclusions are presented.

A general fractional porous medium equation

A general fractional porous medium equation

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Initial design with L2 Monge-Kantorovich theory for the Monge–Ampère equation method of freeform optics

The Monge–Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L2 Monge-Kantorovich (LMK) theory, and introduce an efficient approach for finding the optimal mapping of the LMK problem. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design.

The Monge-Ampére equation method in freeform optics design

The Monge-Ampére equation method could be the most advanced point source algorithm of freeform optics design. This paper introduces this method, and outlines two key issues that should be tackles to improve this method.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Development of somatic embryogenesis for cloning and conservation of mature holm oak trees (Quercus ilex L.)

La encina (Quercus ilex L.) es una de las especies forestales mediterráneas más importantes. Constituye gran parte del estrato arbóreo de dehesas o montados, produce bellota como alimento del ganado y establece simbiosis con hongos micorrizógenos de gran valor económico. La encina está considerada como una especie recalcitrante en términos de conservación de semillas y capacidad morfogénica, lo que dificulta los programas de conservación de recursos genéticos y la mejora de la especie. La propagación vegetativa es una potente herramienta de los programas de mejora, por lo que es preciso desarrollar protocolos de regeneración somática en encina. La embriogénesis somática está considerada como la modalidad más adecuada de regeneración basada en técnicas de cultivo de tejidos vegetales utilizada en biotecnología forestal. Este trabajo se centra en el estudio de determinados aspectos de la embriogénesis somática para la regeneración clonal de encinas adultas. La memoria de esta tesis se ha dividido en capítulos que se corresponden con diferentes aspectos del sistema embriogénico. La embriogénesis somática se indujo en tegumentos maternos de óvulos en desarrollo procedentes de bellotas inmaduras de encinas adultas. A pesar de las bajas frecuencias de inducción, las líneas embriogénicas generadas se amplificaron mediante embriogénesis secundaria observándose cierta pérdida de la capacidad de diferenciación con el tiempo. Tanto el genotipo como la formulación del medio de cultivo influyeron en la respuesta embriogénica, concluyendo que la formulación de macronutrientes de Schenk y Hildebrant del medio sin reguladores de crecimiento fue la combinación más efectiva en la inducción. Los resultados sugirieron la existencia de una ventana en el desarrollo del óvulo más sensible a la inducción. El genotipo in[luyó en la capacidad proliferativa de los cultivos y en la conversión de los embriones somáticos, que se incrementó suplementando el medio con ácido indol-3-butírico y 6-benciladenina. El cultivo en medio líquido de líneas embriogénicas en condiciones de inmersión transitoria incrementó el crecimiento, dependiendo del genotipo, con respecto al cultivo en medio semisólido. Sin embargo, no mejoró la capacidad de diferenciar embriones cotiledonares aislados. Se estableció un protocolo de inicio y mantenimiento de cultivos en suspensión para varias líneas embriogénicas mediante inoculación en alta densidad de agregados embrionarios procedentes del medio semisólido. Para evitar la pérdida de vigor y la capacidad morfogénica debida al cultivo prolongado se desarrolló un protocolo de crioconservación de líneas embriogénicas mediante vitrificación. Al determinar la influencia de los agentes crioprotectores antes y después de su inmersión en nitrógeno líquido se concluyó que las respuestas de capacidad de crecimiento y de diferenciación del material embriogénico son independientes, además de estar bajo influencia del genotipo y el tipo de material crioconservado. La combinación de sacarosa y PVS2 previa a la inmersión en nitrógeno líquido proporcionó la mayor tasa de recuperación. Cuando las líneas fueron crioconservadas 30 días la capacidad de diferenciación se perdió en todas ellas. El análisis de SSR detectó variación somaclonal en el material crioconservado a corto plazo. SSR y RAPD mostraron importantes diferencias genéticas entre los árboles donantes y el material embriogénico que dependieron del genotipo. El grado de detección dependió del marcador empleado. Ambos marcadores revelaron baja inestabilidad intraclonal. Los RAPD revelaron variación genética intra-individuo en las encinas donantes. Se discuten la variación genética pre-existente en encina, su aparición durante las primeras fases de la inducción de embriogénesis, y la presencia de tejidos provenientes de la fertilización en el explanto materno. Esto hace preciso definir la identidad genética del material donante y acometer ensayos de detección precoz de variación somaclonal. ABSTRACT Holm oak (Quercus ilex L.) is one of the most important Mediterranean forest species. It conforms the tree layer of dehesas or montados, it produces acorns to feed the livestock and it establishes symbiosis with profitable mycorrhizal fungi. Holm oak is considered as recalcitrant species in terms of seed conservation and morphogenic capacities, which complicates the development of genetic conservation and improvement programs. Vegetative propagation is one of the mightiest tools for breeding programs therefore; developing protocols for clonal regeneration of holm oak is essential. Somatic embryogenesis is considered the best tissue culture-based way of plant regeneration in forest biotechnology. The present study is focused on the study of certain aspects of somatic embryogenesis for clonal regeneration of mature holm oak. This thesis manuscript is divided into several chapters that match with different aspects of the embryogenic system. Somatic embryogenesis induction was achieved on maternal teguments of developing ovules from immature acorns of adult holm oak trees. Despite the low induction frequencies, the generated embryogenic lines were amplified by secondary embryogenesis. A decline in the differentiation capacity over time was also observed. It was concluded that both genotype and culture media formulation influenced the embryogenic response, being the Schenk and Hildebrandt´s macronutrients formulation from culture medium and the lack of plant growth regulators the most effective combination for the induction of the embryogenic response. It has been suggested the existence of a developmental window in which ovules are prone to induction. Genotype influenced the proliferation capacity and the plant conversion of somatic embryos, which was also favoured by the presence of indol-3-butyric acid and 6-bencyladenine. The use of temporary immersion systems as proliferation in liquid culture of the embryogenic lines increased the growth depending on genotype, when compared to semisolid cultures. However, it did not improve the differentiation of single cotyledonary embryos. A protocol for the initiation and maintenance of embryogenic suspension cultures was established for several embryogenic lines with highly dense inoculi of embryogenic clusters from proliferating semisolid cultures. In order to avoid the loss of vigour and morphogenic ability of embryogenic lines due to prolonged cultures, a cryopreservation protocol for embryogenic lines of holm oak has been developed. During the determination of the influence of cryoprotective agents on the growth and differentiation capacities before and after liquid nitrogen immersion, it was concluded that both responses were independent from each other and also under the influence of genotype and the type of cryopreserved material. The combination of sucrose and PVS2 prior liquid nitrogen immersion provided higher recovery rates. When the same embryogenic lines were cryopreserved for 30 days, none was able to differentiate. The SSRs analysis of the short-term cryopreserved material detected somaclonal variation. Both SSR and RAPD markers showed high sensitivity to detect genetic differences between the donor trees and the generated embryogenic material. Nevertheless, the degree of instability detection depended on the marker. The SSR analysis indicated a relationship between genotype, the studied loci and the located polymorphisms. Also, both markers revealed low intraclonal genetic variation. The RAPD detected genetic variation within the donor trees. The presence of pre-existent genetic variation within mature trees, in addition to its occurrence during the early stages of the embryogenic induction, and the presence of tissues of fertilisation origin within the maternal explants are all discussed. Nonetheless, the determination of the genetic identity of donor material is required, in addition to early detection methods of somaclonal variation.

Development of somatic embryogenesis for cloning and conservation of mature holm oak trees (Quercus ilex L.)

La encina (Quercus ilex L.) es una de las especies forestales mediterráneas más importantes. Constituye gran parte del estrato arbóreo de dehesas o montados, produce bellota como alimento del ganado y establece simbiosis con hongos micorrizógenos de gran valor económico. La encina está considerada como una especie recalcitrante en términos de conservación de semillas y capacidad morfogénica, lo que dificulta los programas de conservación de recursos genéticos y la mejora de la especie. La propagación vegetativa es una potente herramienta de los programas de mejora, por lo que es preciso desarrollar protocolos de regeneración somática en encina. La embriogénesis somática está considerada como la modalidad más adecuada de regeneración basada en técnicas de cultivo de tejidos vegetales utilizada en biotecnología forestal. Este trabajo se centra en el estudio de determinados aspectos de la embriogénesis somática para la regeneración clonal de encinas adultas. La memoria de esta tesis se ha dividido en capítulos que se corresponden con diferentes aspectos del sistema embriogénico. La embriogénesis somática se indujo en tegumentos maternos de óvulos en desarrollo procedentes de bellotas inmaduras de encinas adultas. A pesar de las bajas frecuencias de inducción, las líneas embriogénicas generadas se amplificaron mediante embriogénesis secundaria observándose cierta pérdida de la capacidad de diferenciación con el tiempo. Tanto el genotipo como la formulación del medio de cultivo influyeron en la respuesta embriogénica, concluyendo que la formulación de macronutrientes de Schenk y Hildebrant del medio sin reguladores de crecimiento fue la combinación más efectiva en la inducción. Los resultados sugirieron la existencia de una ventana en el desarrollo del óvulo más sensible a la inducción. El genotipo in[luyó en la capacidad proliferativa de los cultivos y en la conversión de los embriones somáticos, que se incrementó suplementando el medio con ácido indol-3-butírico y 6-benciladenina. El cultivo en medio líquido de líneas embriogénicas en condiciones de inmersión transitoria incrementó el crecimiento, dependiendo del genotipo, con respecto al cultivo en medio semisólido. Sin embargo, no mejoró la capacidad de diferenciar embriones cotiledonares aislados. Se estableció un protocolo de inicio y mantenimiento de cultivos en suspensión para varias líneas embriogénicas mediante inoculación en alta densidad de agregados embrionarios procedentes del medio semisólido. Para evitar la pérdida de vigor y la capacidad morfogénica debida al cultivo prolongado se desarrolló un protocolo de crioconservación de líneas embriogénicas mediante vitrificación. Al determinar la influencia de los agentes crioprotectores antes y después de su inmersión en nitrógeno líquido se concluyó que las respuestas de capacidad de crecimiento y de diferenciación del material embriogénico son independientes, además de estar bajo influencia del genotipo y el tipo de material crioconservado. La combinación de sacarosa y PVS2 previa a la inmersión en nitrógeno líquido proporcionó la mayor tasa de recuperación. Cuando las líneas fueron crioconservadas 30 días la capacidad de diferenciación se perdió en todas ellas. El análisis de SSR detectó variación somaclonal en el material crioconservado a corto plazo. SSR y RAPD mostraron importantes diferencias genéticas entre los árboles donantes y el material embriogénico que dependieron del genotipo. El grado de detección dependió del marcador empleado. Ambos marcadores revelaron baja inestabilidad intraclonal. Los RAPD revelaron variación genética intra-individuo en las encinas donantes. Se discuten la variación genética pre-existente en encina, su aparición durante las primeras fases de la inducción de embriogénesis, y la presencia de tejidos provenientes de la fertilización en el explanto materno. Esto hace preciso definir la identidad genética del material donante y acometer ensayos de detección precoz de variación somaclonal. ABSTRACT Holm oak (Quercus ilex L.) is one of the most important Mediterranean forest species. It conforms the tree layer of dehesas or montados, it produces acorns to feed the livestock and it establishes symbiosis with profitable mycorrhizal fungi. Holm oak is considered as recalcitrant species in terms of seed conservation and morphogenic capacities, which complicates the development of genetic conservation and improvement programs. Vegetative propagation is one of the mightiest tools for breeding programs therefore; developing protocols for clonal regeneration of holm oak is essential. Somatic embryogenesis is considered the best tissue culture-based way of plant regeneration in forest biotechnology. The present study is focused on the study of certain aspects of somatic embryogenesis for clonal regeneration of mature holm oak. This thesis manuscript is divided into several chapters that match with different aspects of the embryogenic system. Somatic embryogenesis induction was achieved on maternal teguments of developing ovules from immature acorns of adult holm oak trees. Despite the low induction frequencies, the generated embryogenic lines were amplified by secondary embryogenesis. A decline in the differentiation capacity over time was also observed. It was concluded that both genotype and culture media formulation influenced the embryogenic response, being the Schenk and Hildebrandt´s macronutrients formulation from culture medium and the lack of plant growth regulators the most effective combination for the induction of the embryogenic response. It has been suggested the existence of a developmental window in which ovules are prone to induction. Genotype influenced the proliferation capacity and the plant conversion of somatic embryos, which was also favoured by the presence of indol-3-butyric acid and 6-bencyladenine. The use of temporary immersion systems as proliferation in liquid culture of the embryogenic lines increased the growth depending on genotype, when compared to semisolid cultures. However, it did not improve the differentiation of single cotyledonary embryos. A protocol for the initiation and maintenance of embryogenic suspension cultures was established for several embryogenic lines with highly dense inoculi of embryogenic clusters from proliferating semisolid cultures. In order to avoid the loss of vigour and morphogenic ability of embryogenic lines due to prolonged cultures, a cryopreservation protocol for embryogenic lines of holm oak has been developed. During the determination of the influence of cryoprotective agents on the growth and differentiation capacities before and after liquid nitrogen immersion, it was concluded that both responses were independent from each other and also under the influence of genotype and the type of cryopreserved material. The combination of sucrose and PVS2 prior liquid nitrogen immersion provided higher recovery rates. When the same embryogenic lines were cryopreserved for 30 days, none was able to differentiate. The SSRs analysis of the short-term cryopreserved material detected somaclonal variation. Both SSR and RAPD markers showed high sensitivity to detect genetic differences between the donor trees and the generated embryogenic material. Nevertheless, the degree of instability detection depended on the marker. The SSR analysis indicated a relationship between genotype, the studied loci and the located polymorphisms. Also, both markers revealed low intraclonal genetic variation. The RAPD detected genetic variation within the donor trees. The presence of pre-existent genetic variation within mature trees, in addition to its occurrence during the early stages of the embryogenic induction, and the presence of tissues of fertilisation origin within the maternal explants are all discussed. Nonetheless, the determination of the genetic identity of donor material is required, in addition to early detection methods of somaclonal variation.