960 resultados para Non-constant coefficient diffusion equations


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This study aimed to carry out experimental work to determine, for Newtonian and non-Newtonian fluids, the friction factor (fc) with simultaneous heat transfer, at constant wall temperature as boundary condition, in fully developed laminar flow inside a vertical helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w). The non-Newtonian fluids were aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations of 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations of 0.1% and 0.2% (w/w). According to the rheological study done, the polymer solutions had shear-thinning behavior and different values of viscoelasticity. The helical coil used has an internal diameter, curvature ratio, length and pitch, respectively: 0.00483 m, 0.0263, 5.0 m and 11.34 mm. It was concluded that the friction factors, with simultaneous heat transfer, for Newtonian fluids can be calculated using expressions from literature for isothermal flows. The friction factors for CMC and XG solutions are similar to those for Newtonian fluids when the Dean number, based in a generalized Reynolds number, is less than 80. For Dean numbers higher than 80, the friction factors of the CMC solutions are lower those of the XG solutions and of the Newtonian fluids. In this range the friction factors decrease with the increase of the viscometric component of the solution and increase for increasing elastic component. The change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, is in accordance with the study of Ali [4]. There is a change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, which is in according to previous studies. The data also showed that the use of the bulk temperature or of the film temperature to calculate the physical properties of the fluid has a residual effect in the friction factor values.

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This study aimed to carry out experimental work to obtain, for Newtonian and non-Newtonian fluids, heat transfer coefficients, at constant wall temperature as boundary condition, in fully developed laminar flow inside a helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w) and the non-Newtonian fluids aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations 0.1%, 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations 0.1% and 0.2% (w/w). According to the rheological study performed, the polymer solutions had shear thinning behavior and different values of elasticity. The helical coil used has internal diameter, curvature ratio, length and pitch, respectively: 0.004575 m, 0.0263, 5.0 m and 11.34 mm. The Nusselt numbers for the CMC solutions are, on average, slightly higher than those for Newtonian fluids, for identical Prandtl and generalized Dean numbers. As outcome, the viscous component of the shear thinning polymer tends to potentiate the mixing effect of the Dean cells. The Nusselt numbers of the XG solutions are significant lower than those of the Newtonian solutions, for identical Prandtl and generalized Dean numbers. Therefore, the elastic component of the polymer tends to diminish the mixing effect of the Dean cells. A global correlation, for Nusselt number as a function of Péclet, generalized Dean and Weissenberg numbers for all Newtonian and non-Newtonian solutions studied, is presented.

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We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

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We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

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Applied Mathematical Modelling, Vol.33

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The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

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This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

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This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

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Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.

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RESMO: Introdução: A anemia de células falciformes doença hereditária, com repercussão multi-orgânica, tem grande variabilidade na sua expressão clínica. Daí o interesse do estudo de indicadores de prognóstico. A investigação realizada foi precedida de um resumo histórico incidindo sobre a compreensão de aspectos fundamentais da doença ao longo dos tempos. Na primeira parte do estudo e após revisão bibliográfica, foram referidos dados da fisiopatologia como base para os estudos que integram a presente dissertação. Abordou-se o estado da arte relativamente às complicações, aos indicadores de prognóstico e à terapêutica utilizada. Objectivos: Constituíram objectivos deste estudo realizado numa amostra populacional representativa: identificar as lesões a nível dos sistemas cardio-respiratório e nervoso central, avaliando-se as respectivas repercussões; avaliar a presença de indicadores de prognóstico entre as variáveis seleccionadas; estudar a eficácia e toxicidade da HU nos doentes com as formas graves da ACF. Para a prossecução destes objectivos foram delineados para além do estudo global três estudos específicos: Estudo 1- repercussão no sistema cardio-respiratório; Estudo 2- repercussão no sistema nervoso central; Estudo 3- terapêutica com hidroxiureia. Doentes e métodos: Procedeu-se a um estudo prospectivo e multi-institucional durante um período de três anos tendo-se seleccionado para a amostra, e de acordo com critérios pré-definidos, 30 doentes com ACF na fase estável da doença, com idades compreendidas entre os sete e os 18 anos, todos de origem africana à excepção de um caucasiano. O diagnóstico baseou-se em técnicas de electroforese e estudo molecular que definiu o genotipo da doença e a presença da delecção da -talassémia assim como os haplotipos da amostra populacional. Foram utilizadas diferentes metodologias para avaliar a existência de lesão pulmonar e cerebral. Através do estudo estatístico foram seleccionadas diversas variáveis como hipotéticos indicadores de prognóstico. Estudo 1. Para determinar a existência de lesão a nível pulmonar usaram-se duas metodologias diferentes, a avaliação da função pulmonar com estudo da saturação da Hb em O2 no sangue arterial e a tomografia computadorizada de alta resolução. Estudou-se também a possível disfunção cardíaca como repercussão da lesão pulmonar, através do ecocardiograma, e os indicadores de prognóstico com significado estatístico para a lesão encontrada. Estudo 2. O desenho deste estudo foi sobreponível ao anterior, mas com metodologia adequada para o SNC. Procedeu-se ao estudo das lesões cerebrais por meio de exames imagiológicos, (RMN-CE e DTC) e de testes psicológicos. Correlacionaram-se as três metodologias utilizadas e a importância de cada uma para a decisão de atitudes terapêuticas preventivas. Estudo 3. Consistiu num estudo aberto prospectivo não controlado com nove crianças e adolescentes com formas graves de ACF, com o objectivo de avaliar a eficácia da terapêutica com hidroxiureia, durante um período de 24 meses. Todos os doentes completaram no mínimo 15 meses de terapêutica, com uma dose final média de 194 mg/K/dia. Resultados globais: Durante o período anterior à investigação caracterizou-se a amostra populacional estudada quanto ao fenotipo genético, clínico e hematológico de acordo com os critérios utilizados por outros investigadores. Verificou-se: predomínio do haplotipo Bantu na forma homozigótica em 53% dos doentes; número total de EVO ≥3/ano em 87,5% dos doentes; crises de sequestração em 18,75%; dactilites no primeiro ano de vida em 31,2%; quadro de sépsis grave apenas num doente; crises de hiper-hemólise em 50%; e STA em 59,38% dos doentes. Quanto ao fenotipo hematológico evidenciaram-se como factores de risco reticulocitose (13,1x103/l) e hiperbilirrubinémia (2,5 mg/dl) e como factores de bom prognóstico a presença de delecção de um gene da -talassémia em 46,9% dos doentes e valor médio de Hb 8,1 g/dl. Resultados dos estudos parcelares: Estudo 1. Deste estudo infere-se que a DPR ligeira foi diagnosticada em 70% dos doentes, uma vez que as alterações da difusão não foram estatisticamente significativas, o estudo dos gases no sangue não evidenciaram resultados anormais e a TCAR evidenciou alterações em 43,3% dos doentes. Apenas num doente se verificou doença pulmonar obstrutiva relacionada com maior número da STA.O estudo da disfunção cardíaca encontrada em 86,7% dos doentes não reflecte a repercussão da DPR a nível cardíaco, podendo estar associada às alterações fisiopatológicas da própria anemia crónica. Encontraram-se indicadores de prognóstico hematológicos e clínicos. Entre os primeiros, valores de Hb ≥8,5 g/dl e de HbF ≥13% foram considerados indicadores de bom prognóstico para a lesão pulmonar. Em relação aos parâmetros clínicos, as STA não foram consideradas indicadoras de prognóstico para a DPR ao contrário do que se verificou com o número de EVO. Pela análise dos parâmetros genéticos e socio-económicos provou-se a ausência de relação estatisticamente significativa com lesão pulmonar. Estudo 2. Pela RMN-CE foram diagnosticados ES em 33,3% com uma localização preferencial na substância branca profunda em 26,6% dos doentes. Relativamente aos parâmetros hematológicos seleccionados, o valor médio da HbF 8,6% constituíu um indicador de bom prognóstico para o aparecimento de ES, enquanto o valor médio de leucócitos 12.39x103/μl foi considerado um indicador de mau prognóstico. No estudo do DTC apenas um doente apresentou aumento da velocidade do fluxo cerebral na ACM igual a 196 cm/segundos, associado a vasculopatia grave. Os testes psicológicos alterados em 80% dos doentes mostraram ser o método mais sensível para detectar alterações do neurodesenvolvimento, mas sem correlação com os ES em 10% dos doentes. Realça-se a baixa percentagem de DTC patológicos encontrados neste estudo em relação ao número elevado de ES e de testes psicológicos alterados, não se verificando concordância entre os três exames. Dos indicadores de prognóstico estudados a -talassémia foi considerada um factor de protecção para o coeficiente de inteligência da escala de Wechsler. Em relação a parâmetros clínicos estudados os doentes com maior número de EVO, tem em média valores inferiores nos testes psicológicos. Estudo 3. Neste estudo verificou-se que o valor médio da HbF aumentou significativamente de 7,0±4% para 13,7±5,3% (p=0,028) ao fim de 15 meses de terapêutica com hidroxiureia. Clinicamente todos os doentes responderam significativamente com uma redução de 80% no número de EVO, 69% no número de internamentos, 76% no número de dias de hospitalização e 67% no número de transfusões. Deste modo comprovou-se não só a eficácia desta terapêutica neste grupo pediátrico como também a falta de efeitos secundários significativos. Considera-se a necessidade de estudos mais prolongados e em grande séries, para com segurança se usar a HU antes que a lesão orgânica se estabeleça, portanto logo nos primeiros anos de vida. Conclusão: Na amostra populacional estudada foram evidenciadas lesões pulmonares e cerebrais na grande maioria dos doentes que condicionaram a sua qualidade de vida. Foram identificados indicadores de prognóstico que poderão eventualmente ditar medidas terapêuticas precoces com o objectivo de diminuir a morbilidade e a mortalidade neste grupo etário. Demonstrou-se que a terapêutica com a HU foi eficaz e bem tolerada----------ABSTRACT: Background: Sickle cell anemia (SCA), a hereditary disease characterized by pain and lifetime multi-organic lesion, is a challenge for all that work with carriers of this disease. The clinical expression variability of SCA is a constant reality and a problem to be solved in the current world of investigation, for which the knowledge of prognostic indicators responsible for the different aspects of clinical evolution diversity wiil be an added value. The study is preceded by a historical summary of the most important factors in the evolution of SCA, which are in themselves, an incentive for future research. In the first part of the study, after an extensive bibliographical revision, physiopathology data is referred to in general and specifically regarding the target organs, that constituted the base for the studies presented in the dissertation. The state of the art for the complications to be studied, the choice of prognostic indicators and the therapeutics application, were approached for the renewed interest in the theme. Aims: In regard to the investigation, the objective was to study the lesions in the most affected organs of a chosen pediatric group, to investigate prognostic indicators for lung and cerebral lesions and to evaluate the protective effect of hydroxyurea in children with severe outcomes. Patients and methods: A prospective and multi-institutional study was carried out during a three-year period, February 1998 to March 2001, with children and adolescents followed up at a Immunohematology Outpatient Clinic of Dona Estefânia's Hospital, Lisbon. Based in predefined criteria, 30 children with SCA were selected in a stable phase of the disease, aged from seven to 18 years old, all of whom were of African origin with exception of one who was Caucasian. The diagnosis was based on electrophoresis techniques and molecular study that allowed to define the genotype, the presence of deletional alpha-thalassemia as well as haplotypes in the population. Different methodologies were used to evaluate the existence of lung and cerebral lesion. Statistical study of the different variables selected the prognostic indicators. In Study 1, to determine the existence of lung lesion two different methodologies were used: pulmonar function study with arterial blood gases determination; and high resolution computerized tomography. Heart dysfunction as a repercussion of lung lesion was also studied through echocardiography, and prognostic indicators were statistically significant for lesions found. The design of Study 2 was similar to Study 1, but with the appropriate methodology for CNS. After neurological examination, which was normal in all patients (control group), cerebral lesions were studied with imagiologic exams (MRN-CE and TCD) and psychological tests. These three methodologies were correlated and the importance of each one in the decision of the therapeutic profilactic attitudes. Study 3 consisted of a controlled prospective open study in children with severe forms of SCA, with the aim of the evaluating therapeutic effectiveness of hydroxyurea, during a period of 24 months. Results: In the global overall study preceding the Studies 1,2 and 3, there were a prevalence of haplotype Bantu (53%) and other risk factors, namely the number of VOC (87,5%), sequestration crisis (18,75%), dactilytis in first year of life(31,2%), hyperhemolysis crisis (50%) and ATC in more than half of the patients (59,38%). This group of bad prognostic indicators, associated with the population of the lower class according to the Graffar scale, demonstrates the importance of primary health care services, information provided to the children and their relatives, as well as the interest in prophylactic therapeutics, specific screening and prenatal diagnosis. Study 1. It was evident from this study that slight RPD was diagnosed in 70% of the patients, because alterations of the diffusion had no statistical significance and arterial blood gases determinations were normal. Only one patient had restrictive lung disease related with numerous ACS. However ACS was not considered a prognostic indicator for RPD, contrary to the number of EVO. HRTC revealed discreet fibrotic lines that could be related with slight RPD, but the lack of correlation of these two exams (33%) supports the value of lung function tests for precocious diagnosis of RPD. Heart dysfunction was found in 86,7% of patients, does not reflect the repercussion of RPD, but with the physiopathology of chronic anemia. Hematologic and clinical prognostic indicators were found. Good prognostic indicators for the non-evolution of RPD with average Hb values of ≥ 8,5 g/dl and average HbF values of ≥13%, respectively. The genetic and social-economic factors had no statistical significance; nevertheless, they were more prevalent among Bantu haplotype (53,3%) in patients with RPD. Study 2. RMN-CE detected SI in 33,3% of the patients, with preferential location in deep white substance in 26,6% and in front lobe in 20%. This distribution can be related to structural aspects of the brain and with the high sensibility of this organ to hypoxia. From the hematological parameters selected, average HbF value 8,6% and average leucocyte count 12.39x103/μl were prognostic indicators with different meaning to SI. The increase in the total bilirubin related to hyperhemolysis clinically explains the genesis of SI In the TCD study, only one patient had increased cerebral flow speed >196 cm/sec in CMA, which corresponded to serious vasculopathy in AngioMR. This patient never present previously neurological symptoms and had several hyperhemolysis crisis and VOC as risk factors. Low percentage of pathological TCD in this study, in relation to the high number of SI and altered tests, although without correlation among the three exams, is probably attributed to factors related to the methodology, aspects of cerebral physiopathology or perhaps a sign of good prognostic if the duration of study had not been so short. TCD should be used as a screening method in the age groups with higher risk of AVC and should never be considered separately in prophylactic therapeutics indication. Psychological tests were the most sensitive method to detect neurodevelopment impairment; in 80% of patients the neuropsychologics tests were altered, but without correlation with SI (10%). Since SI can become evident during the first two years of life and develop with time, the first psychological tests should be carried out between 3 and 5 years of age to timely be referred to special education and stimulation programs. Prognostic indicators to psychological tests were also found: alpha-thalassemia was found to be a protection factor of the IQ, just as other hematologic factors (hematocrit, MGCV and erythrocytes count). In relation to clinical parameters, although without statistical significance, patients with larger number of VOC had average lower scores versus the average in tests, except in TP. Results from different studies were conclusive as to the type of lesion found and the importance of prognostic indicators. Study 3. All the patients completed a minimum of 15 months therapeutic treatment with the final average daily dose of 19±4 mg/kg/day. The average value of the fetal hemoglobin increased significantly from 7,0±3,9% to 13,7±5,3% (p=0.028). The HbF average values increased from 6% to 15% after 15 months of therapeutic treatment. Clinically there was a reduction of 80% in the number of VOE , 69% in the number of hospitalization, 76% in the number of days of hospitalization and 67% in the number of transfusions. Once again the effectiveness of this treatment in this pediatric group, as well as the lack of any significant secondary effects, was evident. The study confirms the need for further detailed research in order to safely effect the appropriate treatment prior to the development of organic lesions, which ideally should be in the first year of life. Conclusions: These results allow us to clarify the importance of either pulmonary lesions or either nervous central system impairment among patients, children and adolescents, with sickle cell anemia. These lesions were demonstrated in most of the patients studied compromising their quality of life and the mortality. The treatment with HU is proved to be effective and having low toxicity.

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A new method for the study and optimization of manu«ipulator trajectories is developed. The novel feature resides on the modeling formulation. Standard system desciptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyze. Moreover, the derived algorithms are suited to "deterministic" tasks, such as those appearing in a repetitivework, and are not well adapted to a "random" operation that occurs in intelligent systems interacting with a non-structured and changing environment. These facts motivate the development of alternative models based on distinct concepts. The proposed embedding of statistics and Fourier trasnform gives a new perspective towards the calculation and optimization of the robot trajectories in manipulating tasks.

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Part of the optical clearing study in biological tissues concerns the determination of the diffusion characteristics of water and optical clearing agents in the subject tissue. Such information is sufficient to characterize the time dependence of the optical clearing mechanisms—tissue dehydration and refractive index (RI) matching. We have used a simple method based on collimated optical transmittance measurements made from muscle samples under treatment with aqueous solutions containing different concentrations of ethylene glycol (EG), to determine the diffusion time values of water and EG in skeletal muscle. By representing the estimated mean diffusion time values from each treatment as a function of agent concentration in solution, we could identify the real diffusion times for water and agent. These values allowed for the calculation of the correspondent diffusion coefficients for those fluids. With these results, we have demonstrated that the dehydration mechanism is the one that dominates optical clearing in the first minute of treatment, while the RI matching takes over the optical clearing operations after that and remains for a longer time of treatment up to about 10 min, as we could see for EG and thin tissue samples of 0.5 mm.

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The study of agent diffusion in biological tissues is very important to understand and characterize the optical clearing effects and mechanisms involved: tissue dehydration and refractive index matching. From measurements made to study the optical clearing, it is obvious that light scattering is reduced and that the optical properties of the tissue are controlled in the process. On the other hand, optical measurements do not allow direct determination of the diffusion properties of the agent in the tissue and some calculations are necessary to estimate those properties. This fact is imposed by the occurrence of two fluxes at optical clearing: water typically directed out of and agent directed into the tissue. When the water content in the immersion solution is approximately the same as the free water content of the tissue, a balance is established for water and the agent flux dominates. To prove this concept experimentally, we have measured the collimated transmittance of skeletal muscle samples under treatment with aqueous solutions containing different concentrations of glucose. After estimating the mean diffusion time values for each of the treatments we have represented those values as a function of glucose concentration in solution. Such a representation presents a maximum diffusion time for a water content in solution equal to the tissue free water content. Such a maximum represents the real diffusion time of glucose in the muscle and with this value we could calculate the corresponding diffusion coefficient.

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The causative agent of cholera, Vibrio cholerae, can enter into a viable but non-culturable (VBNC) state in response to unfavorable conditions. The aim of this study was to evaluate the in situ survival of V. cholerae in an aquatic environment of the Southern Caribbean Sea, and its induction and resuscitation from the VBNC state. V. cholerae non-O1, non-O139 was inoculated into diffusion chambers placed at the Cuare Wildlife Refuge, Venezuela, and monitored for plate, total and viable cells counts. At 119 days of exposure to the environment, the colony count was < 10 CFU/mL and a portion of the bacterial population entered the VBNC state. Additionally, the viability decreased two orders of magnitude and morphological changes occurred from rod to coccoid cells. Among the aquatic environmental variables, the salinity had negative correlation with the colony counts in the dry season. Resuscitation studies showed significant recovery of cell cultivability with spent media addition (p < 0.05). These results suggest that V. cholerae can persist in the VBNC state in this Caribbean environment and revert to a cultivable form under favorable conditions. The VBNC state might represent a critical step in cholera transmission in susceptible areas.

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Tese apresentada como requisito parcial para obtenção do grau de Doutor em Gestão de Informação