Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

Numerical Study of the Behaviour of Wall Shear Stress in Pulsatile Stenotic Flows

This paper presents a numerical study of pulsatile flow through an axisymmetric stenosed artery. Numerical calculations of the incompressible Navier-Stokes equations were carried out in an axisymmetric geometry to investigate how the wall shear stress (WSS) is affected by varying levels of stenosis contractions and pulse periods (reduced velocity). It is found that the distribution and strength of the WSS is closely correlated with the position of the vortex ring formed at the stenosis. Each vortex ring generates high WSS at the stenosis walls and this high WSS propagate downstream with the vortex ring. As the vortex ring convects downstream, it loses its strength due to viscous effects and WSS decreases in magnitude. In general, the strength of the vortex ring increases with increasing stenosis levels which leads to higher WSS values on the walls. The effect of smaller pulse period is to reduce the distance between the vortex rings, thus increasing the spatial variation of WSS along the stenosed artery

A Novel Laboratory Course on Advanced Chemical Engineering Experiments

The chemical engineering curriculum in the United States has trained generations of technical experts who have successfully optimized chemical processes and products once they entered the chemical industry. The U.S. chemical industry, however, has entered a critical stage in which it must be able to create new and differentiated value through technical innovations that arc essential for long-term survival. This innovation process will require new skills that go far beyond the traditional expertise for the optimization of tasks possessed by young chemical engineers. The innovators must be able to identify new opportunities, explore the boundaries of technology, evaluate critical issues, develop and implement technologies, and communicate effectively with scientists and engineers from other disciplines. Therefore, one of the most important educational tasks of a modern university, in combination with a strong theoretical foundation, is to challenge students in laboratory courses to think, explore, hypothesize, plan, solve, and evaluate. The typical sequence of laboratory skills development stops short of introducing young engineers to the most critical aspects of experimental work. Chemical engineers usually begin developing their laboratory skills in chemistry courses, where experiments are closely managed. At this early stage in their development, students follow detailed instructions and learn basic principles by observing the results. In the undergraduate engineering laboratory course (the unit operations lab ), students have more freedom in experimental design but still have well-defined objectives and manipulate equipment someone else has set up. It is rare, however, for undergraduate students to be taught how to create new experiments. It is also rare for undergraduate students, and hence beginning graduate students, to have an appreciation for the care, planning, design, and testing required to produce equipment that will give reliable and useful results. Even such simple issues as leak testing or adapting analytical devices to new tasks are outside most students* experience. Even more important is an absence of opportunities to learn how the lessons learned from the failure of an approach can be fed back into the empirical process to seed the finally successful idea. All these skills require more creative freedom than is usually allowed in a well-structured laboratory course. In the novel laboratory teaching approach described here, we try to provide students with a learning environment that allows them to develop advanced experimental skills that are necessary for success in research and development environments

Upper and Lower Limb Movement Kinematics in Aging

Fragile X-associated tremor/ataxia syndrome (FXTAS) is a neurodegenerative disorder associated with a premutation cytosine-guanine-guanine (CGG) trinucleotide repeat expansion of the FMR1 gene. FXTAS is estimated to be the most common single-gene form of ataxia in the aging population. Gait ataxia and intention tremor are the primary behavioral symptoms of FXTAS, though clinical evaluation of these symptoms often is subjective, contributing to difficulties in reliably differentiating individuals with FXTAS and asymptomatic premutation carriers. This study aimed to clarify the extent to which quantitative measures of gait and upper limb kinematics may serve as biobehavioral markers of FXTAS degeneration. Nineteen premutation carriers (aged 46-77 years), including 9 with possible, probable, or definite FXTAS and 16 sex- and IQ-matched healthy controls, completed tests of non-constrained walking and reaching while both standing (static reaching) and walking (dynamic reaching) to quantify gait and upper limb control, respectively. For the non-constrained walking task, participants wore reflective markers and walked at their preferred speed on a walkway. During the static reaching task, participants reached and lifted boxes of different sizes while standing. During the dynamic reaching task, participants walked to reach and lift the boxes. Movement kinematics were examined in relation to clinical ratings of neuromotor impairments and CGG repeat length. During non-constrained walking, individuals with FXTAS showed decreased stride lengths and stride velocities, increased percentages of double support time, and increased variabilities of cadence and center of mass relative to both asymptomatic premutation carriers and controls. While individuals with FXTAS did not show any static reaching differences relative to the other two groups, they showed multiple differences during dynamic reaching trials, including reduced maximum reaching velocity, prolonged acceleration time, and jerkier movement of the shoulder, elbow, and hand. Gait differences during non-constrained walking were associated with more severe clinically rated posture and gait symptoms. Reduced maximum reaching velocity and increased jerkiness during dynamic reaching were each related to more severe clinically rated kinetic dysfunction and overall neuromotor symptoms in FMR1 premutation carriers. Our findings suggest kinematic alterations consistent with gait ataxia and upper limb bradykinesia are each selectively present in individuals with FXTAS, but not asymptomatic aging premutation carriers. Consistent with neuropathological and magnetic resonance imaging (MRI) studies of FXTAS, these findings implicate cerebellar and basal ganglia degeneration associated with neuromotor decline. Our results showing associations between quantitative kinematic differences in FXTAS and clinical ratings suggest that objective assessments of gait and reaching behaviors may serve as critical and reliable targets for detecting FXTAS risk and monitoring progression

Upper and Lower Limb Movement Kinematics in Aging FMR1 Gene Premutation Carriers

Fragile X-associated tremor/ataxia syndrome (FXTAS) is a neurodegenerative disorder associated with a premutation cytosine-guanine-guanine (CGG) trinucleotide repeat expansion of the FMR1 gene. FXTAS is estimated to be the most common single-gene form of ataxia in the aging population. Gait ataxia and intention tremor are the primary behavioral symptoms of FXTAS, though clinical evaluation of these symptoms often is subjective, contributing to difficulties in reliably differentiating individuals with FXTAS and asymptomatic premutation carriers. This study aimed to clarify the extent to which quantitative measures of gait and upper limb kinematics may serve as biobehavioral markers of FXTAS degeneration. Nineteen premutation carriers (aged 46–77 years), including 9 with possible, probable, or definite FXTAS and 16 sex- and IQ-matched healthy controls, completed tests of non-constrained walking and reaching while both standing (static reaching) and walking (dynamic reaching) to quantify gait and upper limb control, respectively. For the non-constrained walking task, participants wore reflective markers and walked at their preferred speed on a walkway. During the static reaching task, participants reached and lifted boxes of different sizes while standing. During the dynamic reaching task, participants walked to reach and lift the boxes. Movement kinematics were examined in relation to clinical ratings of neuromotor impairments and CGG repeat length. During non-constrained walking, individuals with FXTAS showed decreased stride lengths and stride velocities, increased percentages of double support time, and increased variabilities of cadence and center of mass relative to both asymptomatic premutation carriers and controls. While individuals with FXTAS did not show any static reaching differences relative to the other two groups, they showed multiple differences during dynamic reaching trials, including reduced maximum reaching velocity, prolonged acceleration time, and jerkier movement of the shoulder, elbow, and hand. Gait differences during non-constrained walking were associated with more severe clinically rated posture and gait symptoms. Reduced maximum reaching velocity and increased jerkiness during dynamic reaching were each related to more severe clinically rated kinetic dysfunction and overall neuromotor symptoms in FMR1 premutation carriers. Our findings suggest kinematic alterations consistent with gait ataxia and upper limb bradykinesia are each selectively present in individuals with FXTAS, but not asymptomatic aging premutation carriers. Consistent with neuropathological and magnetic resonance imaging (MRI) studies of FXTAS, these findings implicate cerebellar and basal ganglia degeneration associated with neuromotor decline. Our results showing associations between quantitative kinematic differences in FXTAS and clinical ratings suggest that objective assessments of gait and reaching behaviors may serve as critical and reliable targets for detecting FXTAS risk and monitoring progression