Bernoulli's Method Research Articles

Simplified Bernoulli's method significantly underestimates pulmonary transvalvular pressure drop

PurposeTo determine whether neglecting the flow unsteadiness in simplified Bernoulli's equation significantly affects the pulmonary transvalvular pressure drop estimation.Materials and Methods3.0T magnetic resonance imaging (MRI) 4D velocity mapping was performed on four healthy volunteers, seven patients with repaired tetralogy of Fallot, and thirteen patients with transposition of the great arteries repaired by arterial switch. Pulmonary transvalvular pressure drop was estimated based on two methods: General Bernoulli's Equation (GBE), ie, the most complete form; and Simplified Bernoulli's Equation (SBE), known as 4V2. More than 2300 individual pressure drop measurements were used to compare the simplified and the general Bernoulli's methods. A linear mixed‐effects model was employed for statistical analyses, fully accounting for clustering of observations among the methods and systolic phases.ResultsThe simplified Bernoulli's method systematically underestimated the pressure drop compared to general Bernoulli's method during the entire systolic phase (P < 0.05), including the peak systole, where on average .ConclusionThe simplified Bernoulli method underestimated the pressure drop during all systolic phases in all the studied subjects. Therefore, it is necessary to take into account the flow unsteadiness for more accurate estimation of the pressure drop. J. Magn. Reson. Imaging 2016;43:1313–1319.

Solitary Solutions for some Nonlinear Evolution Equations using Bernoulli Method

Solitary Solutions for some Nonlinear Evolution Equations using Bernoulli Method

Ion acoustic shock and solitary waves in highly relativistic plasmas with nonextensive electrons and positrons

The Korteweg-de Vries Burgers (KdVB)-like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.

Simplified Bernoulli's method significantly underestimates pulmonary transvalvular pressure drop

To determine whether neglecting the flow unsteadiness in simplified Bernoulli's equation significantly affects the pulmonary transvalvular pressure drop estimation. 3.0T magnetic resonance imaging (MRI) 4D velocity mapping was performed on four healthy volunteers, seven patients with repaired tetralogy of Fallot, and thirteen patients with transposition of the great arteries repaired by arterial switch. Pulmonary transvalvular pressure drop was estimated based on two methods: General Bernoulli's Equation (GBE), ie, the most complete form; and Simplified Bernoulli's Equation (SBE), known as 4V(2) . More than 2300 individual pressure drop measurements were used to compare the simplified and the general Bernoulli's methods. A linear mixed-effects model was employed for statistical analyses, fully accounting for clustering of observations among the methods and systolic phases. The simplified Bernoulli's method systematically underestimated the pressure drop compared to general Bernoulli's method during the entire systolic phase (P < 0.05), including the peak systole, where on average ΔpSBE/ΔpGBE=78%. The simplified Bernoulli method underestimated the pressure drop during all systolic phases in all the studied subjects. Therefore, it is necessary to take into account the flow unsteadiness for more accurate estimation of the pressure drop. J. Magn. Reson. Imaging 2016;43:1313-1319.

Spatiotemporal clusters of malaria cases at village level, northwest Ethiopia.

BackgroundMalaria attacks are not evenly distributed in space and time. In highland areas with low endemicity, malaria transmission is highly variable and malaria acquisition risk for individuals is unevenly distributed even within a neighbourhood. Characterizing the spatiotemporal distribution of malaria cases in high-altitude villages is necessary to prioritize the risk areas and facilitate interventions.MethodsSpatial scan statistics using the Bernoulli method were employed to identify spatial and temporal clusters of malaria in high-altitude villages. Daily malaria data were collected, using a passive surveillance system, from patients visiting local health facilities. Georeference data were collected at villages using hand-held global positioning system devices and linked to patient data. Bernoulli model using Bayesian approaches and Marcov Chain Monte Carlo (MCMC) methods were used to identify the effects of factors on spatial clusters of malaria cases. The deviance information criterion (DIC) was used to assess the goodness-of-fit of the different models. The smaller the DIC, the better the model fit.ResultsMalaria cases were clustered in both space and time in high-altitude villages. Spatial scan statistics identified a total of 56 spatial clusters of malaria in high-altitude villages. Of these, 39 were the most likely clusters (LLR = 15.62, p < 0.00001) and 17 were secondary clusters (LLR = 7.05, p < 0.03). The significant most likely temporal malaria clusters were detected between August and December (LLR = 17.87, p < 0.001). Travel away home, males and age above 15 years had statistically significant effect on malaria clusters at high-altitude villages.ConclusionThe study identified spatial clusters of malaria cases occurring at high elevation villages within the district. A patient who travelled away from home to a malaria-endemic area might be the most probable source of malaria infection in a high-altitude village. Malaria interventions in high altitude villages should address factors associated with malaria clustering.

Risk analysis for occurrences of schistosomiasis in the coastal area of Porto de Galinhas, Pernambuco, Brazil

BackgroundManson’s schistosomiasis continues to be a severe public health problem in Brazil, where thousands of people live under the risk of contracting this parasitosis. In the Northeast of Brazil, schistosomiasis has expanded from rural areas to the coast of Pernambuco State, where the intermediate host is Biomphalaria glabrata snails. This study aims at presenting situational analyses on schistosomiasis at the coastal locality of Porto de Galinhas, Pernambuco, Brazil, by determining the risk factors relating to its occurrence from the epidemiological and spatial perspectives.MethodsIn order to gather prevalence data, a parasitological census surveys were conducted in 2010 in the light of the Kato-Katz technique. Furthermore, malacological surveys were also conducted in the same years so as to define the density and infection rates of the intermediate host. Lastly, socioeconomic-behavioral survey was also conducted to determine the odds ratio for infection by Schistosoma mansoni. Based on these data, spatial analyses were done, resulting in maps of the risk of disease transmission. To predict the risk of schistosomiasis occurrence, a multivariate logistic regression was performed using R 2.13 software.ResultsBased on prevalence, malacological and socioeconomic-behavioural surveys, it was identified a prevalence of 15.7% in the investigated population (2,757 individuals). Due to the malacological survey, 36 breeding sites were identified, of which 11 were classified as foci of schistosomiasis transmission since they pointed out snails which were infected by Schistosoma mansoni. Overall, 11,012 snails (Biomphalaria glabrata) were collected. The multivariate regression model identified six explanatory variables of environmental, socioeconomic and demographic nature. Spatial sweep analysis by means of the Bernoulli method identified one statistically significant cluster in Salinas (RR = 2.2; p-value < 0.000), the district with the highest occurrence of cases.ConclusionsBased on the resulting information from this study, the epidemiological dimensions of this disease are significant and severe, within the scenario of schistosomiasis in Pernambuco state. The risk factors which were identified in the predictive model made it clear that the environmental and social conditions influence on the schistosomiasis occurrences.

Algorithms for quaternion polynomial root-finding

In 1941 Niven pioneered root-finding for a quaternion polynomial P(x), proving the fundamental theorem of algebra (FTA) and proposing an algorithm, practical if the norm and trace of a solution are known. We present novel results on theory, algorithms and applications of quaternion root-finding. Firstly, we give a new proof of the FTA resulting in explicit formulas for both exact and approximate quaternion roots of P(x) in terms of exact and approximate complex roots of the real polynomial F(x)=P(x)P¯(x), where P¯(x) is the conjugate polynomial. In particular, if |F(c)|≤ϵ, then for a computable quaternion conjugate q of c, |P(q)|≤ϵ. Consequences of these include relevance of root-finding methods for complex polynomials, computation of bounds on zeros, and algebraic solution of special quaternion equations. Secondly, working directly in the quaternion space, we develop Newton and Halley methods and analyze their local behavior. Surprisingly, even for a quadratic quaternion polynomial Newton’s method may not converge locally. Finally, we derive an analogue of the Bernoulli method in the quaternion space for computing the dominant root in certain cases. This requires the development of an independent theory for the solution of quaternion homogeneous linear recurrence relations. These results also lay a foundation for quaternion polynomiography.

Study of the tip mass and interaction force effects on the frequency response and mode shapes of the AFM cantilever

The vibrational characteristics of an atomic force microscope (AFM) cantilever beam play a key role in dynamic mode of the atomic force microscope. As the oscillating AFM cantilever tip approaches the sample, the tip–sample interaction force influences the cantilever dynamics. In this paper, we present a detailed theoretical analysis of the frequency response and mode shape behavior of a cantilever beam in the dynamic mode subject to changes in the tip mass and the interaction regime between the AFM cantilever system and the sample. We consider a distributed parameter model for AFM and use Euler–Bernoulli method to derive an expression for AFM characteristics equation contains tip mass and interaction force terms. We study the frequency response of AFM cantilever under variations of interaction force between AFM tip and sample. Also, we investigate the effect of tip mass on the frequency response and also the quality factor and spring constant of each eigenmodes of AFM micro-cantilever. In addition, the mode shape analysis of AFM cantilever under variations of tip mass and interaction force is investigated. This will incorporate the presentation of explicit analytical expressions and numerical analysis. The results show that by considering the tip mass, the resonance frequencies of the cantilever are decreased. Also, the tip mass has a significant effect on the mode shape of the higher eigenmodes of the AFM cantilever. Moreover, tip mass affects the quality factor and spring constant of each modes.

Equivalence Scale in Terms of Polish Households' Source of Income

Equivalence Scale in Terms of Polish Households' Source of Income The paper presents a comparison of the costs of Polish households by their main source of income. In order to compare these costs the author estimated three kinds of equivalence scales using the Engel method, ELES (Extended Linear Expenditure System), the demand equation and the Bernoulli well-being function. Estimation for household groups determined on account of the main source of income produced by the scales confirmed differences in households' maintenance costs compared to the costs of the reference household. A comparison of the values of equivalence scales revealed a similarity of the results produced by the ELES and the Bernoulli methods which differed from the results obtained by means of the Engel method.

Reliable root detection with the qd-algorithm: When Bernoulli, Hadamard and Rutishauser cooperate

When using Rutishauser's qd-algorithm for the determination of the roots of a polynomial (originally the poles of a meromorphic function), or for related problems, conditions have been formulated for the interpretation of the computed q- and e-values. For a correct interpretation, the so-called critical indices play a crucial role. They index a column of e-values that tends to zero because of a jump in modulus among the poles. For more than 50 years the qd-algorithm in exact arithmetic was considered to be fully understood. In this presentation we push the detailed theoretical investigation of the qd-algorithm even further and we present a new aspect that seems to have been overlooked. We indicate a new element that makes a column of e-values tend to zero, namely a jump in multiplicity among equidistant poles. This result is obtained by combining the qd-algorithm with a deflation technique, and hence mainly relying on Bernoulli's method and Hadamard's formally orthogonal polynomials. Our results round up the theoretical analysis of the qd-algorithm as formulated in its original form, and are of importance in a variety of practical applications as outlined in the introduction.

Comparison of Poisson and Bernoulli spatial cluster analyses of pediatric injuries in a fire district

BackgroundWith limited resources available, injury prevention efforts need to be targeted both geographically and to specific populations. As part of a pediatric injury prevention project, data was obtained on all pediatric medical and injury incidents in a fire district to evaluate geographical clustering of pediatric injuries. This will be the first step in attempting to prevent these injuries with specific interventions depending on locations and mechanisms.ResultsThere were a total of 4803 incidents involving patients less than 15 years of age that the fire district responded to during 2001–2005 of which 1997 were categorized as injuries and 2806 as medical calls. The two cohorts (injured versus medical) differed in age distribution (7.7 ± 4.4 years versus 5.4 ± 4.8 years, p < 0.001) and location type of incident (school or church 12% versus 15%, multifamily residence 22% versus 13%, single family residence 51% versus 28%, sport, park or recreational facility 3% versus 8%, public building 8% versus 7%, and street or road 3% versus 30%, respectively, p < 0.001). Using the medical incident locations as controls, there was no significant clustering for environmental or assault injuries using the Bernoulli method while there were four significant clusters for all injury mechanisms combined, 13 clusters for motor vehicle collisions, one for falls, and two for pedestrian or bicycle injuries. Using the Poisson cluster method on incidence rates by census tract identified four clusters for all injuries, three for motor vehicle collisions, four for fall injuries, and one each for environmental and assault injuries. The two detection methods shared a minority of overlapping geographical clusters.ConclusionSignificant clustering occurs overall for all injury mechanisms combined and for each mechanism depending on the cluster detection method used. There was some overlap in geographic clusters identified by both methods. The Bernoulli method allows more focused cluster mapping and evaluation since it directly uses location data. Once clusters are found, interventions can be targeted to specific geographic locations, location types, ages of victims, and mechanisms of injury.

SPATIAL DISTRIBUTION OF COARCTATION OF THE AORTA MAPS TO LAND USE AS CROPLAND

Introduction Left heart obstructions [LHO] including coarctation of the aorta [CoAo], aortic stenosis [AS] and hypoplastic left heart [HLH] are thought to share genetic potential. Family history of congenital cardiovascular malformations [CCVM] is more common in the LHO group than in CCVM as a whole. Methods In using a case control series of congenital cardiovascular malformations and population-based controls, we analyzed spatial distribution of CoAo in infants diagnosed before one year of age. Statistical analysis included spatial distribution and extensive personal sociodemographic, occupational exposures, and life style exposure factors as well as family history of cardiac or other malformations. Cases and controls were mapped in the State of Maryland and the District of Columbia in the United States, including the years 1981 through 1989. Results 102 cases of coarctation of the aorta and 1990 controls were included in the analysis. Spatial scanning by Bernoulli method demonstrated five clusters of cases of CoAo containing a total of 33 cases. The largest cluster contains 20 cases and is significantly distributed compared to controls with #61539;229.5882, p. 000 and odds ratio of 3.9. For all cases of coarctation, clustered or not, case status is associated in a multiple regression model with family history of cardiac malformations, family history of other malformations, father's occupational or leisure exposure to solder; or mother's occupational or leisure exposure to solvents. When the largest cluster of CoAo cases is analyzed however, its characteristics are association with cropland, odds ratio 8.91, 95% confidence intervals 2.6 to 30.8, and with maternal exposure to solvents, odds ratio 12.9 with 95% confidence intervals .0.98 to 171.0. If all clusters are considered together, the combined area is associated with cropland with similar odds. If the region of the clustered coarctation cases is analyzed for association using the larger control population, the cluster is associated with orchards, cropland, and race. In analyses by racial groups, the association with cropland persists. The clusters of coarctation of the aorta are geographically distinct from clusters identified of aortic stenosis. Conclusion We conclude that clusters of coarctation of the aorta are present in population-based studies of Maryland and the District of Columbia. These clusters are characterized by land use as orchards or cropland. The largest cluster is in a region of the state where tobacco and soybeans are the primary crops in contrast to the regions of the state in which aortic stenosis is clustered where corn, soybeans and hay are grown. Possible exposure to environmental chemicals may be important to gene environment interactions that are causal for congenital cardiovascular malformations.

LASE measurements of aerosol and water vapor profiles during TARFOX

The Lidar Atmospheric Sensing Experiment (LASE) was operated autonomously from the NASA high‐altitude ER‐2 aircraft on nine flights during July 10–26, 1996, as part of the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). LASE measured high‐resolution profiles of water vapor and aerosols in regions of urban haze plumes over the U.S. eastern seaboard. Real‐time LASE aerosol measurements were used to guide the in situ aircraft to sample haze layers. In this paper the vertical and horizontal distributions of aerosol backscatter measured by LASE are presented along with the temporal evolution of the haze layers. The aerosol backscatter data also identify the presence of gradients in the aerosol plumes, the presence of low‐altitude clouds, and optically thin cirrus. This information is useful for many of the radiometeric observations made during TARFOX and can help explain observational differences among ground, airborne, and satellite observations. An iterative procedure is discussed which was used to invert lidar data to retrieve aerosol scattering ratios, extinction, and total optical depths from the LASE measurements. The sensitivity of these retrievals to assumed parameters is discussed and the results of retrievals are also compared to the well‐known Bernoulli method. LASE water vapor measurements were made across the entire troposphere using a three “line pair” method to cover the range of water vapor mixing ratio from &lt; 0.01 g/kg near the tropopause to ∼ 20 g/kg near the surface in a single aircraft pass over the experiment region. These measurements also show two‐dimensional distributions of large spatial gradients in water vapor in the lower and upper troposphere. These observations are useful in the calculation of IR radiation fields and relative humidity fields, since relative humidity has a strong influence on the growth of aerosols and their scattering properties. Water vapor profiles, aerosol scattering ratios, aerosol extinction coefficients and aerosol optical depths were derived using the methodology presented in this paper from LASE measurements during TARFOX. These measurements are compared with other in situ and remote measurements during TARFOX in the companion papers [Ferrare et al., this issue (a, b)]

P-Vector inverse method evaluated using the modular ocean model (MOM)

Several major inverse methods (Stommel-Schott method, Wunsch method, and Bernoulli method) have been successfully developed to quantitatively estimate the geostrophic velocity at the reference level from hydrographic data. No matter the different appearance, they are based on the same dynamical sophistication: geostrophy, hydrostatic, and potential density (ρ) conservation (Davis, 1978). The current inverse methods are all based on two conservation principles: potential density and potential vorticity ( q = f∂ρ/ ∂z) and require β-turning. Thus, two necessary conditions can be incorporated into any inverse methods: (1) non-coincidence of potential density and potential vorticity surfaces and (2) existence of vertical turning of the velocity ( β-turning.) This can be done using the P-Vector, a unit vector in the direction of ∇ ρ × ∇ q (Chu, 1994, 1995). The first necessary condition becomes the existence of the P-vector, and the second necessary condition leads to the existence of the P-vector turning in the water column. Along this line, we developed the P-vector inverse method with a pre-requirement check-up. The method was verified in this study using the Modular Ocean Model (MOM) from Pacanowski et al. (1991) version of Bryan-Cox-Semtner ocean general circulation model (OGCM), which is based on the work of Bryan (1969). The statistically steady solutions of temperature and salinity from MOM are used as a “no-error data” set for computing absolute geostrophic velocities by the P-vector inverse method. Circulations are similar between the MOM statistically steady solutions and the P-vector solutions. Furthermore, the quantitative analysis shows that this inverse method has capability of picking up the major signal of the velocity field.

The resolution of the gibbs phenomenon for “spliced” functions in one and two dimensions

In this paper we study approximation methods for analytic functions that have been “spliced” into nonintersecting subdomains. We assume that we are given the first 2 N + 1 Fourier coefficients for the functions in each subdomain. The objective is to approximate the “spliced” function in each subdomain and then to “glue” the approximations together in order to recover the original function in the full domain. The Fourier partial sum approximation in each subdomain yields poor results, as the convergence is slow and spurious oscillations occur at the boundaries of each subdomain. Thus once we “glue” the subdomain approximations back together, the approximation for the function in the full domain will exhibit oscillations throughout the entire domain. Recently methods have been developed that successfully eliminate the Gibbs phenomenon for analytic but nonperiodic functions in one dimension. These methods are based on the knowledge of the first 2 N + 1 Fourier coefficients and use either the Gegenbauer polynomials (Gottlieb et al.) or the Bernoulli polynomials (Abarbanel, Gottlieb, Cai et al., and Eckhoff). We propose a way to accurately reconstruct a “spliced” function in a full domain by extending the current methods to eliminate the Gibbs phenomenon in each nonintersecting subdomain and then “gluing” the approximations back together. We solve this problem in both one and two dimensions. In the one-dimensional case we provide two alternative options, the Bernoulli method and the Gegenbauer method, as well as a new hybrid method, the Gegenbauer-Bernoulli method. In the two-dimensional case we prove, for the very first time, exponential convergence of the Gegenbauer method, and then we apply it to solve the “spliced” function problem.

The vibration of disc cam mechanism

In this paper, the longitudinal vibrations of a follower which is the linear active component of a cam mechanism is studied as if it has a constant cross section. The basic Bernoulli method is applied to solve the partial differential equation which is supplied by taking the viscous damping factor into consideration and by adding a new term. For the first time, in addition to the viscous damping, in this investigation, the internal damping term has been imposed to the motion of the follower. The resultant integration constants are determined by using the boundary conditions, and the eigen frequencies are calculated. As a result, two different families of eigen frequencies are remained. The results are formed as computer graphics to be easily understandable.

Systolic designs for Bernoulli's method

In this paper systolic designs are presented for the implementation of Bernoulli's method for polynomial root solving. From a linear systolic array with feedback a systolic ring is derived that calculates the coefficients of Newton's Theorem. The ring is incorporated in a systolic system for calculating the dominant zeros of polynomial equations. The design is simulated soft-systolically in an OCCAm program which is listed in the Appendix.

An Intercomparison of Inverse Methods Using an Eddy-Resolving General Circulation Model

Abstract Three inverse methods (the Bernoulli, beta-spiral, and box inverse methods) are used on mean data from an eddy-resolving oceanic general circulation model, in an attempt to reconstruct the observed mean flow field. Inversions are performed in the Gulf Stream extension, a quiet region which is relatively eddy-free, the center of the region of homogenized potential vorticity, and a near-equatorial area, together with an inversion of the flow across a transoceanic sector. Resolutions for the inversions of ⅓°, 1° and 2° are used. Numerical estimates of geostrophy using the wider resolutions can give top-to-bottom thermal wind shears in error by up to 1 cm s−1 in a flow change of around 8 cm s−1. Two “scores” for the methods are created, one which tests pointwise accuracy (the “global” score) and one which tests fluxes of mass through a section (the “flux” score). The Bernoulli method yields accurate global scores except in the homogenized region; the box inverse method yields fairly accurate global s...

A systolic ring architecture for solving polynomial equations

In this paper some systolic designs are presented for the implementation of Bernoulli's method for polynomial root solving. From a linear systolic array with feedback a systolic ring is derived that calculates the coefficients of Newton's theorem. The ring is incorporated in a systolic system for calculating the dominant zeros of polynomial equations. The design has been simulated soft-systolically in an OCCAM program.

Bernoulli's method for relativistic brachistochrones

The author obtains relativistic brachistochrones for both a uniform electric and uniform gravitational field, applying the same method as that used by Bernoulli (1696) in order to solve the classic brachistochrone problem.