In this paper we apply the concept of thermodynamic geometry to the Bañados-Teitelboim-Zanelli ͑BTZ͒ black hole. We find the thermodynamic curvature diverges at the extremal limit of the black hole, which means the extremal black hole is the critical point with the temperature zero. We also study the effective dimensionality of the underlying statistical model. Near the critical point, the picture is clear; the spatial dimension of the underlying statistical model is just one, which agrees with other results. However, far from the critical point, the dimension becomes less than one and even negative. In order to interpret this result, we resort to a qualitative analogy with the Takahashi gas model. ͓S0556-2821͑99͒04516-6͔ PACS number͑s͒: 04.70.Dy, 04.60. Kz, 05.70.Jk Over the decades the statistical interpretation of blackhole entropy has been one of the most fascinating subjects. There have been many approaches to the problem, although nothing was completely successful. One curiosity about black-hole thermodynamics is that it looks different from an ordinary thermodynamical system, due to the negative heat capacity. This makes it hard to compose its thermodynamic ensemble and to make the underlying statistical model. One way to study the statistical aspects is to assume the microcanonical ensemble for an isolated black hole. Actually, in this way one can understand the critical behavior for the near extremal black hole. The critical exponents satisfying the scaling law even tells us the dimensionality of the underlying statistical model.In this paper, we suggest another tool useful for studying the statistical properties including the fluctuation, the critical behavior, and so on. This is the thermodynamic geometry. It defines a metric on the space of thermodynamic variables. ͑Of course, it has nothing to do with the geometry of space and time.͒ Here, the thermodynamic potential becomes the geometrical potential generating the metric components. The thermodynamic variables constitute the coordinates for the geometry. Details will be given below through the example of the Bañados-Teitelboim-Zanelli ͑BTZ͒ black hole ͓2͔. As is known, the BTZ black hole could play an important role in understanding entropy and some dynamical properties of certain five-and four-dimensional black holes in supergravity theories, because of the U duality between the BTZ black hole and those high-dimensional black holes ͓3͔. For a review see ͓4͔.In general, it is technically difficult to define the zerotemperature critical point, as is the case with the black hole. Conventional definition for the zero-temperature critical point is the point where at least one of the second derivatives of some thermodynamic potential diverges ͓1͔. However, in the language of thermodynamic geometry one can define it unambiguously as the point where the thermodynamic curvature ͑the curvature with respect to the thermodynamic metric͒ diverges. This is based on the fact that thermodynamic curvature is proportional to the correlation volume ͓5͔:where 2 is ...
PurposeTo identify the structural integrity of the healing site after arthroscopic repair of a posterior root tear of the medial meniscus by second-look arthroscopy and to determine the clinical relevance of the findings.Materials and MethodsFrom January 2005 to December 2010, 20 consecutive patients underwent arthroscopic modified pull-out suture repair for a posterior root tear of the medial meniscus. Thirteen patients were available for second-look arthroscopic evaluation. The healing status of the medial meniscus was classified as complete healing, lax healing, scar tissue healing, and failed healing. We evaluated the correlation between the clinical symptoms and second-look arthroscopic findings. Clinical evaluation was based on the Lysholm knee scores and Hospital for Special Surgery (HSS) scores.ResultsThere were 4 cases of complete healing, 4 lax healing, 4 scar tissue healing, and 1 failed healing. The healing status of the repaired meniscus appeared to be related to the clinical symptoms. Patients who achieved complete tissue healing had no complaint. The healing status exhibited no relationship with age, mechanical axis, degree of subluxation, and symptom duration. The mean Lysholm score improved from 34.7 preoperatively to 75.6 at follow-up and the mean HSS score also significantly increased from 33.5 to 82.2.ConclusionsWe achieved 4 complete and 8 partial healing (lax or scar) of the medial meniscus in this retrospective case series of posterior horn meniscus root repairs performed by 1 surgeon. Further research is needed to clarify why all patients showed clinical improvement despite findings of partial healing on second-look arthroscopy.
Microphones for hearing aid systems are required to have high sensitivity, an appropriate bandwidth, and a wide dynamic range. In this paper, a high sensitivity microphone, 4 mm in diameter and using a multilayer graphene-PMMA laminated diaphragm that can be applied in hearing aids, is designed, optimized, and implemented. Typically, polyphenylene sulfide (PPS) has been used for the diaphragm of electret condenser microphones (ECM), and this method provides simple, low cost mass production. Generally, the sensitivity of the commercial 4 mm diameter ECM is about -30 to 35 dB (0 dB = 1 V/Pa). A microphone using a nanometer-thick graphene diaphragm has been found to have higher sensitivity than the conventional ECM. However, nanometer-thick multilayer graphene is vulnerable to large mechanical shocks or high sound pressures, and the practical production of nanometer-thick diaphragms also poses a challenge. However, if a multilayer graphene diaphragm of the same thickness as the conventional ECM is used, displacement during diaphragm vibration will be severely attenuated due to the high elastic modulus of graphene, and the microphone sensitivity will be greatly reduced. In this paper, we fabricate a multilayer graphene/poly(methyl methacrylate) (PMMA) laminated diaphragm with sensitivity higher than that of any other microphones currently available for hearing aids, with the appropriate bandwidth in the auditory range. The high sensitivity arises from the laminated structure of the thin graphene membrane with high elastic modulus and from the PMMA membrane with lower elastic modulus and higher dielectric constant. The optimal thickness ratio of the graphene-PMMA layered diaphragm was studied by both analytical and experimental methods, and then a fabricated diaphragm was assembled in a 4 mm diameter microphone package. The performance of the implemented microphone was evaluated, including the sensitivity and total harmonic distortion. It is demonstrated that the microphone using a multilayer graphene-PMMA diaphragm has an excellent sensitivity of -20 dB and a dynamic range of 90 dB, which is on average 9 dB higher than the microphone using the conventional ECM diaphragm.
We study 'Myers effect' for a bunch of D1-branes with IIB superstrings moving in one direction along the branes. We show that the 'blown-up' configuration is the helical D1-brane, which is self-supported from collapse by the axial momentum flow. The tilting angle of the helix is determined by the number of D1-branes. The radius of the helix is stabilized to a certain value depending on the number of D1-branes and the momentum carried by IIB superstrings. This is actually T-dual version of the supertube recently found as the 'blown-up' configuration of a bunch of IIA superstrings carrying D0-brane charge. It is found that the helical D1 configuration preserves one quarter of the supersymmetry of IIB vacuum.
Our results provide insight into the role of MsrB3 in hearing function and bring us one step closer to hearing restoration as a fundamental therapy.
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