Kinetic model of poly(3-hydroxybutyrate) thermal degradation from experimental non-isothermal data

The non-isothermal data given by TG curves for poly(3-hydroxybutyrate) (PHB) were studied in order to obtain a consistent kinetic model that better represents the PHB thermal decomposition. Thus, data obtained from the dynamic TG curves were suitably managed in order to obtain the Arrhenius kinetic parameter E according to the isoconversional F-W-O method. Once the E parameters is found, a suitable logA and kinetic model (f(alpha)) could be calculated. Hence, the kinetic triplet (E +/- SD, logA +/- SD and f(alpha)) obtained for the thermal decomposition of PHB under non-isothermal conditions was E=152 +/- 4 kJ mol(-1), logA=14.1 +/- 0.2 s(-1) for the kinetic model, and the autocatalytic model function was: f(alpha)=alpha(m)(1-alpha)(n)=alpha(0.42)(1-alpha)(0.56).

A kinetic model for the ultrasound catalyzed hydrolysis of solventless TEOS-water mixtures and the role of the initial additions of ethanol

The acid and ultrasound catalyzed hydrolysis of solventless TEOS-water mixtures are studied, as a function of the initial additions of ethanol to the mixtures, by means of flux calorimetry measurements. A device was specially designed for this purpose. Under acid conditions, our proposed method has been able to resolve hydrolysis from other condensation reactions, by detecting the exothermal hydrolysis reaction heat. The process has been explained by a dissolution and reaction mechanism. Ultrasound forces the dissolution process to start the reaction. The alcohol produced in the reaction helps the dissolution process to further enhance the hydrolysis. Initial amounts of pure ethanol added to the mixtures shorten the start time of the reaction, due to an additional effect of dissolution, and diminish the reaction rate, as a result of the solvent dilution effect. Our dissolution and reaction mechanism modeling describes the main points arising from the experimental data and yields k(H) = 0.24 M(-1) min(-1) for the second-order hydrolysis rate constant at 39 degrees C.

A kinetic model of phosphorus metabolism in growing goats

The effect of increasing phosphorus (P) intake on P utilization was investigated in balance experiments using 12 Saanen goats, 4 to 5 mo of age and weighing 20 to 30 kg. The goats were given similar diets with various concentrations of P, and 32P was injected to trace the movement of P in the body. A P metabolism model with four pools was developed to compute P exchanges in the system. The results showed that P absorption, bone resorption, and excretion of urinary P and endogenous and fecal P all play a part in the homeostatic control of P. Endogenous fecal output was positively correlated to P intake (P < .01). Bone resorption of P was not influenced by intake of P, and P recycling from tissues to the blood pool was lesser for low P intake. Endogenous P loss occurred even in animals fed an inadequate P diet, resulting in a negative P balance. The extrapolated minimum endogenous loss in feces was .067 g of P/d. The minimum P intake for maintenance in Saanen goats was calculated to be .61 g of P/ d or .055 g of P/(kg.75·d) at 25 kg BW. Model outputs indicate greater P flow from the blood pool to the gut and vice versa as P intake increased. Intake of P did not significantly affect P flow from bone and soft tissue to blood. The kinetic model and regressions could be used to estimate P requirement and the fate of P in goats and could also be extrapolated to both sheep and cattle.

A macroscopic kinetic model for DNA polymerase elongation and high-fidelity nucleotide election

The enzymatically catalyzed template-directed extension of ssDNA/primer complex is an impor-tant reaction of extraordinary complexity. The DNA polymerase does not merely facilitate the insertion of dNMP, but it also performs rapid screening of substrates to ensure a high degree of fidelity. Several kinetic studies have determined rate constants and equilibrium constants for the elementary steps that make up the overall pathway. The information is used to develop a macro-scopic kinetic model, using an approach described by Ninio [Ninio J., 1987. Alternative to the steady-state method: derivation of reaction rates from first-passage times and pathway probabili-ties. Proc. Natl. Acad. Sci. U.S.A. 84, 663–667]. The principle idea of the Ninio approach is to track a single template/primer complex over time and to identify the expected behavior. The average time to insert a single nucleotide is a weighted sum of several terms, in-cluding the actual time to insert a nucleotide plus delays due to polymerase detachment from ei-ther the ternary (template-primer-polymerase) or quaternary (+nucleotide) complexes and time delays associated with the identification and ultimate rejection of an incorrect nucleotide from the binding site. The passage times of all events and their probability of occurrence are ex-pressed in terms of the rate constants of the elementary steps of the reaction pathway. The model accounts for variations in the average insertion time with different nucleotides as well as the in-fluence of G+C content of the sequence in the vicinity of the insertion site. Furthermore the model provides estimates of error frequencies. If nucleotide extension is recognized as a compe-tition between successful insertions and time delaying events, it can be described as a binomial process with a probability distribution. The distribution gives the probability to extend a primer/template complex with a certain number of base pairs and in general it maps annealed complexes into extension products.

A stochastic spatially structured epidemic model with diffusive processes

We developed a stochastic lattice model to describe the vector-borne disease (like yellow fever or dengue). The model is spatially structured and its dynamical rules take into account the diffusion of vectors. We consider a bipartite lattice, forming a sub-lattice of human and another occupied by mosquitoes. At each site of lattice we associate a stochastic variable that describes the occupation and the health state of a single individual (mosquito or human). The process of disease transmission in the human population follows a similar dynamic of the Susceptible-Infected-Recovered model (SIR), while the disease transmission in the mosquito population has an analogous dynamic of the Susceptible-Infected-Susceptible model (SIS) with mosquitos diffusion. The occurrence of an epidemic is directly related to the conditional probability of occurrence of infected mosquitoes (human) in the presence of susceptible human (mosquitoes) on neighborhood. The probability of diffusion of mosquitoes can facilitate the formation of pairs Susceptible-Infected enabling an increase in the size of the epidemic. Using an asynchronous dynamic update, we study the disease transmission in a population initially formed by susceptible individuals due to the introduction of a single mosquito (human) infected. We find that this model exhibits a continuous phase transition related to the existence or non-existence of an epidemic. By means of mean field approximations and Monte Carlo simulations we investigate the epidemic threshold and the phase diagram in terms of the diffusion probability and the infection probability.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Phage therapy: A software system for phage quantification and kinetic model inference.

One of the most serious problems of the modern medicine is the growing emergence of antibiotic resistance among pathogenic bacteria. In this circumstance, different and innovative approaches for treating infections caused by multidrug-resistant bacteria are imperatively required. Bacteriophage Therapy is one among the fascinating approaches to be taken into account. This consists of the use of bacteriophages, viruses that infect bacteria, in order to defeat specific bacterial pathogens. Phage therapy is not an innovative idea, indeed, it was widely used around the world in the 1930s and 1940s, in order to treat various infection diseases, and it is still used in Eastern Europe and the former Soviet Union. Nevertheless, Western scientists mostly lost interest in further use and study of phage therapy and abandoned it after the discovery and the spread of antibiotics. The advancement of scientific knowledge of the last years, together with the encouraging results from recent animal studies using phages to treat bacterial infections, and above all the urgent need for novel and effective antimicrobials, have given a prompt for additional rigorous researches in this field. In particular, in the laboratory of synthetic biology of the department of Life Sciences at the University of Warwick, a novel approach was adopted, starting from the original concept of phage therapy, in order to study a concrete alternative to antibiotics. The innovative idea of the project consists in the development of experimental methodologies, which allow to engineer a programmable synthetic phage system using a combination of directed evolution, automation and microfluidics. The main aim is to make “the therapeutics of tomorrow individualized, specific, and self-regulated” (Jaramillo, 2015). In this context, one of the most important key points is the Bacteriophage Quantification. Therefore, in this research work, a mathematical model describing complex dynamics occurring in biological systems involving continuous growth of bacteriophages, modulated by the performance of the host organisms, was implemented as algorithms into a working software using MATLAB. The developed program is able to predict different unknown concentrations of phages much faster than the classical overnight Plaque Assay. What is more, it gives a meaning and an explanation to the obtained data, making inference about the parameter set of the model, that are representative of the bacteriophage-host interaction.

Efficacy of telavancin against penicillin-resistant pneumococci and Staphylococcus aureus in a rabbit meningitis model and determination of kinetic parameters

The penetration of telavancin was 2% into inflamed meninges and ca. 1 per thousand into noninflamed meninges after two intravenous injections (30 mg/kg of body weight). In experimental meningitis, telavancin was significantly superior to vancomycin combined with ceftriaxone against a penicillin-resistant pneumococcal strain. Against a methicillin-sensitive staphylococcal strain, telavancin was slightly but not significantly superior to vancomycin.

Implementation of a phenomenological evaporation model into a porous network simulation for water management in low temperature fuel cells

A phenomenological transition film evaporation model was introduced to a pore network model with the consideration of pore radius, contact angle, non-isothermal interface temperature, microscale fluid flows and heat and mass transfers. This was achieved by modeling the transition film region of the menisci in each pore throughout the porous transport layer of a half-cell polymer electrolyte membrane (PEM) fuel cell. The model presented in this research is compared with the standard diffusive fuel cell modeling approach to evaporation and shown to surpass the conventional modeling approach in terms of predicting the evaporation rates in porous media. The current diffusive evaporation models used in many fuel cell transport models assumes a constant evaporation rate across the entire liquid-air interface. The transition film model was implemented into the pore network model to address this issue and create a pore size dependency on the evaporation rates. This is accomplished by evaluating the transition film evaporation rates determined by the kinetic model for every pore containing liquid water in the porous transport layer (PTL). The comparison of a transition film and diffusive evaporation model shows an increase in predicted evaporation rates for smaller pore sizes with the transition film model. This is an important parameter when considering the micro-scaled pore sizes seen in the PTL and becomes even more substantial when considering transport in fuel cells containing an MPL, or a large variance in pore size. Experimentation was performed to validate the transition film model by monitoring evaporation rates from a non-zero contact angle water droplet on a heated substrate. The substrate was a glass plate with a hydrophobic coating to reduce wettability. The tests were performed at a constant substrate temperature and relative humidity. The transition film model was able to accurately predict the drop volume as time elapsed. By implementing the transition film model to a pore network model the evaporation rates present in the PTL can be more accurately modeled. This improves the ability of a pore network model to predict the distribution of liquid water and ultimately the level of flooding exhibited in a PTL for various operating conditions.

New fully kinetic model for the study of electric potential, plasma, and dust above lunar landscapes

We have developed a new fully kinetic electrostatic simulation, HYBes, to study how the lunar landscape affects the electric potential and plasma distributions near the surface and the properties of lifted dust. The model embodies new techniques that can be used in various types of physical environments and situations. We demonstrate the applicability of the new model in a situation involving three charged particle species, which are solar wind electrons and protons, and lunar photoelectrons. Properties of dust are studied with test particle simulations by using the electric fields derived from the HYBes model. Simulations show the high importance of the plasma and the electric potential near the surface. For comparison, the electric potential gradients near the landscapes with feature sizes of the order of the Debye length are much larger than those near a flat surface at different solar zenith angles. Furthermore, dust test particle simulations indicate that the landscape relief influences the dust location over the surface. The study suggests that the local landscape has to be taken into account when the distributions of plasma and dust above lunar surface are studied. The HYBes model can be applied not only at the Moon but also on a wide range of airless planetary objects such as Mercury, other planetary moons, asteroids, and nonactive comets.

Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Kinetic Model for Micro Algae Cell Concentration and Size Distribution: Application to Nannochloropsis gaditana

The cell concentration and size distribution of the microalgae Nannochloropsis gaditana were studied over the whole growth process. Various samples were taken during the light and dark periods the algae were exposed to. The distributions obtained exhibited positive skew, and no change in the type of distribution was observed during the growth process. The size distribution shifted to lower diameters in dark periods while in light periods the opposite occurred. The overall trend during the growth process was one where the size distribution shifted to larger cell diameters, with differences between initial and final distributions of individual cycles becoming smaller. A model based on the Logistic model for cell concentration as a function of time in the dark period that also takes into account cell respiration and growth processes during dark and light periods, respectively, was proposed and successfully applied. This model provides a picture that is closer to the real growth and evolution of cultures, and reveals a clear effect of light and dark periods on the different ways in which cell concentration and diameter evolve with time.

Kinetic model for selective cultivation of microfungi in a microscreen process for food processing wastewater treatment and biomass production

The research was aimed at developing a technology to combine the production of useful microfungi with the treatment of wastewater from food processing. A recycle bioreactor equipped with a micro-screen was developed as a wastewater treatment system on a laboratory scale to contain a Rhizopus culture and maintain its dominance under non-aseptic conditions. Competitive growth of bacteria was observed, but this was minimised by manipulation of the solids retention time and the hydraulic retention time. Removal of about 90% of the waste organic material (as BOD) from the wastewater was achieved simultaneously. Since essentially all fungi are retained behind the 100 mum aperture screen, the solids retention time could be controlled by the rate of harvesting. The hydraulic retention time was employed to control the bacterial growth as the bacteria were washed through the screen at a short HRT. A steady state model was developed to determine these two parameters. This model predicts the effluent quality. Experimental work is still needed to determine the growth characteristics of the selected fungal species under optimum conditions (pH and temperature).

Anisotropic model of kinetic roughening:he strong-coupling regime

We study the strong coupling (SC) limit of the anisotropic Kardar-Parisi-Zhang (KPZ) model. A systematic mapping of the continuum model to its lattice equivalent shows that in the SC limit, anisotropic perturbations destroy all spatial correlations but retain a temporal scaling which shows a remarkable crossover along one of the two spatial directions, the choice of direction depending on the relative strength of anisotropicity. The results agree with exact numerics and are expected to settle the long-standing SC problem of a KPZ model in the infinite range limit. © 2007 The American Physical Society.