Generalized Burgers equations and Euler–Painlevé transcendents. III

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1parameter family of exact single hump solutions, similar to those found for the nonplanar Burgers equations in Paper II. Thus the parametric value β=βn seems to bifurcate the families of solutions, which remain bounded at η=±∞. Other GBE’s considered here are also found to be reducible to Euler–Painlevé equations.

Perinatal mortality and maternal health in rural China

Background and context Since the economic reforms of 1978, China has been acclaimed as a remarkable economy, achieving 9% annual growth per head for more than 25 years. However, China's health sector has not fared well. The population health gains slowed down and health disparities increased. In the field of health and health care, significant progress in maternal care has been achieved. However, there still remain important disparities between the urban and rural areas and among the rural areas in terms of economic development. The excess female infant deaths and the rapidly increasing sex ratio at birth in the last decade aroused serious concerns among policy makers and scholars. Decentralization of the government administration and health sector reform impacts maternal care. Many studies using census data have been conducted to explore the determinants of a high sex ratio at birth, but no agreement has been so far reached on the possible contributing factors. No study using family planning system data has been conducted to explore perinatal mortality and sex ratio at birth and only few studies have examined the impact of the decentralization of government and health sector reforms on the provision and organization of maternal care in rural China. Objectives The general objective of this study was to investigate the state of perinatal health and maternal care and their determinants in rural China under the historic context of major socioeconomic reforms and the one child family planning policy. The specific objectives of the study included: 1) to study pregnancy outcomes and perinatal health and their correlates in a rural Chinese county; 2) to examine the issue of sex ratio at birth and its determinants in a rural Chinese county; 3) to explore the patterns of provision, utilization, and content of maternal care in a rural Chinese county; 4) to investigate the changes in the use of maternal care in China from 1991 to 2003. Materials and Methods This study is based on a project for evaluating the prenatal care programme in Dingyuan county in 1999-2003, Anhui province, China and a nationwide household health survey to describe the changes in maternal care utilization. The approaches used included a retrospective cohort study, cross sectional interview surveys, informant interviews, observations and the use of statistical data. The data sources included the following: 1) A cohort of pregnant women followed from pregnancy up to 7 days after birth in 20 townships in the study county, collecting information on pregnancy outcomes using family planning records; 2) A questionnaire interview survey given to women who gave birth between 2001 and 2003; 3) Various statistical and informant surveys data collected from the study county; 4) Three national household health interview survey data sets (1993-2003) were utilized, and reanalyzed to described the changes in maternity care utilization. Relative risks (RR) and their confidence intervals (CI) were calculated for comparison between parity, approval status, infant sex and township groups. The chi-square test was used to analyse the disparity of use of maternal care between and within urban and rural areas and its trend across the years in China. Logistic regression was used to analyse the factors associated with hospital delivery in rural areas. Results There were 3697 pregnancies in the study cohort, resulting in 3092 live births in a total population of 299463 in the 20 study townships during 1999-2000. The average age at pregnancy in the cohort was 25.9 years. Of the women, 61% were childless, 38% already had one child and 0.3% had two children before the current pregnancy. About 90% of approved pregnancies ended in a live birth while 73% of the unapproved ones were aborted. The perinatal mortality rate was 69 per thousand births. If the 30 induced abortions in which the gestational age was more than 28 weeks had been counted as perinatal deaths, the perinatal mortality rate would have been as high as 78 per thousand. The perinatal mortality rate was negatively associated with the wealth of the township. Approximately two thirds of the perinatal deaths occurred in the early neonatal period. Both the still birth rate and the early neonatal death rate increased with parity. The risk of a stillbirth in a second pregnancy was almost four times that for a first pregnancy, while the risk of early neonatal deaths doubled. The early neonatal mortality rate was twice as high for female as for male infants. The sex difference in the early neonatal mortality rate was mainly attributable to mortality in second births. The male early neonatal mortality rate was not affected by parity, while the female early neonatal mortality rate increased dramatically with parity: it was about six times higher for second births than for first births. About 82% early neonatal deaths happened within 24 hours after birth, and during that time, girls were almost three times more likely to die than boys. The death rate of females on the day of birth increased much more sharply with parity than that of males. The total sex ratio at birth of 3697 registered pregnancies was 152 males to 100 females, with 118 and 287 in first and second pregnancies, respectively. Among unapproved pregnancies, there were almost 5 live-born boys for each girl. Most prenatal and delivery care was to be taken care of in township hospitals. At the village level, there were small private clinics. There was no limitation period for the provision of prenatal and postnatal care by private practitioners. They were not permitted to provide delivery care by the county health bureau, but as some 12% of all births occurred either at home or at private clinics; some village health workers might have been involved. The county level hospitals served as the referral centers for the township hospitals in the county. However, there was no formal regulation or guideline on how the referral system should work. Whether or not a woman was referred to a higher level hospital depended on the individual midwife's professional judgment and on the clients' compliance. The county health bureau had little power over township hospitals, because township hospitals had in the decentralization process become directly accountable to the township government. In the township and county hospitals only 10-20% of the recurrent costs were funded by local government (the township hospital was funded by the township government and the county hospital was funded by the county government) and the hospitals collected user fees to balance their budgets. Also the staff salaries depended on fee incomes by the hospital. The hospitals could define the user charges themselves. Prenatal care consultations were however free in most township hospitals. None of the midwives made postnatal home visits, because of low profit of these services. The three national household health survey data showed that the proportion of women receiving their first prenatal visit within 12 weeks increased greatly from the early to middle 1990s in all areas except for large cities. The increase was much larger in the rural areas, reducing the urban-rural difference from more than 4 times to about 1.4 times. The proportion of women that received antenatal care visits meeting the Ministry of Health s standard (at least 5 times) in the rural areas increased sharply from 12% in 1991-1993 to 36% in 2001-2003. In rural areas, the proportion increase was much faster in less developed areas than in developed areas. The hospital delivery rate increased slightly from 90% to 94% in urban areas while the proportion increased from 27% to 69% in rural areas. The fastest change was found to be in type 4 rural areas, where the utilization even quadrupled. The overall difference between rural and urban areas was substantially narrowed over the period. Multiple logistic regression analysis shows that time periods, residency in rural or urban areas, income levels, age group, education levels, delivery history, occupation, health insurance and distance from the nearest health care facilities were significantly associated with hospital delivery rates. Conclusions 1. Perinatal mortality in this study was much higher than that for urban areas as well as any reported rate from specific studies in rural areas of China. Previous studies in which calculations of infant mortality were not based on epidemiological surveys have been shown to underestimate the rates by more than 50%. 2. Routine statistics collected by the Chinese family planning system proved to be a reliable data source for studying perinatal health, including still births, neonatal deaths, sex ratio at birth and among newborns. National Household Health Survey data proved to be a useful and reliable data source for studying population health and health services. Prior to this research there were few studies in these areas available to international audiences. 3.Though perinatal mortality rate was negatively associated with the level of township economic development, the excess female early neonatal mortality rate contributed much more to high perinatal mortality rate than economic factors. This was likely a result of the role of the family planning policy and the traditional preferences for sons, which leads to lethal neglect of female newborns and high perinatal mortality. 4. The selective abortions of female foetuses were likely to contribute most to the high sex ratio at birth. The underreporting of female births seemed to have played a secondary role. The higher early neonatal mortality rate in second-born as compared to first-born children, particularly in females, may indicate that neglect or poorer care of female newborn infants also contributes to the high sex ratio at birth or among newborns. Existing family planning policy proved not to effectively control the steadily increased birth sex ratio. 5. The rural-urban gap in service utilization was on average significantly narrowed in terms of maternal healthcare in China from 1991 to 2003. This demonstrates that significant achievements in reducing inequities can be made through a combination of socio-economic development and targeted investments in improving health services, including infrastructure, staff capacities, and subsidies to reduce the costs of service utilization for the poorest. However, the huge gap which persisted among cities of different size and within different types of rural areas indicated the need for further efforts to support the poorest areas. 6. Hospital delivery care in the study county was better accepted by women because most of women think delivery care was very important while prenatal and postnatal care were not. Hospital delivery care was more systematically provided and promoted than prenatal and postnatal care by township hospital in the study area. The reliance of hospital staff income on user fees gave the hospitals an incentive to put more emphasis on revenue generating activities such as delivery care instead of prenatal and postnatal care, since delivery care generated much profits than prenatal and postnatal care . Recommendations 1. It is essential for the central government to re-assess and modify existing family planning policies. In order to keep national sex balance, the existing practice of one couple one child in urban areas and at-least-one-son a couple in rural areas should be gradually changed to a two-children-a-couple policy throughout the country. The government should establish a favourable social security policy for couples, especially for rural couples who have only daughters, with particular emphasis on their pension and medical care insurance, combined with an educational campaign for equal rights for boys and girls in society. 2. There is currently no routine vital-statistics registration system in rural China. Using the findings of this study, the central government could set up a routine vital-statistics registration system using family planning routine work records, which could be used by policy makers and researchers. 3. It is possible for the central and provincial government to invest more in the less developed and poor rural areas to increase the access of pregnant women in these areas to maternal care services. Central government together with local government should gradually provide free maternal care including prenatal and postnatal as well as delivery care to the women in poor and less developed rural areas. 4. Future research could be done to explore if county and the township level health care sector and the family planning system could be merged to increase the effectiveness and efficiency of maternal and child care. 5. Future research could be done to explore the relative contribution of maternal care, economic development and family planning policy on perinatal and child health using prospective cohort studies and community based randomized trials. Key words: perinatal health, perinatal mortality, stillbirth, neonatal death, sex selective abortion, sex ratio at birth, family planning, son preference, maternal care, prenatal care, postnatal care, equity, China

Application of novel method for surface-ray tracing over hyperboloidal scatterers

A novel geodesic constant method has been developed for the hitherto unsolved problem of surface-ray tracing over a class of surface, namely the general hyperboloid of revolution (GHOR). All the ray-geometric parameters are obtained analytically in a one-parameter form. The ray parameters derived here for the first time can be readily used in the UTD formulation for computing the mutual coupling between the antennas located on the GHOR.

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Propagation of quasi-simple waves in a compressible rotating atmosphere

A class of self-propagating linear and nonlinear travelling wave solutions for compressible rotating fluid is studied using both numerical and analytical techiques. It is shown that, in general, a three dimensional linear wave is not periodic. However, for some range of wave numbers depending on rotation, horizontally propagating waves are periodic. When the rotation ohgr is equal to $$\sqrt {(\gamma - 1)/(4\gamma )}$$ , all horizontal waves are periodic. Here, gamma is the ratio of specific heats. The analytical study is based on phase space analysis. It reveals that the quasi-simple waves are periodic only in some plane, even when the propagation is horizontal, in contrast to the case of non-rotating flows for which there is a single parameter family of periodic solutions provided the waves propagate horizontally. A classification of the singular points of the governing differential equations for quasi-simple waves is also appended.

Non-conservatively loaded stochastic columns

A new finite element method is developed to analyse non-conservative structures with more than one parameter behaving in a stochastic manner. As a generalization, this paper treats the subsequent non-self-adjoint random eigenvalue problem that arises when the material property values of the non-conservative structural system have stochastic fluctuations resulting from manufacturing and measurement errors. The free vibration problems of stochastic Beck's column and stochastic Leipholz column whose Young's modulus and mass density are distributed stochastically are considered. The stochastic finite element method that is developed, is implemented to arrive at a random non-self-adjoint algebraic eigenvalue problem. The stochastic characteristics of eigensolutions are derived in terms of the stochastic material property variations. Numerical examples are given. It is demonstrated that, through this formulation, the finite element discretization need not be dependent on the characteristics of stochastic processes of the fluctuations in material property value.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Plates on Elastic Foundation

Analysis of rectangular plates resting on a Winkler-type, one-parameter foundation is studied. The finite element method is applied and a 12-degree-of-freedom, nonconforming rectangular plate element is adopted. Based on shape functions of the plate element, an energy approach is used to derive a closed-form, 12-by-12, consistent foundation stiffness matrix for a rectangular plate on an elastic subgrade. A commonly used method of modeling structural elements on an elastic foundation is the application of discrete springs at the element nodes. The model developed in this paper is compared with the discrete spring model and the convergence of both models is discussed. The convergence of the models is compared with the well-known classical solution of plates on elastic foundation developed in the 1950s. Both models show good convergence to the classical solution. The continuous subgrade response model converges in a manner more consistent with the flexibility of the plate element.

Device oriented statistical modeling method for process variability in 45nm analog CMOS technology

With the rapid scaling down of the semiconductor process technology, the process variation aware circuit design has become essential today. Several statistical models have been proposed to deal with the process variation. We propose an accurate BSIM model for handling variability in 45nm CMOS technology. The MOSFET is designed to meet the specification of low standby power technology of International Technology Roadmap for Semiconductors (ITRS).The process parameters variation of annealing temperature, oxide thickness, halo dose and title angle of halo implant are considered for the model development. One parameter variation at a time is considered for developing the model. The model validation is done by performance matching with device simulation results and reported error is less than 10%.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Dense shallow granular flows

Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development (L) is large compared with the cross-stream height (h). The mass and diameter of the particles are set equal to 1 in the analysis without loss of generality. In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function chi proportional to (phi(ad) - phi)(-alpha), and a faster divergence of the derivativ rho(d chi/d rho) similar to (d chi/d phi), where rho and phi are the density and volume fraction, and phi(ad) is the volume fraction for arrested dynamics. When the height h is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). In the shallow limit, the stress reduces to a simplified Bagnold stress, where all components of the stress are proportional to (partial derivative u(x)/partial derivative y)(2), which is the cross-stream (y) derivative of the stream-wise (x) velocity. In the simplified equations for dense shallow flows, the inertial terms are neglected in the y momentum equation in the shallow limit because the are O(h/L) smaller than the divergence of the stress. The resulting model contains two equations, a mass conservation equations which reduces to a solenoidal condition on the velocity in the incompressible limit, and a stream-wise momentum equation which contains just one parameter B which is a combination of the Bagnold coefficients and their derivatives with respect to volume fraction. The leading-order dense shallow flow equations, as well as the first correction due to density variations, are analysed for two representative flows. The first is the development from a plug flow to a fully developed Bagnold profile for the flow down an inclined plane. The analysis shows that the flow development length is ((rho) over barh(3)/B) , where (rho) over bar is the mean density, and this length is numerically estimated from previous simulation results. The second example is the development of the boundary layer at the base of the flow when a plug flow (with a slip condition at the base) encounters a rough base, in the limit where the momentum boundary layer thickness is small compared with the flow height. Analytical solutions can be found only when the stream-wise velocity far from the surface varies as x(F), where x is the stream-wise distance from the start of the rough base and F is an exponent. The boundary layer thickness increases as (l(2)x)(1/3) for all values of F, where the length scale l = root 2B/(rho) over bar. The analysis reveals important differences between granular flows and the flows of Newtonian fluids. The Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. The compressibility number (ratio of the variation in volume fraction and mean volume fraction) is independent of the flow velocity and layer height, and depends only on the volume fraction and Bagnold coefficients.

Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

Validity ranges of interfacial wave theories in a two-layer fluid system

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness d(1), and lower layer thickness d(2), instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehautes plot for free surface waves if water depth ratio r = d(1)/d(2) approaches to infinity and the upper layer water density rho(1) to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of sigma = (rho(2) - rho(1))/rho(2) -> 1.0 and r > 1.0. In the end, several figures of the validity ranges for various interfacial wave theories in the two-layer fluid are given and compared with the results for surface waves.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.

单参数极小连续流的两个充分条件

讨论了单参数连续流的基本性质，并给出了关于单参数连续流为极小流和单参数连续半流为极小流的充分条件。

Micromechanical damage and fracture in elastomeric polymers

This thesis aims at a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. The failure model is motivated by post-mortem fractographic observations of void nucleation, growth and coalescence in polyurea stretched to failure, and accounts for the specific fracture energy per unit area attendant to rupture of the material.

Furthermore, it is shown that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. Optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains, and to the strain-gradient elasticity regularization, are derived. Based on optimal scaling laws, it is shown how the critical energy-release rate of specific materials can be determined from test data. In addition, the scope and fidelity of the model is demonstrated by means of an example of application, namely Taylor-impact experiments of polyurea rods. Hereby, optimal transportation meshfree approximation schemes using maximum-entropy interpolation functions are employed.

Finally, a different crazing model using full derivatives of the deformation gradient and a core cut-off is presented, along with a numerical non-local regularization model. The numerical model takes into account higher-order deformation gradients in a finite element framework. It is shown how the introduction of non-locality into the model stabilizes the effect of strain localization to small volumes in materials undergoing softening. From an investigation of craze formation in the limit of large deformations, convergence studies verifying scaling properties of both local- and non-local energy contributions are presented.