*PLoS One ; 15(3): e0229738, 2020.*

##### RESUMO

Ultrasound has many uses, such as in medical imaging, monitoring of crystallization, characterization of emulsions and suspensions, and disruption of cell membranes in the food industry. It can also affect microbial cells by promoting or slowing their growth and increasing the production of some metabolites. However, the exact mechanism explaining the effect of ultrasound has not been identified yet. Most equipment employed to study the effect of ultrasound on microorganisms has been designed for other applications and then only slightly modified. This results in limited control over ultrasound frequency and input power, or pressure distribution in the reactor. The present study aimed to obtain a well-defined reactor by simulating the pressure distribution of a sonobioreactor. Specifically, we optimized a sonotrode to match the bottle frequency and compared it to measured results to verify the accuracy of the simulation. The measured pressure distribution spectrum presented the same overall trend as the simulated spectrum. However, the peaks were much less intense, likely due to non-linear events such as the collapse of cavitation bubbles. To test the application of the sonobioreactor in biological systems, two biotechnologically interesting microorganisms were assessed: an electroactive bacterium, Geobacter sulfurreducens, and a lignocellulose-degrading fungus, Fusarium oxysporum. Sonication resulted in increased malate production by G. sulfurreducens, but no major effect on growth. In comparison, morphology and growth of F. oxysporum were more sensitive to ultrasound intensity. Despite considerable morphological changes at 4 W input power, the growth rate was not adversely affected; however, at 12 W, growth was nearly halted. The above findings indicate that the novel sonobioreactor provides an effective tool for studying the impact of ultrasound on microorganisms.

##### Assuntos

Reatores Biológicos/microbiologia , Fusarium/crescimento & desenvolvimento , Geobacter/crescimento & desenvolvimento , Análise Numérica Assistida por Computador , Sonicação , Calorimetria , Simulação por Computador , Fusarium/ultraestrutura , Geobacter/metabolismo , Malatos/metabolismo , Metaboloma , Pressão , Vibração*PLoS One ; 15(1): e0228106, 2020.*

##### RESUMO

We conducted regional scale CO2 simulations using the Weather Research and Forecasting model (WRF) coupled with the Vegetation Photosynthesis and Respiration Model (VPRM). We contrasted simulated concentrations with column, ground and aircraft observations during the Korea-United States Air Quality (KORUS-AQ) 2016 field campaign. Overall, WRF-VPRM slightly underestimates CO2 concentrations at ground and column monitoring sites, but it significantly underestimates at an inland tower measurement site, especially within the stable (nocturnal) boundary layer in nighttime. The model successfully captures the airborne vertical profiles but showed a large offset within the planetary boundary layer (PBL) in the areas surrounding Seoul and around the Taeahn point source emissions in the west coastal area of the Korean Peninsula. A case study flight intended to capture Chinese influence observed no clear signals of long-range transport of CO2, due mainly to the much larger magnitude of background CO2 concentrations. The calculated Net Ecosystem Exchange (NEE) with flux measurements at a tower site in the South Korean Peninsula has also been evaluated comparing with CO2 flux measurements at a flux tower site, resulting in the underestimation by less than a factor of 1.

##### Assuntos

Dióxido de Carbono/análise , Simulação por Computador , Previsões , Modelos Teóricos , Análise Numérica Assistida por Computador , Fotossíntese , Tempo (Meteorologia) , Aeronaves , Respiração Celular , Ritmo Circadiano , Ecossistema , Geografia , República da Coreia , Seul , Análise Espaço-Temporal , Fatores de Tempo*Comput Methods Biomech Biomed Engin ; 23(5): 169-181, 2020 Apr.*

##### RESUMO

In this paper, a numerical and experimental study of the shock absorption properties of bike helmets is presented. Laboratory compression and tensile tests were carried out on samples of expanded polystyrene (EPS) and polycarbonate (PC), respectively constituting the internal shock absorption layer and the external hard shell of composite helmets. The measured responses of the two materials were then exploited to calibrate the relevant elasto-plastic constitutive models, adopted in full-scale finite element analyses of a helmet subject to standardized impacts. The simulations allowed assessing the time evolution of the acceleration measured inside the headform (according e.g., to EN 1078) and the failure mechanisms of the helmet, if any, as induced by the localization of plastic deformations.

##### Assuntos

Ciclismo , Dispositivos de Proteção da Cabeça , Análise Numérica Assistida por Computador , Choque Traumático/diagnóstico , Aceleração , Adsorção , Força Compressiva , Análise de Elementos Finitos , Humanos , Cimento de Policarboxilato/química , Poliestirenos/química , Resistência à Tração*Am J Hum Genet ; 106(1): 3-12, 2020 01 02.*

##### RESUMO

In biobank data analysis, most binary phenotypes have unbalanced case-control ratios, and this can cause inflation of type I error rates. Recently, a saddle point approximation (SPA) based single-variant test has been developed to provide an accurate and scalable method to test for associations of such phenotypes. For gene- or region-based multiple-variant tests, a few methods exist that can adjust for unbalanced case-control ratios; however, these methods are either less accurate when case-control ratios are extremely unbalanced or not scalable for large data analyses. To address these problems, we propose SKAT- and SKAT-O- type region-based tests; in these tests, the single-variant score statistic is calibrated based on SPA and efficient resampling (ER). Through simulation studies, we show that the proposed method provides well-calibrated p values. In contrast, when the case-control ratio is 1:99, the unadjusted approach has greatly inflated type I error rates (90 times that of exome-wide sequencing α = 2.5 × 10-6). Additionally, the proposed method has similar computation time to the unadjusted approaches and is scalable for large sample data. In our application, the UK Biobank whole-exome sequence data analysis of 45,596 unrelated European samples and 791 PheCode phenotypes identified 10 rare-variant associations with p value < 10-7, including the associations between JAK2 and myeloproliferative disease, HOXB13 and cancer of prostate, and F11 and congenital coagulation defects. All analysis summary results are publicly available through a web-based visual server, and this availability can help facilitate the identification of the genetic basis of complex diseases.

##### Assuntos

Bancos de Espécimes Biológicos , Exoma/genética , Estudo de Associação Genômica Ampla , Fenômica , Polimorfismo de Nucleotídeo Único , Sequenciamento Completo do Exoma/métodos , Estudos de Casos e Controles , Simulação por Computador , Humanos , Análise Numérica Assistida por Computador , Fenótipo , Reino Unido*PLoS One ; 14(12): e0226299, 2019.*

##### RESUMO

A common problem when analyzing models, such as mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given input-output data. The total number of such values over the complex numbers is called the identifiability degree of the model. Unidentifiable models are models such that the unknown parameters can have an infinite number of values given input-output data. For unidentifiable models, a set of identifiable functions of the parameters are sought so that the model can be reparametrized in terms of these functions yielding an identifiable model. In this work, we use numerical algebraic geometry to determine if a model given by polynomial or rational ordinary differential equations is identifiable or unidentifiable. For identifiable models, we present a novel approach to compute the identifiability degree. For unidentifiable models, we present a novel numerical differential algebra technique aimed at computing a set of algebraically independent identifiable functions. Several examples are used to demonstrate the new techniques.

##### Assuntos

Algoritmos , Simulação por Computador , Modelos Biológicos , Análise Numérica Assistida por Computador , Humanos*PLoS One ; 14(12): e0225773, 2019.*

##### RESUMO

We present numerical methods for modeling the dynamics of arbitrarily shaped particles trapped within optical tweezers, which improve the predictive power of numerical simulations for practical use. We study the dependence of trapping on the shape and size of particles in a single continuous wave beam setup. We also consider the implications of different particle compositions, beam types and media. The major result of the study is that for different irregular particle shapes, a range of beam powers generally leads to trapping. The trapping power range depends on whether the particle can be characterized as elongated or flattened, and the range is also limited by Brownian forces.

##### Assuntos

Análise Numérica Assistida por Computador , Pinças Ópticas , Simulação por Computador , Campos Eletromagnéticos , Movimento (Física) , Distribuição Normal , Rotação*Molecules ; 25(1)2019 Dec 24.*

##### RESUMO

We present a framework based on the atomistic continuum model, combining the Molecular Dynamics (MD) and Two Temperature Model (TTM) approaches, to characterize the growth of metal nanoparticles (NPs) under ultrashort laser ablation from a solid target in water ambient. The model is capable of addressing the kinetics of fast non-equilibrium laser-induced phase transition processes at atomic resolution, while in continuum it accounts for the effect of free carriers, playing a determinant role during short laser pulse interaction processes with metals. The results of our simulations clarify possible mechanisms, which can be responsible for the observed experimental data, including the presence of two populations of NPs, having a small (5-15 nm) and larger (tens of nm) mean size. The formed NPs are of importance for a variety of applications in energy, catalysis and healthcare.

##### Assuntos

Lasers , Nanopartículas Metálicas/química , Modelos Teóricos , Análise Numérica Assistida por Computador , Simulação por Computador , Condutividade Elétrica , Nanopartículas Metálicas/ultraestrutura , Tamanho da Partícula , Temperatura*PLoS One ; 14(11): e0225094, 2019.*

##### RESUMO

We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different frequencies. In this regime, the amplitude of the mean field undergoes low-frequency modulations, which may contribute to the mechanism of the emergence of slow oscillations of neural activity observed in spectral power of local field potentials or electroencephalographic signals at high frequencies. In addition to numerical simulations of such multi-clusters, we investigate the mechanisms of the observed phenomena using the simplest case of two clusters. In particular, we propose a phenomenological model which describes the dynamics of two clusters taking into account the adaptation of coupling weights. We also determine the set of plasticity functions (update rules), which lead to multi-clustering.

##### Assuntos

Modelos Neurológicos , Plasticidade Neuronal/fisiologia , Neurônios/fisiologia , Análise por Conglomerados , Análise Numérica Assistida por Computador*PLoS One ; 14(11): e0224994, 2019.*

##### RESUMO

Inlet unstart and buzz in scramjet engines must be prevented for the stable operation of the engines. In the present study, the characteristics of the inlet start, unstart and buzz phenomena in a scramjet engine inlet model are investigated using numerical analysis with the RANS-based OpenFOAM solver. The results for the inlet start case with a small computational domain that includes only the inlet-isolator part are in good agreement with existing numerical and experimental results. However, for the inlet unstart case, the computational domain must be wide enough to consider the interactions between the upstream of the inlet and the internal flow of the inlet to predict the inlet unstart and buzz phenomena in the inlet test model. The present results show fairly good agreement with existing experimental results with the buzz phenomenon. The effects of boundary layer profiles on the buzz oscillation frequency and amplitude are also addressed.

##### Assuntos

Análise Numérica Assistida por Computador , Pressão , Fatores de Tempo*Molecules ; 24(21)2019 Oct 31.*

##### RESUMO

In order to understand the impacts of dielectric barrier on the discharge characteristics of a nanosecond pulsed surface dielectric barrier discharge (NS-DBD), the effects of dielectric constant and dielectric barrier thickness are numerically investigated by using a three-equation drift-diffusion model with a 4-species 4-reaction air chemistry. When the dielectric constant increases, while the dielectric barrier thickness is fixed, the streamer propagation speed (V), the maximum streamer length (L), the discharge energy ( Q D _ e i ), and the gas heating ( Q G H ) of a pulse increase, but the plasma sheath thickness (h), the fast gas heating efficiency Î· , and the charge densities on the wall surface decrease. When the dielectric barrier thickness increases, while the dielectric constant is fixed, V, L, Q D _ e i , and Q G H of a pulse decrease, but h, Î· , and the charge densities on the wall surface increase. It can be concluded that the increase of the dielectric constant or the decrease of the dielectric barrier thickness results in the increase of the capacitance of the dielectric barrier, which enhances the discharge intensity. Increasing the dielectric constant and thinning the dielectric barrier layer improve the performance of the NS-DBD actuators.

##### Assuntos

Eletricidade , Nanopartículas/química , Análise Numérica Assistida por Computador , Simulação por Computador , Elétrons , Gases em Plasma/química , Eletricidade Estática , Propriedades de Superfície , Termodinâmica*PLoS One ; 14(10): e0222706, 2019.*

##### RESUMO

Exploration and exploitation are contradictory in differential evolution (DE) algorithm. In order to balance the search behavior between exploitation and exploration better, a novel self-adaptive dual-strategy differential evolution algorithm (SaDSDE) is proposed. Firstly, a dual-strategy mutation operator is presented based on the "DE/best/2" mutation operator with better global exploration ability and "DE/rand/2" mutation operator with stronger local exploitation ability. Secondly, the scaling factor self-adaption strategy is proposed in an individual-dependent and fitness-dependent way without extra parameters. Thirdly, the exploration ability control factor is introduced to adjust the global exploration ability dynamically in the evolution process. In order to verify and analyze the performance of SaDSDE, we compare SaDSDE with 7 state-of-art DE variants and 3 non-DE based algorithms by using 30 Benchmark test functions of 30-dimensions and 100-dimensions, respectively. The experiments results demonstrate that SaDSDE could improve global optimization performance remarkably. Moreover, the performance superiority of SaDSDE becomes more significant with the increase of the problems' dimension.

##### Assuntos

Algoritmos , Benchmarking , Análise Numérica Assistida por Computador , Probabilidade , Fatores de Tempo*Sensors (Basel) ; 19(20)2019 Oct 11.*

##### RESUMO

The use of metasurfaces operating in the terahertz regime as biosensor devices has attracted increased interest in recent years due to their enhanced sensitivity and more accurate detection capability. Typical designs are based on the replica of relatively simple unit cells, usually called metaatoms. In a previous paper, we proposed a new paradigm for ultrasensitive thin-film sensors based on complex unit cells, called generically metageometries or labyrinth metasurfaces. Here, we extend this concept towards biosensing, evaluating the performance of the labyrinth as a fungi detector. The sensing capabilities are numerically evaluated and a comparison with previous works in this field is performed, showing that metageometries improve the performance compared to metaatoms both in sensitivity and figure of merit, by a factor of more than four. In particular, we find that it is able to detect five fungi elements scattered on the unit cell, equivalent to a concentration of only 0.004/µm2.

##### Assuntos

Técnicas Biossensoriais/instrumentação , Análise Numérica Assistida por Computador , Eletricidade , Fungos/isolamento & purificação , Polipropilenos/química*Cardiovasc Eng Technol ; 10(4): 583-589, 2019 12.*

##### RESUMO

PURPOSE: In-stent restenosis (ISR) is related to local haemodynamics in the arteries after stent intervention. However, the haemodynamics of stents implanted into tapered vessels is rarely studied and remains unclear. This study aimed to study the haemodynamic performance of a stent in a tapered artery to reveal the haemodynamic differences between tapered and cylindrical stents after stent implantation and guide the stent selection for the treatment of coronary artery stenosis. METHODS: Cylindrical and tapered stents were implanted into the tapered arteries. A model of a cylindrical stent implanted into a cylindrical artery was established as the contrast model. Using the finite element method, the flow velocity and wall shear stress distribution of the three models were compared. RESULTS: At t1, t2, t3 and t4, the flow rate of the tapered artery with tapered stents (TT) after the implantation increased by 8.59, 3.80, 12.81 and 3.66%, respectively. In addition, the wall shear stress in the tapered arteries of TT was 23.48, 36.67, 13.00 and 8.06% higher than that of the tapered arteries with cylindrical stents (TC). CONCLUSIONS: The implantation of a tapered stent in the tapered artery can effectively improve intravascular haemodynamics. The tapered stent allows the tapered artery to obtain better haemodynamics and reduces the probability of ISR.

##### Assuntos

Simulação por Computador , Circulação Coronária , Estenose Coronária/terapia , Vasos Coronários/fisiopatologia , Hemodinâmica , Modelos Cardiovasculares , Intervenção Coronária Percutânea/instrumentação , Stents , Velocidade do Fluxo Sanguíneo , Reestenose Coronária/etiologia , Reestenose Coronária/fisiopatologia , Estenose Coronária/fisiopatologia , Análise de Elementos Finitos , Humanos , Análise Numérica Assistida por Computador , Intervenção Coronária Percutânea/efeitos adversos , Desenho de Prótese , Fatores de Risco , Estresse Mecânico*Cardiovasc Eng Technol ; 10(4): 553-567, 2019 12.*

##### RESUMO

PURPOSE: Patient-specific models of the heart can be used to improve the diagnosis of cardiac diseases, but practical application of these models can be impeded by the computational costs and numerical uncertainties of fitting mechanistic models to clinical measurements from individual patients. Reliable and efficient tuning of these models within clinically appropriate error bounds is a requirement for practical deployment in the time-constrained environment of the clinic. METHODS: We developed an optimization framework to tune parameters of patient-specific mechanistic models using routinely-acquired non-invasive patient data more efficiently than manual methods. We employ a hybrid particle swarm and pattern search optimization algorithm, but the framework can be readily adapted to use other optimization algorithms. RESULTS: We apply the proposed framework to tune full-cycle lumped parameter circulatory models using clinical data. We show that our framework can be easily adapted to optimize cross-species models by tuning the parameters of the same circulation model to four canine subjects. CONCLUSIONS: This work will facilitate the use of biomechanics and circulatory cardiac models in both clinical and research environments by ameliorating the tedious process of manually fitting the parameters.

##### Assuntos

Imagem de Tensor de Difusão , Insuficiência Cardíaca/diagnóstico por imagem , Hemodinâmica , Imagem Cinética por Ressonância Magnética , Modelos Cardiovasculares , Modelagem Computacional Específica para o Paciente , Função Ventricular Esquerda , Idoso , Algoritmos , Animais , Fenômenos Biomecânicos , Terapia de Ressincronização Cardíaca , Cães , Análise de Elementos Finitos , Insuficiência Cardíaca/fisiopatologia , Insuficiência Cardíaca/terapia , Humanos , Interpretação de Imagem Assistida por Computador , Masculino , Pessoa de Meia-Idade , Análise Numérica Assistida por Computador , Valor Preditivo dos Testes , Reprodutibilidade dos Testes , Especificidade da Espécie*Opt Express ; 27(14): 19369-19381, 2019 Jul 08.*

##### RESUMO

Photoacoustic endomicroscopy (PAEM) is capable of imaging fine structures in digestive tract. However, conventional PAEM employs a tightly focused laser beam to irradiate the object, which results in a limited depth-of-field (DOF). Here, we propose a scanning-domain synthesis of optical beams (SDSOB) to optimize both transverse resolution and the DOF by synthetic effective focused beams in scanning domain for the PAEM. By utilizing the SDSOB technique, multiple defocused and scattered beams are refocused to synthesize virtual focuses covering a large range of depth. A transverse point spread function that is 5.7-time sharper, and a transverse spatial bandwidth that is 8.5-time broader than those of the conventional PAEM were simulatively obtained through SDSOB-PAEM at the defocus distance of 2.4â mm. We validated the transverse resolution improvement at both in- and out-focus positions via phantom experiments of carbon fibers. In addition, in vivo rabbit experiments were conducted to acquire vascular images over radial depth range of 900 µm. And further morphological analysis revealed that the SDSOB images were acquired with abundant vascular branches and nodes, large total-length and small average-length of blood vessels, which indicated that the SDSOB-PAEM achieved high-resolution imaging in distinct rectal layers. All these results suggest that the SDSOB-PAEM possesses high transverse resolution and extended DOF, which demonstrates the SDSOB-PAEM can provide more accurate information for clinical assessment.

##### Assuntos

Microscopia , Fenômenos Ópticos , Técnicas Fotoacústicas/métodos , Animais , Simulação por Computador , Feminino , Análise Numérica Assistida por Computador , Imagens de Fantasmas , Coelhos*Comput Methods Biomech Biomed Engin ; 22(16): 1269-1281, 2019 Dec.*

##### RESUMO

Modeling tumor growth in biological systems is a challenging problem with important consequences for diagnosis and treatment of various forms of cancer. This growth process requires large simulation complexity due to evolving biological and chemical processes in living tissue and interactions of cellular and vascular constituents in living organisms. Herein, we describe with a phase-field model, namely the Cahn-Hilliard equation the intricate interactions between the tumors and their host tissue. The spatial discretization uses highly-continuous isogeometric elements. For fast simulation of the time-dependent Cahn-Hilliard equation, we employ an alternating directions implicit methodology. Thus, we reduce the original problems to Kronecker products of 1 D matrices that can be factorized in a linear computational cost. The implementation enables parallel multi-core simulations and shows good scalability on shared-memory multi-core machines. Combined with the high accuracy of isogeometric elements, our method shows high efficiency in solving the Cahn-Hilliard equation on tensor-product meshes.

##### Assuntos

Algoritmos , Modelos Biológicos , Proliferação de Células , Humanos , Neoplasias/patologia , Análise Numérica Assistida por Computador*Med Biol Eng Comput ; 57(10): 2159-2178, 2019 Oct.*

##### RESUMO

In finite element method (FEM) simulations of the mechanical response of bones, proper selection of stiffness versus density (E-ρ) formulae for bone constituents is necessary for obtaining accurate results. A considerable number of such formulae can be found in the biomechanics' literature covering both cortical and cancellous constituents. For determining the first and second modal frequencies (in both cranial-caudal and medial-lateral planes) of bovine tibia bone, this work assembled and numerically tested 22 isotropic and 21 orthotropic stiffness-density formulae combinations (cases). To accurately reproduce bone geometry, anatomical 3D models were generated from computed tomography (CT) scans. By matching the bone's digital mass to its actual mass, cortical and cancellous constituents were faithfully segmented by utilizing suitable values of three variables: (1) critical cutoff Hounsfield unit (HU) values, (2) cutoff density value, and (3) utilized number of sub-materials. Consequently, a balanced distribution of finite elements was generated with stiffness values congruent with their cancellous or cortical demarcations. Of the considered 22 isotropic formulae cases and 21 orthotropic (reduced to transversely isotropic) cases, only few yielded accurate frequency estimates. For verifying the accuracy of the solutions emanating from the various formulae, experimental vibration tests of corresponding mode frequencies and shapes (ProSig©) were conducted. When compared with the measured experimental frequency values, the most accurate isotropic formulae yielded numerical estimates of + 0.95% and + 10.65% for the first and second cranial-caudal (C-C) frequencies, respectively. The formulae yielding most accurate estimates also proved successful in estimating frequencies of a second tibia bone yielding numerical estimates within + 4.75% and + 1.88% of the said mode frequencies. For the transversely isotropic material assignment, the closest case scenario computed numerical estimates with a percentage difference of + 2.05% and + 9.36% for the first and second cranial-caudal (C-C) frequencies, respectively. Graphical abstract Mode shapes (left) 1 and (right) 2 for transversely isotropic case 15 T (Bone A): (a) cranial-caudal and (b) medial-lateral plane.

##### Assuntos

Tíbia/anatomia & histologia , Tíbia/fisiologia , Animais , Fenômenos Biomecânicos , Osso Esponjoso/anatomia & histologia , Osso Esponjoso/fisiologia , Bovinos , Osso Cortical/anatomia & histologia , Osso Cortical/fisiologia , Elasticidade , Análise de Elementos Finitos , Modelos Biológicos , Análise Numérica Assistida por Computador*Commun Biol ; 2: 311, 2019.*

##### RESUMO

During intraerythrocytic development, the human malaria parasite Plasmodium falciparum alters the mechanical deformability of its host cell. The underpinning biological processes involve gain in parasite mass, changes in the membrane protein compositions, reorganization of the cytoskeletons and its coupling to the plasma membrane, and formation of membrane protrusions, termed knobs. The hemoglobinopathies S and C are known to partially protect carriers from severe malaria, possibly through additional changes in the erythrocyte biomechanics, but a detailed quantification of cell mechanics is still missing. Here, we combined flicker spectroscopy and a mathematical model and demonstrated that knob formation strongly suppresses membrane fluctuations by increasing membrane-cytoskeleton coupling. We found that the confinement increased with hemoglobin S but decreases with hemoglobin C in spite of comparable knob densities and diameters. We further found that the membrane bending modulus strongly depends on the hemoglobinopathetic variant, suggesting increased amounts of irreversibly oxidized hemichromes bound to membranes.

##### Assuntos

Membrana Eritrocítica/parasitologia , Hemoglobina C/metabolismo , Hemoglobina Falciforme/metabolismo , Plasmodium falciparum/fisiologia , Fenômenos Biomecânicos , Simulação por Computador , Humanos , Mutação/genética , Análise Numérica Assistida por Computador*PLoS One ; 14(8): e0220840, 2019.*

##### RESUMO

In this paper we consider the process of the second harmonic generation in a gradient waveguide, taking into account diffraction and relatively weak temporal dispersion. Using the slowly varying envelope approximation and neglecting the dispersion of the nonlinear part of the response of the medium we obtain the system of parabolic equations for the envelopes of both harmonics. We also derive integrals of motion of this system. To solve it numerically we construct a nonlinear finite-difference scheme based on the Crank-Nicolson method preserving the integrals. Primarily, we focus our investigations on the processes of a two-component light bullets generation. We demonstrate that the generation of a coupled pair is possible in a planar waveguide even at normal group velocity dispersion.

##### Assuntos

Luz , Modelos Teóricos , Espalhamento de Radiação , Simulação por Computador , Análise Numérica Assistida por Computador*PLoS One ; 14(8): e0220994, 2019.*

##### RESUMO

Reaction-diffusion schemes are widely used to model and interpret phenomena in various fields. In that context, phenomena driven by Turing instabilities are particularly relevant to describe patterning in a number of biological processes. While the conditions that determine the appearance of Turing patterns and their wavelength can be easily obtained by a linear stability analysis, the estimation of pattern amplitudes requires cumbersome calculations due to non-linear terms. Here we introduce an expansion method that makes possible to obtain analytical, approximated, solutions of the pattern amplitudes. We check and illustrate the reliability of this methodology with results obtained from numerical simulations.