194 research outputs found
The nonlinear future stability of the FLRW family of solutions to the Euler–Einstein system with a positive cosmological constant
No full textOriginal manuscript January 24, 2012In this article, we study small perturbations of the family of Friedmann–Lemaître–Robertson–Walker cosmological background solutions to the 1 + 3 dimensional Euler–Einstein system with a positive cosmological constant. These background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. Our nonlinear analysis shows that under the equation of state p=c[2 over s]ρ, 0 < c[2 over s] < 1/3 , the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,∞) × T[superscript 3], are future-causally geodesically complete. These results are extensions of previous results derived by the author in a collaboration with I. Rodnianski, in which the fluid was assumed to be irrotational. Our novel analysis of a fluid with non-zero vorticity is based on the use of suitably defined energy currents.National Science Foundation (U.S.). All-Institutes Postdoctoral Fellowship (Mathematical Sciences Research Institute (Berkeley, Calif.) Grant DMS-0441170
On the questions of local and global well-posedness for the hyperbolic PDEs occurring in some relativistic theories of gravity and electromagnetism
No full textThe two hyperbolic systems of PDEs we consider in this work are the source-free Maxwell-Born-Infeld (MBI) field equations and the Euler-Nordstr??m system for gravitationally self-interacting fluids. The former system plays a central role in Kiessling's recently proposed self-consistent model of classical
electrodynamics with point charges, a model that does not suffer from the infinities found in the classical Maxwell-Maxwell model with point charges. The latter system is a scalar gravity caricature of the incredibly more complex Euler-Einstein system. The primary original contributions of the thesis can be summarized as follows:
1) We give a sharp non-local criterion for the formation of singularities in plane-symmetric solutions to the source-free MBI field equations. We also use a domain of dependence argument to show that 3-d initial data agreeing with certain plane-symmetric data on a large enough ball lead to solutions that form singularities in finite time. This work is an extension of a theorem of Brenier, who studied singularity formation in periodic plane-symmetric solutions.
2) We prove well-posedness for the Euler-Nordstr??m system with a cosmological constant k (EN_k) for initial data that are an H^N perturbation (not necessarily small) of a uniform, quiet fluid, for N [greater than]= 3. The method of proof relies on the framework of energy currents that has been recently developed by Christodoulou. We turn to this method out of necessity: two common frameworks for showing well-posedness in H^N, namely symmetric hyperbolicity and strict hyperbolicity, do not apply to the EN_k system, while Christodoulou's techniques apply to all hyperbolic systems derivable from a Lagrangian, of which the EN_k system is an example.
3) We insert the speed of light c as a parameter into the EN_k system (and designate the family of systems EN_k^c) in order to study the non-relativistic limit c to infinity. Taking the formal limit in the equations gives the Euler-Poisson system with a cosmological constant (EP_k). Using energy currents, we prove that for fixed initial data, as c goes to infinity, the solutions to the EN_k^c system converge uniformly on a spacetime slab [0,T] x R^3 to the solution of the EP_k system.Ph.D.Includes bibliographical references (p. 140-143)
Grangeville crew portrait, 2007
No full textA group portrait of the crew for the Grangeville Smokejumper base.
Front Row L-R: Scott Chehock, Willie Acton, Robin Embry, Jodie Baxter, Nate Hess, James Greenwood, Ted McClanahan, Dan Vanderpool, Chris Hertel, Jodi Stone, Jason Junes, Garrit Craig.
Back Row L-R: Matt Sweet Pea Smith, Walt Curry, Kelvin Thompson, Russ Frei, Floyd Whitaker, Randy Nelson, Isaac Karuzas, Joe Forthofer, Clem Pope, Will Markwardt, Rick Tidwell, Chris Young, Darby Thomson, Diane Rahn, Audrey Banfill, Mike Dunn, Mike Blinn, Mike Nelson, Ryan Desautel, Amanda Holt, Willie Kelly.
Not Pictured: Gabe Cortez, Spencer Long, Jared Schuster, Cameron Chambers.https://dc.ewu.edu/nsa_crewpics/1396/thumbnail.jp
Changes in Achilles tendon stiffness and energy cost following a prolonged run in trained distance runners
No full textDuring prolonged running, the magnitude of Achilles tendon (AT) length change may increase, resulting in increased tendon strain energy return with each step. AT elongation might also affect the magnitude of triceps surae (TS) muscle shortening and shortening velocity, requiring greater activation and increased muscle energy cost. Therefore, we aimed to quantify the tendon strain energy return and muscle energy cost necessary to allow energy storage to occur prior to and following prolonged running. 14 trained male (n = 10) and female (n = 4) distance runners (24 +/- 4 years, 1.72 +/- 0.09 m, 61 +/- 10 kg, (V) over barO(2)max 64.6 +/- 5.8 ml.kg(-1).min(-1)) ran 90 minutes (RUN) at approximately 85% of lactate threshold speed (sLT). Prior to and following RUN, AT stiffness and running energy cost (E-run) at 85% sLT were determined. AT energy return was calculated from AT stiffness, measured with dynamometry and ultrasound and estimated TS force during stance. TS energy cost was estimated on the basis of AT force and assumed crossbridge mechanics and energetics. Following RUN, AT stiffness was reduced from 328 +/- 172 N.mm(-1) to 299 +/- 148 N.mm(-1) (p = 0.022). E-run increased from 4.56 +/- 0.32 J.kg(-1).m-1 to 4.62 +/- 0.32 J.kg(-1).m-1 (p = 0.049). Estimated AT energy return was not different following RUN (p = 0.99). Estimated TS muscle energy cost increased significantly by 11.8 +/- 12.3 J.stride(-1), (p = 0.0034), accounting for much of the post-RUN increase in E-run (8.6 +/- 14.5 J.stride(-1), r(2) = 0.31). These results demonstrate that a prolonged, submaximal run can reduce AT stiffness and increase E-run in trained runners, and that the elevated TS energy cost contributes substantially to the elevated E-run.articl
A methodology for the concurrent design of products and their assembly sequence
No full textThis thesis reports on the development of a Two-Tier methodology that provides
support for assembly sequence construction, validation and evaluation in parallel with
the design. This facilitates the production of products that are optimised for
assemblability. The proposed approach diverges significantly from many of the
sequence generation methods developed to date, which assume that assembly
planning starts at the conclusion of the design process. It is believed that the latter
approach misses an important opportunity to concurrently implement design and
sequence improvements that would result in products inherently suited to assembly.
The industrial assembly planning process was found to be completely different from
the automatic sequence generation approach. The Two-Tier methodology has its
foundations in this manual process, which uses a breadth-first, depth-second search. A
constraint-based method is used to interactively validate the sequence. In direct
contrast to traditional sequence generators, the hard and soft constraints are invoked
throughout the process. A novel approach to sequence evaluation allows the user to
quantitatively determine the suitability of the sequence at any time during the
construction process.
However, designers are rarely assembly experts and it is unreasonable to expect
practical sequences to be generated without assistance. Thus, a set of generic
assembly planning rules was identified from industrial surveys by the author. These
were collaboratively implemented into an Expert Assembler, which currently consists
of two mini advisors. Support is available to identify the most suitable base
component and the most appropriate component to add next.
The Two-Tier methodology has been implemented into a computer-based system
called SPADE (Sequence Planning And Design Environment). A four-layer model
holds the product data that underpins this implementation. The methodology and
SPADE have been successfully tested using representative case studies and the results
are reported as part of this thesis
Running economy from a muscle energetics perspective
No full textThe economy of running has traditionally been quantified from the mass-specific oxygen uptake; however, because fuel substrate usage varies with exercise intensity, it is more accurate to express running economy in units of metabolic energy. Fundamentally, the understanding of the major factors that influence the energy cost of running (E-run) can be obtained with this approach. E-run is determined by the energy needed for skeletal muscle contraction. Here, we approach the study of E-run from that perspective. The amount of energy needed for skeletal muscle contraction is dependent on the force, duration, shortening, shortening velocity, and length of the muscle. These factors therefore dictate the energy cost of running. It is understood that some determinants of the energy cost of running are not trainable: environmental factors, surface characteristics, and certain anthropometric features. Other factors affecting E-run are altered by training: other anthropometric features, muscle and tendon properties, and running mechanics. Here, the key features that dictate the energy cost during distance running are reviewed in the context of skeletal muscle energetics.articl
Energy cost of running and Achilles tendon stiffness in man and woman trained runners
No full textThe energy cost of running (Erun), a key determinant of distance running performance, is influenced by several factors. Although it is important to express Erun as energy cost, no study has used this approach to compare similarly trained men and women. Furthermore, the relationship between Achilles tendon (AT) stiffness and Erun has not been compared between men and women. Therefore, our purpose was to determine if sex‐specific differences in Erun and/or AT stiffness existed. Erun (kcal kg−1 km−1) was determined by indirect calorimetry at 75%, 85%, and 95% of the speed at lactate threshold (sLT) on 11 man (mean ± SEM, 35 ± 1 years, 177 ± 1 cm, 78 ± 1 kg, V˙O2max = 56 ± 1 mL kg−1 min−1) and 18 woman (33 ± 1 years, 165 ± 1 cm, 58 ± 1 kg, V˙O2max = 50 ± 0.3 mL kg−1 min−1) runners. AT stiffness was measured using ultrasound with dynamometry. Man Erun was 1.01 ± 0.06, 1.04 ± 0.07, and 1.07 ± 0.07 kcal kg−1 km−1. Woman Erun was 1.05 ± 0.10, 1.07 ± 0.09, and 1.09 ± 0.10 kcal kg−1 km−1. There was no significant sex effect for Erun or RER, but both increased with speed (P < 0.01) expressed relative to sLT. High‐range AT stiffness was 191 ± 5.1 N mm−1 for men and 125 ± 5.5 N mm−1, for women (P < 0.001). The relationship between low‐range AT stiffness and Erun was significant at all measured speeds for women (r2 = 0.198, P < 0.05), but not for the men. These results indicate that when Erun is measured at the same relative intensity, there are no sex‐specific differences in Erun or substrate use. Furthermore, differences in Erun cannot be explained solely by differences in AT stiffness. e00178 Here, we show that when energy cost of running is normalized to body mass, at similar relative speeds of running, no sex‐specific differences in substrate use nor in the energy cost of running exist among similarly trained runners. Furthermore, the stiffness of the Achilles tendon (AT) of women is lower than in males, but the relationship between Erun and AT stiffness is not different between the sexes.articl
Procedures of rat in situ skeletal muscle contractile properties
No full textThere are many circumstances where it is desirable to obtain the contractile response of skeletal muscle under physiological circumstances: normal circulation, intact whole muscle, at body temperature. This includes the study of contractile responses like posttetanic potentiation, staircase and fatigue. Furthermore, the consequences of disease, disuse, injury, training and drug treatment can be of interest. This video demonstrates appropriate procedures to set up and use this valuable muscle preparation. To set up this preparation, the animal must be anesthetized, and the medial gastrocnemius muscle is surgically isolated, with the origin intact. Care must be taken to maintain the blood and nerve supplies. A long section of the sciatic nerve is cleared of connective tissue, and severed proximally. All branches of the distal stump that do not innervate the medial gastrocnemius muscle are severed. The distal nerve stump is inserted into a cuff lined with stainless steel stimulating wires. The calcaneus is severed, leaving a small piece of bone still attached to the Achilles tendon. Sonometric crystals and/or electrodes for electromyography can be inserted. Immobilization by metal probes in the femur and tibia prevents movement of the muscle origin. The Achilles tendon is attached to the force transducer and the loosened skin is pulled up at the sides to form a container that is filled with warmed paraffin oil. The oil distributes heat evenly and minimizes evaporative heat loss. A heat lamp is directed on the muscle, and the muscle and rat are allowed to warm up to 37 degrees C. While it is warming, maximal voltage and optimal length can be determined. These are important initial conditions for any experiment on intact whole muscle. The experiment may include determination of standard contractile properties, like the force-frequency relationship, force-length relationship, and force-velocity relationship. With care in surgical isolation, immobilization of the origin of the muscle and alignment of the muscle-tendon unit with the force transducer, and proper data analysis, high quality measurements can be obtained with this muscle preparation.articl
Can changes in midsole bending stiffness of shoes affect the onset of joint work redistribution during a prolonged run?
No full textObjective: To investigate if changing the midsole bending stiffness of athletic footwear can affect the onset of lower limb joint work redistribu-tion during a prolonged run.Methods: Fifteen trained male runners (10-km time of<44 min) performed 10-km runs at 90% of their individual speed at lactate threshold (i.e.,when change in lactate exceeded 1 mmol during an incremental running test) in a control and stiff shoe condition on two occasions. Lower limbjoint kinematics and kinetics were measured using a motion capture system and a force-instrumented treadmill. Data were acquired every 500 m.Results: Prolonged running resulted in a redistribution of positive joint work from distal to proximal joints in both shoe conditions. Compared tothe beginning of the run, less positive work was performed at the ankle (approximately 9%;p0.001) and more positive work was performedat the knee joint (approximately 17%;p0.001) at the end of the run. When running in the stiff shoe condition, the onset of joint work redistri-bution at the ankle and knee joints occurred at a later point during the run.Conclusion: A delayed onset of joint work redistribution in the stiff condition may result in less activated muscle volume, because ankle plantarflexor muscles have shorter muscles fascicles and smaller cross-sectional areas compared to knee extensor muscles. Less active muscle volumecould be related to previously reported decreases in metabolic cost when running in stiff footwear. These results contribute to the notion thatfootwear with increased stiffness likely results in reductions in metabolic cost by delaying joint work redistribution from distal to proximal joints.articl
How Can Biomechanics Improve Physical Preparation and Performance in Paralympic Athletes?: A Narrative Review
No full textRecent research in Paralympic biomechanics has offered opportunities for coaches, athletes, and sports practitioners to optimize training and performance, and recent systematic reviews have served to summarize the state of the evidence connecting biomechanics to Paralympic performance. This narrative review serves to provide a comprehensive and critical evaluation of the evidence related to biomechanics and Paralympic performance published since 2016. The main themes within this review focus on sport-specific body posture: the standing, sitting, and horizontal positions of current summer Paralympic sports. For standing sports, sprint and jump mechanics were assessed in athletes with cerebral palsy and in lower-limb amputee athletes using running-specific prostheses. Our findings suggest that running and jumping-specific prostheses should be ‘tuned’ to each athlete depending on specific event demands to optimize performance. Standing sports were also inclusive to athletes with visual impairments. Sitting sports comprise of athletes performing on a bike, in a wheelchair (WC), or in a boat. WC configuration is deemed an important consideration for injury prevention, mobility, and performance. Other sitting sports like hand-cycling, rowing, and canoeing/kayaking should focus on specific sitting positions (e.g., arm-crank position, grip, or seat configuration) and ways to reduce aero/hydrodynamic drag. Para-swimming practitioners should consider athlete-specific impairments, including asymmetrical anthropometrics, on the swim-start and free-swim velocities, with special considerations for drag factors. Taken together, we provide practitioners working in Paralympic sport with specific considerations on disability and event-specific training modalities and equipment configurations to optimize performance from a biomechanical perspective.articl
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