We have performed a Monte Carlo study of a classical three dimensional Coulomb system in which we systematically increase the positional disorder. We start from a completely ordered system and gradually transition to a Coulomb glass. The phase transition as a function of temperature is second order for all values of disorder. We use finite size scaling to determine the transition temperature TC and the critical exponent ν. We find that TC decreases and that ν increases with increasing disorder. We also observe changes in the specific heat, the single particle density of states, and the staggered occupation as a function of disorder and temperature.
We have performed a Monte Carlo study of a three dimensional system of classical electrons with Coulomb interactions at half filling. We systematically increase the positional disorder by starting from a completely ordered system and gradually transitioning to a Coulomb glass. The phase transition as a function of temperature is second order for all values of disorder. We use finite size scaling to determine the transition temperature T C and the critical exponent n. We find that T C decreases and that n increases with increasing disorder.Electrons with long range Coulomb interactions in three dimensions display a rich and complex behavior. If there is translational invariance and a background of compensating positive charge, the system forms a Wigner crystal at low densities where the potential energy dominates the kinetic energy [1,2]. In the presence of quenched disorder the competition between interactions and disorder produces a Coulomb glass. Comparing these two extremes reveals similarities and differences. For example both undergo a phase transition when the temperature is lowered. In one case an ordered arrangement of electrons is formed while in the case of the Coulomb glass a highly disordered arrangement is frozen into place. Yet both low temperature phases have a gap in their single particle density of states.In this paper we study the effect of gradually introducing disorder into a three dimensional system of electrons with long range Coulomb interactions. The system is discrete in the sense that the electrons sit on half of the available sites. In the ordered case the sites form a cubic lattice. The disorder is introduced in the positions of the sites and their deviation from a cubic lattice. The Hamiltonian iswhere we set the charge e ¼ 1, n i is the number operator for site i, r ij ¼ jr i À r j j, and K is a compensating background charge making the whole system charge neutral. n i ¼ 1 (À1) for an occupied (unoccupied) site. We consider half-filling with K ¼ 1=2.We have simulated three dimensional systems of linear size L ¼ 4, 6, and 8. We place N ¼ L 3 sites in the system. We have only considered the case of half filling in order to take advantage of the particle-hole symmetry. For the ordered case the sites form a cubic lattice. In the ground state, every other site is occupied; the occupied sites form a face centered cubic (FCC) lattice. We can gradually introduce disorder by allowing the deviation of a site from its position in a cubic lattice to be chosen from a Gaussian distribution with a standard deviation of s. This gives the radial distance from the cubic lattice site. The angular coordinates of the site are chosen randomly using a uniform distribution. The ordered case corresponds to s ¼ 0. s ¼ 1 corresponds to a very disordered case with a standard deviation equal to the cubic lattice constant a. For all values of the disorder, the system
Disclosures: W. Yang, None. Objective: To report 4 clinical cases in which patients had improved gait and function with microprocessor controlled stance knee ankle foot orthosis (KAFO). Design: Case series report. Patients or Programs: Patient A was a 52-year-old man with Charcot-Marie-Tooth (CMT) disease. Patient B was a 64-year-old man with paraplegia and bilateral knee osteoarthritis. Patient C was a 42-year-old woman with right femoral nerve injury. Patient D was an 84-year-old man with right leg weakness after a cervical surgery with severe right knee hyperextension.Program Description: Patient A had muscular atrophy and only walked 100 feet each time because of leg weakness and fatigue. Bilateral microprocessor controlled KAFOs with electronic stance control and pressure-sensor (PS-KAFO) were prescribed. Patient B had bilateral lower extremity weakness and cardiac problem. He did not use his traditional KAFO due to high energy consumption and difficulty with donning and doffing. He was prescribed with bilateral PS-KAFO. Patient C had muscle strength of 3-/5 on her right leg. With a traditional plastic and metal KAFO, she experienced increased fatigue that led to decreased usage of the brace. A right microprocessor controlled KAFO with electromagnetic stance control and gyroscope-sensor (GS-KAFO) was prescribed. Patient D had been using a traditional plastic and metal KAFO for many years, with progressively worsening right knee hyperextension and pain on weight bearing. A right GS-KAFO was fitted for this patient. Setting: Hospital-based outpatient clinic. Results: Patient A walked more than 1000 feet each time with the PS-KAFO and regained some lost muscle strength. Patient B walked about 100 feet with a better gait with the PS-KAFO. Patient C walked up to 4 hours a day with much better gait with her GS-KAFO. Patient D walked 125 feet each time with his GS-KAFO. Discussion: A new generation of KAFOs, such as PS-KAFO and GS-KAFO, provides better gait and less energy expenditure. It leads to better mobility and compliance. The pros and cons of different KAFOs, ranging from mechanically controlled to microprocessor controlled KAFOs are discussed. Conclusions: Microprocessor stance control KAFOs improve mobility and compliance.
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