Browsing by Subject "Stability"

Now showing 1 - 16 of 16
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    Analysis of generalized Forchheimer flows of compressible fluids in porous media
    (University of Minnesota. Institute for Mathematics and Its Applications, 2009-06) Aulisa, Eugenio; Bloshanskaya, Lidia; Hoang, Luan; Ibragimov, Akif
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    Application of Caquot's solution to the analysis of stability of shallow circular cavities in Tresca material
    (2016-11) Reich, Tyler
    The primary objective of this study is to expand upon and investigate a stress field solution for the stability of shallow cavities proposed by Caquot in 1934. Despite its relevance, this solution appears to have been overlooked in the literature. In this thesis, Caquot's analytical model is re-formulated to express the stability condition of a shallow cavity (a section of long cylindrical tunnel or a spherical opening) in terms of a factor of safety using the strength reduction technique, as commonly done in the evaluation of stability of slopes, embankments and levees. Caquot's analytical model is also extended to account for the presence of a mechanical surcharge on the ground surface, water pressure in the ground, and two conditions of water presence inside the cavity, namely, dry or flooded cavities. For the purpose of this study, the plastic constitutive model assumed for the ground is the Tresca shear failure criterion. This material model is a particular case of the Mohr-Coulomb material model with zero internal friction angle and cohesive strength only. Closed-form solutions for computation of factor of safety under dry and saturated ground conditions are presented and the effect of input variables involved in the problem are evaluated. Results of factor of safety obtained with the closed-form solutions presented here are shown to compare well with those obtained with the commercial finite difference software FLAC, a program that is widely used in the practical design of underground structures. All this suggests that the extended Caquot's solution presented in this thesis could be a valuable tool for practical evaluation of stability conditions of circular cavities, such as sections of long cylindrical tunnels or spherical openings, excavated near the ground surface.
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    Boosting Max-Pressure Signal Control Into Practical Implementation: Methodologies And Simulation Studies In City Networks
    (2023-08) Xu, Te
    This dissertation presents innovative modifications to the Max-Pressure (MP) control policy, an adaptive traffic signal control strategy tailored to various urban traffic conditions. The max-pressure control offers two pivotal advantages that underscore its significance for in-depth research and future implementation: Firstly, MP operates on a decentralized basis, enabling real-time solutions. Secondly, MP control guarantees maximum stability, implying it can accommodate as much given demand as any alternative signal timing strategy. Initially, the MP control policy was adapted to transit signal priority (MP-TSP). It delivered enhanced bus travel times, outperforming both fixed-time signal controls with TSP and other adaptive signal controls in efficiency. Subsequently, the pedestrian-friendly max-pressure signal controller (Ped-MP) was developed. This marked a pioneering effort in crafting an MP control to boost pedestrian access without compromising vehicle throughput. The Ped-MP, backed by analytical proof for maximum stability, illustrated an inverse relation between pedestrian delay and tolerance time during simulations on the Sioux Falls network. This suggests the potential for urban spaces that are more pedestrian-oriented, even in areas of elevated pedestrian traffic. The third innovation addressed the practical feasibility of the position-weighted back-pressure (PWBP) controller. Although the initial PWBP controller was effective in simulations, it was found to be impractical due to its need for density information from everywhere of the road link. This observation paved the way for the approximate position-weighted back-pressure (APWBP) control, which significantly reduces sensor requirements by utilizing only two loop detectors per link (one downstream and one upstream). A comparative analysis revealed that the APWBP's efficacy closely paralleled the original PWBP, validating its practicality. Finally, recognizing the MP controller’s deficit in coordinated phase selection, the Smoothing-MP approach was conceptualized. Incorporating signal coordination, this novel strategy not only maintained its maximum stability properties but also amplified traffic flow efficiency, as confirmed by mathematical proofs and numerical studies in both the Grid Network and the Downtown Austin Network.
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    Computational study of hypersonic boundary layer stability on cones
    (2012-12) Gronvall, Joel Edwin
    Due to the complex nature of boundary layer laminar-turbulent transition in hypersonic flows and the resultant effect on the design of re-entry vehicles, there remains considerable interest in developing a deeper understanding of the underlying physics. To that end, the use of experimental observations and computational analysis in a complementary manner will provide the greatest insights. It is the intent of this work to provide such an analysis for two ongoing experimental investigations. . The first focuses on the hypersonic boundary layer transition experiments for a slender cone that are being conducted at JAXA’s free-piston shock tunnel HIEST facility. Of particular interest are the measurements of disturbance frequencies associated with transition at high enthalpies. The computational analysis provided for these cases included two-dimensional CFD mean flow solutions for use in boundary layer stability analyses. The disturbances in the boundary layer were calculated using the linear parabolized stability equations. Estimates for transition locations, comparisons of measured disturbance frequencies and computed frequencies, and a determination of the type of disturbances present were made. It was found that for the cases where the disturbances were measured at locations where the flow was still laminar but nearly transitional, that the highly amplified disturbances showed reasonable agreement with the computations. Additionally, an investigation of the effects of finite-rate chemistry and vibrational excitation on flows over cones was conducted for a set of theoretical operational conditions at the HIEST facility. . The second study focuses on transition in three-dimensional hypersonic boundary layers, and for this the cone at angle of attack experiments being conducted at the Boeing/AFOSR Mach-6 quiet tunnel at Purdue University were examined. Specifically, the effect of surface roughness on the development of the stationary crossflow instability are investigated in this work. One standard mean flow solution and two direct numerical simulations of a slender cone at an angle of attack were computed. The direct numerical simulations included a digitally-filtered, randomly distributed surface roughness and were performed using a high-order, low-dissipation numerical scheme on appropriately resolved grids. Comparisons with experimental observations showed excellent qualitative agreement. Comparisons with similar previous computational work were also made and showed agreement in the wavenumber range of the most unstable crossflow modes.
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    Constrained Buckling of Variable Length Elastica
    (2017-10) Liakou, Anna
    The physical understanding of the response of slender elastic bodies restrained inside constraints under various loading and boundary conditions is of a great importance in engineering and medical applications. The research work presented in this thesis is especially concerned with the buckling response of an elastic rod (the elastica) subjected to unilateral constraints under axial compression. It seeks to address two main issues: (i) the conditions that lead to the onset of instability, and (ii) the factors that define the bifurcation diagram. Two distinct classes of problems are analyzed; (i) the classical buckling problem of a constant length elastica and (ii) the insertion buckling problem of a variable length elastica. Their main difference is the generation of a configurational force at the insertion point of the sliding sleeve in the insertion problem, which is not present in the classical problem. The thesis describes two distinct methodologies that can solve these constrained buckling problems; (1) a geometry-based method, and (2) an optimal control method. The geometry-based method is used to analyze the post-buckling response of a weightless planar elastica subjected to unilateral constraints. The method rests on assuming a deformed shape of the elastica and on uniquely segmenting the elastica consistent with a single canonical segment (clamped-pinned). An asymptotic solution of the canonical problem is then derived and the complete solution of the constrained elastica is constructed by assembling the solution for each segment. Nevertheless, the application of the optimal control method is more generic. It can be used to solve any constrained buckling problem under general boundary and loading conditions. Based on Hamiltonian mechanics, the optimality conditions, which constitute the Pontryagin’s minimum principle, involve the minimization of the Hamiltonian with respect to the control variables, the canonical equations and the transversality conditions. The main advantage of the optimal control method is the assumption of strong rather than weak variation of the involved variables, which leads to the additional Weierstrass necessary condition (“optimal” equilibrium state). Based on it, several factors such as the effect of the self-weight of the elastica and the clearance of the walls are investigated.
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    Critical considerations in development of mesoporous silica nanoparticles for biological applications.
    (2012-04) Lin, Yu-Shen
    In the past ten years, mesoporous silica nanoparticles have been some of the hottest materials investigated for biomedical use. Mesoporous silica nanoparticles are size-controllable and discrete particles with high surface area, large pore volume, and easy surface modification properties. These unique characteristics make mesoporous silica nanoparticles promising for biological applications. Although there is extensive literature precedent for the synthesis and applications of mesoporous silica nanoparticles, there are several critical issues resulting in limited use of multifunctional mesoporous silica nanoparticles in vitro or in vivo. For example, the large particle size (> 100-nm-diameter) and poor particle stability (aggregation) result in rapid uptake by the reticuloendothelial system, a portion of immune system which removes the nanoparticles from circulation before they reach their tumor target. Another hurdle is the possible unintentional toxicity of such nanoparticles. If the designed mesoporous silica nanoparticles cause unintentional damage to benign cells or healthy tissue and organs, their use will be greatly limited in therapeutic applications. Prior to in vivo animal experiments, unintentional cytotoxicity must be minimized and well studied. Based on the critical considerations described above, an ideal mesoporous therapeutic should possess the following characteristics prior to in vivo studies: (1) small size (<50 nm); (2) high surface area; (3) high stability; and (4) minimal unintentional cytotoxicity. Chapter One reviews the development and use of mesoporous silica nanoparticles for biomedical use. Various components have been incorporated into mesoporus silica nanoparticles to yield various functionalities, like controlled drug release, targeting, and multimodal imaging for diagnosis. With more and more complex designs for mesoporous silica nanoparticles, practical considerations for in vivo use must be taken into account. Chapter Two describes our novel method to synthesize highly stable, redispersible, and small mesoporous silica nanotherapeutics. This chapter discusses the particle stability of bare and modified mesoporous silica in various biological media. Critical synthetic parameters including introduction of hydrophilic and hydrophobic organosilanes and hydrothermal treatment are key to synthesize ultrastable and redispersible mesoporous silica nanoparticles. Chapter Three examines the cytotoxicity of mesoporous silica nanoparticles to human RBCs, mouse mast cells, and human endothelial cells using (1) a hemolysis assay, (2) an electrochemical assay of cell function and (3) a microfluidic device. The experimental results reveal that mesoporous silica nanoparticles have lower adverse effects on RBCs and mast cells than their similarly sized nonporous counterparts. In addition, shear stress effects on the cytotoxicity of unmodified mesoporous silica will be discussed. In Chapter Four, a novel one-pot synthesis route was developed to fabricate size-tunable multifunctional mesoporous silica nanoparticles. Based on the experience from improving bare mesoporous silica stability, the hydrothermally assisted organosilane modification method was applied to improve the particle stability, T2 relaxivity stability, and acid resistance of magnetic mesoporous silica nanoparticles. In the last part of my research work, Chapter Five investigates cytotoxicity of new carbon nanomaterials, graphene oxide and graphene in human erythrocytes and skin fibroblasts. The cytotoxicity results show that the physico-chemical properties, including the particle size, exfoliation extent, oxygen content, and aggregation state of graphene oxide and graphene greatly influence their cytotoxicity. This collaborative work also inspired me to consider a possible future direction involving the incorporation of graphene oxide or graphene into mesoporous silica nanoparticles to control drug release via a heat-driven route. To conclude, Chapter Six reviews my thesis work and highlights the advances I have made in the fields of nanomedicine and nanotoxicity. In addition, possible future directions are also described.
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    Dynamics and stabilities of generalized Forchheimer flows with the flux boundary condition
    (University of Minnesota. Institute for Mathematics and Its Applications, 2011-02) Hoang, Luan; Ibragimov, Akif
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    Investigating the Effects of Inverter Based Resources on an Electrical Grid System
    (2022-05) Dancler, Shannon
    The addition of renewable generation to the electricity grid, with either the reduction or retirement of conventional generation, is increasing due to the impending climate crisis. Advancements in power electronics technologies are also contributing to the increased connection of renewable energy. Despite the increased commonality of renewable generation and the use of inverter-based resources (IBRs) and reactive power components, will system stability hold in a primarily renewable electricity grid? This thesis investigates how the addition of IBR models affected a system that previously had only conventional generation, if the IBRs could improve system stability, if reactive power components were needed in conjunction with renewable generation, how renewable generation variability affected the system, and if flexible AC transmission system (FACTS) devices were more beneficial than fixed shunt capacitors and inductors. The system used was a pre-existing example network from the power systems software for engineers (PSS®E), created by Siemens, which had an adequate combination of generation, load, reactive power components, and a swing bus. Steady state analysis showed that the addition of IBRs and reactive power components increased the stability through maintaining system voltage and avoiding thermal loading violations. Expected behavior was displayed when investigating renewable generation variability through which the importance of compensating for lost reactive power, properly distributing it throughout the system, and the probability of thermal loading issues were seen.
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    Long term mechanical performance of MEMS in liquid environments
    (2009-04) Ali, Shaikh Mubassar
    Micro-electro-mechanical-systems (MEMS) are exposed to a variety of liquid environments in applications such as chemical and biological sensors, and microfluidic devices. Environmental interactions between the liquids and micron sized structures can lead to unpredictable long-term performance of MEMS in liquid environments. The present understanding of long-term mechanical performance of MEMS is based on studies conducted in air or vacuum. The objective of this study was to extend the present understanding of long-term mechanical performance of MEMS to liquid environments. Two broad categories of long-term mechanical failures reported in the literature were experimentally investigated: operational failures and structural fatigue failures. Typically operational failures are observed to occur at low stress levels, while fatigue failures are reported at higher stress levels. In order to investigate these failure modes, two different designs of test specimens and experimental techniques were developed. Low stress level (0-5 MPa) tests to investigate operational failures of MEMS in liquids were performed on microcantilever test specimens. Higher stress level (~ 0.2 GPa) tests were conducted on MEMS tensile specimens for investigating fatigue failures in liquids. Microcantilever specimens were made of silicon and silicon nitride. In addition, performance of silicon microcantilevers coated with common MEMS coating materials such as Titanium and SU-8 was also investigated. Microcantilever specimens were tested in liquids such as de-ionized water, saline, and glucose solution and compared with results in air. The microcantilevers were subjected to long term cyclic actuation (10e8 to 10e9 cycles) in liquid filled enclosures. Mechanical performance of the microcantilevers was evaluated by periodically monitoring changes in resonant frequency. Any unpredictable change in resonant frequency was deemed to constitute an operational failure. Despite low stress levels, mechanical performance of microcantilever test specimens was affected to a varying degree depending on environmental interactions between the structural/ coating material and the liquid environment. The changes in resonant frequency, often to the extent of ~1%, were attributed to factors such as mineral deposition, corrosion fatigue, water absorption, and intrinsic stresses. Tensile-tensile fatigue tests (high stress level) were performed on aluminum MEMS tensile specimens, in air and saline solution. Fatigue life was observed to range between 1.2 x 10e6 to 2.2 x 10e6 cycles at mean and alternating stresses of 0.13 GPa. The effect of saline environment on fatigue failures of aluminum tensile specimens was inconclusive from the experiments performed in this study. In conclusion, experimental results indicate subtle operational failures to be a potential critical failure mode for MEMS operating in liquid environments. Long-term mechanical failures in MEMS are expected to depend on the particular combination of material, stress level, and environment.
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    Modeling the traffic flow evolution process after a network disruption.
    (2010-12) He, Xiaozheng
    Major disruption to a transportation network can disturb traffic flow patterns significantly. To deploy effective and efficient traffic restoration projects, a good prediction of the traffic flow pattern under network disruption is vital. Although traffic flow evolution processes have been modeled in various ways in the literature, very limited attention has been paid to the traffic flow evolution process after an unexpected network disruption. In fact, due to the lack of data, none of the existing day-to-day traffic assignment models have been compared against reality, and thus their quality has not yet been verified. There clearly exists a gap between day-to-day traffic flow evolution modeling and their practical applications, especially under network disruption scenarios that are of great interest to traffic management authorities. This doctoral research is dedicated to bridging that gap by developing and validating innovative new models for deterministic day-to-day traffic assignment problem. The first innovation is the development of a link-based traffic dynamic model for studying traffic evolution. Existing deterministic day-to-day traffic assignment models were all built upon path flow variables. Most path-based models, however, suffer two essential shortcomings. One is that their application requires a given initial path flow pattern, which is typically unidentifiable, i.e., mathematically nonunique and practically unobservable. In addition, different initial path flow patterns constituting the same link flow pattern generally gives different day-to-day link flow evolutions. The second shortcoming is the path overlapping problem, whereby the interdependence of paths is ignored, leading to unreasonable results for networks with overlapping paths. The proposed link-based day-to-day traffic dynamic model avoids the two shortcomings, and captures travelers' cost-minimization behavior in their path finding as well as their inertia. The stable point of the link-based dynamical system is rigorously proven to be the classic Wardrop user equilibrium. Its asymptotic stability is guaranteed under mild conditions. Our second innovation is the establishment of a "prediction-correction" framework for modeling traffic evolution after an unexpected network disruption. By studying actual behavioral changes of drivers after the collapse of the I-35W Mississippi River Bridge in Minneapolis, we found that most existing day-to-day traffic assignment models would not be suitable for modeling traffic evolution under network disruption, because they assume that drivers' travel cost perception depends solely on their experience from previous days. They do not recognize that, when a significant network change occurs unexpectedly, travelers' past experience on a traffic network may not be entirely useful if the disturbance to traffic patterns is extensive. To remedy this, this research proposes a "prediction-correction" model to describe the traffic equilibration process, in which travelers predict traffic patterns after network changes and gradually correct their predictions according to their new travel experience. We also prove rigorously that, under mild assumptions, the proposed "prediction-correction" process has the Wardrop user equilibrium flow pattern as a globally attractive point. Most importantly, this doctoral research verifies the proposed models against a real network disruption scenario. The proposed models are calibrated and validated with field data collected after the collapse of the I-35W Bridge. This study bridges the gap between theoretical modeling and practical applications of day-to-day traffic equilibration approaches and promotes a further understanding of traffic equilibration processes after an unexpected network disruption.
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    Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization
    (2017-06) Choi, Hyungjin
    Rampant integration of renewable resources (e.g., photovoltaic and wind-energy conversion systems) and uncontrollable and elastic loads (e.g., plug-in hybrid electric vehicles) are rapidly transforming power systems. In this environment, an analytic method to quantify the impact of parametric and input uncertainty will be critical to ensure the reliable operation of next-generation power systems. This task is analytically and computationally challenging since power-system dynamics are nonlinear in nature. In this thesis, we present analytic methods to quantify the impact of parametric and input uncertainties for two important applications in power systems: i) uncertainty propagation in power-system differential-algebraic equation model and power flow, and ii) robust stability assessment of power-system dynamics. For the first topic, an optimization-based method is presented to estimate maximum and minimum bounds on state variables while acknowleding worst-case parametric and input uncertainties in the model. The approach leverages a second-order Taylor-series expansion of the states around a nominal (known) solution. Maximum and minimum bounds are then estimated from either Semidefinite relaxation of Quadratically-Constrained Quadratic-Programming or Alternating Direction Method of Multipliers. For the second topic, an analytical method to quantify power systems stability margins while acknowleding uncertainty is presented within the framework of Lyapunov's direct method. It focuses on the algorithmic construction of Lyapunov functions and the estimation of the robust Region-Of-Attraction with Sum-of-Squares optimization problems which can be translated into semidefinite problems. For both topics, numerical case studies are presented for different test systems to demonstrate and validate the proposed methods.
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    Regularization methods for inverse problems.
    (2011-03) Orozco Rodr´ıguez, Jos´e Alberto
    Many applications in industry and science require the solution of an inverse problem. To obtain a stable estimate of the solution of such problems, it is often necessary to im- plement a regularization strategy. In the first part of the present work, a multiplicative regularization strategy is analyzed and compared with Tikhonov regularization. In the second part, an inverse problem that arises in financial mathematics is analyzed and its solution is regularized. Tikhonov regularization for the solution of discrete ill-posed problems is well doc- umented in the literature. The L-curve criterion is one of a few techniques that are preferred for the selection of the Tikhonov parameter. A more recent regularization ap- proach less well known is a multiplicative regularization strategy, which unlike Tikhonov regularization, does not require the selection of a parameter. We analyze a multiplica- tive regularization strategy for the solution of discrete ill-posed problems by comparing it with Tikhonov regularization aided with the L-curve criterion. We then proceed to analyze the stability of a method for estimating the risk-neutral density (RND) for the price of an asset from option prices. RND estimation is an inverse problem. The method analyzed first applies the principle of maximum entropy, where the maximum entropy solution (MES) corresponds to the estimated RND. Next, it pro- vides an effective characterization of the constraint qualification (CQ) under which the MES can be computed by solving the dual problem, where an explicit function in finitely many variables is minimized. In our analysis, we show that the MES is stable under pa- rameter perturbation, but the parameters are unstable under data perturbation. When noisy data are used, we show how to project the data so that the CQ is satisfied and the method can be used. To stabilize the method, we use Tikhonov regularization and choose the penalty parameter via the L-curve method. We demonstrate with numerical examples that the method becomes then much more stable to perturbation in data. Accordingly, we perform a convergence analysis of the regularized solution.
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    The Relationship between Core Stability and a Hockey Specific Sport Performance in Elite vs. Non-Elite Hockey Athletes
    (2016-12) Rourk, Zachary
    The relationship between core stability and sport performance is unclear. Proponents of core exercise theorize that improved core stability will lead to improvements in sport performance. Detractors argue that current measures of core stability have shown little relationship to sport performance. Current measures of core stability focus on core endurance and core strength, characteristics of subsystems of the greater construct of core stability. Sport performance can generally be characterized as being high in complexity. During these performances it can be reasoned that the demands placed on the core stability system will be similarly complex. However, the current measures of Core Stability are low in complexity, calling into question their validity, by virtue of the principle of dynamic correspondence. PURPOSE: To assess the validity of two common core stability tests (The Sahrmann Core Stability Test (SCST and The Sport Specific Endurance Plank Test (SSEPT)) within the context of level of sport performer (Elite vs. Non-elite). As well as to compare the neuromuscular activity of core muscles between Elite and Non-Elite athletes during a specific sport performance, an ice hockey slapshot. METHODS: Athletes were recruited into two groups, Elite (n=9, Age= 23.11 ± 1.69yrs, Weight= 190.3 ± 5.88lbs, Playing Experience= 18.33 ± 1.55yrs), and Non-Elite (n=8, Age= 28.25 ± 3.26yrs, Weight= 186.2 ± 2.91lbs, Playing Experience= 2.90 ± .83yrs). After being outfitted with an electromyogram device attached to 5 core muscles (Transversus abdominus, Rectus abdominus, Gluteus Medius, Gluteus Maximus, Multifidus), participants completed 10 slapshot trials, the SCST and the SSEPT. RESULTS: There were no significant between group differences for SCST (Elite 2.00 ± 0.47, Non-Elite 2.50 ± 0.38 p = .429) or SSEPT (Elite 228.89 ± 24.07, Non-Elite 215.38 ± 29.65 p = .726). There were significant between group differences in slapshot accuracy (Elite 5.00 ± 0.76, Non-Elite 0.75 ± .53, p = <.001). There were also significant between group differences in EMG Duration, Relative Energy and Relative Power. The Elite group had shorter EMG Duration in TVA (555.70 ± 21.97ms, 1111.29 ± 59.67ms), RA (367.33 ± 25.85ms, 803.63 ± 65.03ms), GMed (584.05 ± 35.69ms, 1486.89 ± 134.35ms), GMax (786.21 ± 54.94ms, 1522.92 ± 81.28ms) and Multi (961.11 ± 46.81ms, 1973.34 ± 115.7ms) , lower Relative Energy in TVA (56.94 ± 2.81mV•ms, 209.76 ± 29.16mV•ms), RA (27.65 ± 3.06mV•ms, 94.77 ± 10.09mV•ms), GMax (62.04 ± 4.72mV•ms, 128.30 ± 5.64mV•ms) and Multi (93.57 ± 3.67mV•ms, 218.18 ± 16.03mV•ms), as well as lower Relative Power in TVA (.1053 ± .0050, .1589 ± .0117mV) and RA (.0746 ± .0054, .1119 ± .0071 mV) and higher Relative Power in GMed (.0592 ± .0026, .0447 ± .0028 mV). CONCLUSION: The SCST and the SSEPT are not valid measures of core stability within the context of level of sport performance. Neither measure was able to distinguish between Elite and Non-Elite groups. It is important to stress the difference in playing experience between the two groups (Playing Experience, Elite= 18.33 ± 1.55yrs, Non-Elite= 2.90 ± .83yrs). The Elite group was comprised of professional and D-I NCAA hockey players, whereas the Non-Elite group was comprised of bottom level recreational players described as working on skills such as learning to skate with the puck. The differences in sport specific skill level were further reinforced by the significant between group differences observed in the slapshot accuracy test. The inability of the two studied measures to differentiate between such different levels of athlete bring into question their validity within the broader context of sport performance in general. Further research is necessary to justify such extrapolations of findings. The neuromuscular activity of the core musculature of Elite and Non-Elite hockey athletes during a slapshot differs in terms of muscle activation duration, relative energy and relative power. These differences imply that neuromuscular coordination may play a role in the core stability of an athlete during a specific sport performance. Based on these results, a valid measure of Core Stability should be similar in complexity to the targeted sport performance and related to meaningful outcomes specific to the nature of that sport, in accordance with the principle of dynamic correspondence. An approach in which exercises are chosen based on their similarity to desired sport performance in terms of neuromuscular coordination, as opposed to training general athletic qualities such as, in this case, core endurance or core strength.
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    Stability of solutions to generalized Forchheimer equations of any degree
    (University of Minnesota. Institute for Mathematics and Its Applications, 2012-04) Hoang, Luan Thach; Ibragimov, Akif; Kieu, Thinh; Sobol, Zeev
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    Structural stability of generalized Forchheimer equations for compressible fluids in porous media
    (University of Minnesota. Institute for Mathematics and Its Applications, 2010-01) Hoang, Luan; Ibragimov, Akif