Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics

We present quantum numerical methods for the typical initial boundaryvalue problems (IBVPs) of convection-diffusion equations in fluid dynamics. The IBVPis discretized into a series of linear systems via finite difference methods and explicittime marching schemes. To solve these discrete systems in quantum computers, wedesign a series of quantum circuits, including four stages of encoding, amplification,adding source terms, and incorporating boundary conditions. In the encoding stage,the initial condition is encoded in the amplitudes of quantum registers as a state vectorto take advantage of quantum algorithms in space complexity. In the following threestages, the discrete differential operators in classical computing are converted into unitary evolutions to satisfy the postulate in quantum systems. The related arithmeticcalculations in quantum amplitudes are also realized to sum up the increments fromthese stages. The proposed quantum algorithm is implemented within the open-sourcequantum computing framework Qiskit [2]. By simulating one-dimensional transientproblems, including the Helmholtz equation, the Burgers’ equation, and Navier-Stokesequations, we demonstrate the capability of quantum computers in fluid dynamics.     

Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT

We propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented with the non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the corresponding two-dimensional (2D) model under a strongly anisotropic confining potential. Different from existing methods, the NUFFT based DDI solver removes the singularity by adopting the spherical/polar coordinates in the Fourier space in 3D/2D, respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary and/or needed. Then, we incorporate this solver into existing successful methods for computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our new methods outperform existing methods in terms of both accuracy and efficiency.     

Some Mathematical and Numerical Issues in Geophysical Fluid Dynamics and Climate Dynamics

In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and their related mathematical and computational issues, 2) climate variability, predictability and successive bifurcation, and 3) a new dynamical systems theory and its applications to GFD and climate dynamics.     

A Multilevel Approach to the Path to Expertise in Three Different Competitive Settings

The objectives of the study were to analyze the deliberate practice variables in three different youth competitive sport settings; to analyze the effects of a season-long exposure on deliberate practice variables. The study explores three contexts in two different sports, soccer and volleyball, and at two competitive levels. The athletes fulfilled the questionnaire at the beginning and at the end of the season. A multilevel analysis was performed. Forty eight boys aged 15-17 years (14 from a volleyball club; 14 from an elite volleyball centre; 20 from a professional soccer club) participated in the study. The measure was an adapted version for soccer and volleyball of the Deliberate Practice Motivation Questionnaire, which assesses two dimensions: the will to compete and the will to excel. Fewer people in the volleyball group showed a will to excel, the soccer group showed an increase in the scores. In will to compete, the three teams showed a decrease in their means. The decrease is more pronounced in the will to excel but the context effect is not significant. The biggest decrease is shown by the elite volleyball team, followed by the club teams. The findings raise questions for managers and coaches who look for physical and technical gifted young athletes and aim to develop their qualities through a careful planned training programme. The insertion in programmes that are believed to foster expertise seems to have unexpected consequences. Sport participation cannot rely exclusively on an orientation toward expertise, forgetting the autonomy of young people to set their goals.

Key Points

• The need for the adolescents to focus on game performance can be a deterrent for their own perspectives of a career or just to have fun.
• The crucial factor to influence the players’ answers seems to be the perspective of a rewarding professional career in sport.
• It is possible that young athletes, after a hard season, re-evaluate their priorities and think that their dedication to sport did not fit their initial expectations.
• Managers and coaches should be aware of important pedagogical implications, and the effectiveness of sport participation cannot rely exclusively on an orientation toward expertise.

Key Words: Deliberate practice, multilevel, expertise, soccer, volleyball     

Numerical Bifurcation Methods and Their Application to Fluid Dynamics: Analysis Beyond Simulation

We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated withthese transitions, popularly referred to as 'tipping points', is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system. The numerical challenges involved in both methods are mentioned and possible solutions to current bottlenecks are given. To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems, we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.     

A New Approach to Implement Sigma Coordinate in a Numerical Model

This study shows a new way to implement terrain-following σ-coordinate in a numerical model, which does not lead to the well-known "pressure gradient force (PGF)" problem. First, the causes of the PGF problem are analyzed with existing methods that are categorized into two different types based on the causes. Then, the new method that bypasses the PGF problem all together is proposed. By comparing these three methods and analyzing the expression of the scalar gradient in a curvilinear coordinate system, this study finds out that only when using the covariant scalar equations of σ-coordinate will the PGF computational form have one term in each momentum component equation, thereby avoiding the PGF problem completely. A convenient way of implementing the covariant scalar equations of σ-coordinate in a numerical atmospheric model is illustrated, which is to set corresponding parameters in the scalar equations of the Cartesian coordinate. Finally, two idealized experiments manifest that the PGF calculated with the new method is more accurate than using the classic one. This method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.     

A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty

Robust control design for quantum systems with uncertainty is a key taskfor developing practical quantum technology. In this paper, we apply neural networksto learn the control of a quantum system with uncertainty. By exploiting the auto differentiation function developed for neural network models, our method avoids themanual computation of the gradient of the cost function as required in traditionalmethods. We implement our method using two algorithms. One uses neural networks to learn both the states and the controls and one uses neural networks to learnonly the controls but solve the states by finite difference methods. Both algorithms incorporate the sampling-based learning process into the training of the networks. Theperformance of the algorithms is evaluated on a practical numerical example, followedby a detailed discussion about the advantage and trade-offs between our method andthe other numerical schemes.     

Path to the Interpeduncular Fossa: Anatomical Comparison of Endoscopic-Assisted versus Standard Subtemporal Approach

Objective The aim of this study was to assess the assumed advantage of endoscopic assistance to the standard subtemporal approach. The idea was to measure qualitatively and quantitatively visibility versus operability.Design We performed eight subtemporal dissections on four cadaver heads. Our dissections integrated an operating microscope, endoscope, and neuronavigation. Comparison was made between visibility and operability afforded by the microscope alone or by the microscope–endoscope combination. Visibility was recorded as complete or incomplete and was quantified for key structures using linear measurements taken by the navigation system. Operability was determined by whichever maneuvers could be safely and comfortably accomplished in the space afforded.Results From our survey, the structures whose visibility most benefitted from the addition of the endoscope include: contralateral third nerve, posterior perforated substance, mammillary bodies, and contralateral superior cerebellar artery. With regard to quantitative evaluation, we found increased visibility of both basilar artery and posterior cerebral artery. With regard to the operability, no objective advantage was afforded by the addition of the endoscope. Subjectively, the maneuvers were easier to perform while using the endoscope.Conclusion Using the endoscope as an assistance tool during conducting classical subtemporal approach can help in overcome a lot of the classical subtemporal approach limitations.     

Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

We use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the "Impulse method" which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency. This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.     

Cardiorespiratory Responses to Stationary Running in Water and on Land

The aim of the study was to compare maximal and submaximal cardiorespiratory responses between progressive tests on a treadmill on land (TRE), and stationary running on land (SRL) and in water (SRW), while also comparing two methods of determining the second turn point (ST) (ventilatory curve and heart rate deflection point). The study sample consisted of nine active women (23 ± 1.94 years) that performed three maximal protocols in separate days. Heart rate (HR) and oxygen uptake (VO₂) were measured in all sessions. The data were analyzed using repeated-measures ANOVA and two-way repeated measures ANOVA with post-hoc Bonferroni test. Greater values of maximal HR (HR_max) and HR at ST (HR_ST) were observed during exercise performed on TRE and during the SRL, compared to the SRW (p < 0.05). The results for maximal VO₂ (VO_2max) and VO₂ at ST (VO_2ST) showed greater and significant values on TRE compared to STL and STW (p < 0.05). Furthermore, the HR and VO₂ corresponding to the ST showed similar values between the two methods. Thus, the main conclusion of the present study was that the HR deflection point seems to be a simple and practical alternative method for determining the ST in all protocols analyzed.

Key Points

• The maximal and submaximal (second turn point) oxygen uptake were influenced by the type of exercise, as these responses were similar in both water-based and land-based stationary running protocols and different from those obtained during the treadmill running, that presented greater values compared with both stationary running protocols.
• The heart rate deflection point can be used for determining the second turn point during stationary running test in aquatic environment.
• Caution is necessary in the interpretation of the application of the heart rate deflection point in water aerobics exercises because we analyzed only young women performing one water-based exercise.

Key words: Ventilatory curve, deflection point, second turn point, heart rate, oxygen uptake, water-based exercise     

A Generalized Numerical Approach for Modeling Multiphase Flow and Transport in Fractured Porous Media

A physically based numerical approach is presented for modeling multiphase flow and transport processes in fractured rock. In particular, a general framework model is discussed for dealing with fracture-matrix interactions, which is applicable to both continuum and discrete fracture conceptualization. The numerical modeling approach is based on a general multiple-continuum concept, suitable for modeling any types of fractured reservoirs, including double-, triple-, and other multiple-continuum conceptual models. In addition, a new, physically correct numerical scheme is discussed to calculate multiphase flow between fractures and the matrix, using continuity of capillary pressure at the fracture-matrix interface. The proposed general modeling methodology is verified in special cases using analytical solutions and laboratory experimental data, and demonstrated for its application in modeling flow through fractured vuggy reservoirs.     

The Anterior Approach to Hip and Pelvis

Objective Exposure of the anterior pelvic column and the anterior hip in the internervous plane between the femoral nerve (sartorius and rectus muscle) and the superior gluteal nerve (tensor fasciae latae, gluteus medius, and gluteus minimus muscle) as well as between the blood supply of the external (medial) and internal iliac artery (lateral). Indications All pelvic osteotomies. Shelf procedures. Anterior labral lesions. Fractures of the femoral head, anterior column, anterior acetabular wall, and high transverse acetabular fractures. Contraindications None. Surgical Technique Incision along the iliac crest, over the anterosuperior iliac spine to the lateral aspect of the proximal thigh. Separation of sartorius and tensor fasciae latae. Osteotomy and medial reflection of the anterosuperior iliac spine. Subperiosteal detachment of the abdominal muscles and the iliacus muscle. Division of both origins of the rectus. Elevation of the iliocapsular muscle and the psoas tendon. Incision and medial retraction of the periosteum at the anterior surface of the anterior acetabular wall to exposure the acetabular floor. Detachment of the tensor fasciae latae, gluteus medius, and gluteus minimus muscles to expose the outer ilium. Results To date, this modified Smith-Petersen approach has been used in approximately 700 periacetabular osteotomies. Complications: transient femoral (n = 1), sciatic (n = 5), and lateral femorocutaneous (30%) nerve deficits. Distal aspect of the scar always large, revision rare (n = 3). No vascular injuries. Resection of heterotopic ossification in five of six patients. Very low rates of infection, hematoma, deep thrombophlebitis, and embolism.     

Laparoscopic Approach to Incarcerated and Strangulated Inguinal Hernias

Introduction:

Acute inguinal hernias are a common presentation as surgical emergencies, which have been routinely managed with open surgery. In recent years, the laparoscopic approach has been described by several authors but has been controversial amongst surgeons. We describe the laparoscopic approach to incarcerated/strangulated inguinal hernias based on a review of the literature with regards to its feasibility in laparoscopically managing the acute hernia presentation.

Methods:

A systematic literature search was carried out including Medline with PubMed as the search engine, and Ovid, Embase, Cochrane Collaboration, and Google Scholar databases to identify articles reporting on laparoscopic treatment, reduction, and repair of incarcerated or strangulated inguinal hernias from 1989 to 2008.

Results:

Forty-three articles were found, and 7 were included according to the inclusion criteria set. Articles reporting on the use of laparoscopy for the evaluation of the hernia but not reducing and repairing it, the use of the open technique, elective hernia repairs, pediatric series, review articles, and other kinds of hernias were excluded after title and abstract review. This resulted in 16 articles that were reviewed in full. Of these 16 articles, 7 reported on the use of the laparoscopic approach exclusively. From these 7 studies, there were 328 cases reported, 6 conversions, average operating time of 61.3 minutes (SD±12.3), average hospital stay of 3.8 days (SD±1.2), 34 complications (25 of which were reported as minor), and 17 bowel resections performed either laparoscopically or through a minilaparotomy incision guided laparoscopically.

Conclusion:

The laparoscopic repair is a feasible procedure with acceptable results; however, its efficacy needs to be studied further, ideally with larger multicenter randomized controlled trials.     

Approach to cartilage lesions and algorithm for treatment

Cartilage symptoms in the knee may be encountered in various forms in orthopedic practice. The first stage from history to treatment is to establish the diagnosis; if the diagnosis is made as a cartilage lesion in the knee, priority must be given to current treatment approaches. The surgeon must provide information regarding etiology, defect thickness, lesion size, the containment of cartilage, localization, stability, meniscal integrity, anatomic alignment of the knee, previous assessments, radiological assessment (direct radiography, magnetic resonance imaging), and general, medical, and systemic conditions, and family history. In this review, a treatment algorithm is presented for the management of articular cartilage lesions.