Thermoelastic Damping in Micro- and Nano-Mechanical Systems

The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electro-mechanical systems (MEMS and NEMS). The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener's well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.Comment: 10 pages. Submitted to Phys. Rev.

Coarse-Graining the Lin-Maldacena Geometries

The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.Comment: 29 pages, LaTeX, 3 figures; v2 references adde

Quantum geometry and gravitational entropy

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.Comment: 29 pages, 2 figures; references adde

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte

Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval

[[abstract]]In this paper, the vectorial Sturm-Liouville operator L Q =−d 2 dx 2 +Q(x) is considered, where Q(x) is an integrable m×m matrix-valued function defined on the interval [0,π] . The authors prove that m 2 +1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if Q(x) is real symmetric, then m(m+1) 2 +1 characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then m 2 +1 spectral data can determine Q(x) uniquely.[[notice]]補正完畢[[incitationindex]]SCI[[cooperationtype]]國外[[booktype]]電子

Corneal perforation in ocular graft-versus-host disease

PURPOSE: Corneal perforation is a rare, vision-threatening complication of ocular graft-versus-host disease (GVHD) and is not well understood. Our objective was to examine the clinical disease course and histopathologic correlation in patients who progressed to this outcome. METHODS: This study is a retrospective case series from four academic centers in the United States. All patients received a hematopoietic stem cell transplant (HSCT) prior to developing ocular GVHD. Variables of interest included patient demographics, time interval between HSCT and ocular events, visual acuity throughout clinical course, corticosteroid and infection prophylaxis regimens at time of corneal perforation, medical/surgical interventions, and histopathology. RESULTS: Fourteen eyes from 14 patients were analyzed. Most patients were male (86%) and Caucasian (86%), and average age at time of hematopoietic stem cell transplant was 47 years. The mean interval between hematopoietic stem cell transplant and diagnosis of ocular graft-versus-host disease was 9.5 months, and between hematopoietic stem cell transplant and corneal perforation was 37 months. Initial best-corrected visual acuity was 20/40 or better in 9 eyes, and all eyes had moderate or poor visual outcomes despite aggressive management, including corneal gluing in all patients followed by keratoplasty in 8 patients. The mean follow-up after perforation was 34 months (range 2-140 months). Oral prednisone was used prior to perforation in 11 patients (79%). On histopathology, representative specimens in the acute phase demonstrated ulcerative keratitis with perforation but minimal inflammatory cells and no microorganisms, consistent with sterile corneal melt in the setting of immunosuppression; and in the healed phase, filling in of the perforation site with fibrous scar. CONCLUSIONS: In these patients, an extended time interval was identified between the diagnosis of ocular graft-versus-host disease and corneal perforation. This represents a critical window to potentially prevent this devastating outcome. Further study is required to identify those patients at greatest risk as well as to optimize prevention strategies

Strings on Bubbling Geometries

We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.Comment: 41 pages, 12 figures, published version in JHE

320 Gb/s Nyquist OTDM received by polarization-insensitive time-domain OFT

We have demonstrated the generation of a 320 Gb/s Nyquist-OTDM signal by rectangular filtering on an RZ-OTDM signal with the filter bandwidth (320 GHz) equal to the baud rate (320 Gbaud) and the reception of such a Nyquist-OTDM signal using polarization-insensitive time-domain optical Fourier transformation (TD-OFT) followed by passive filtering. After the time-to-frequency mapping in the TD-OFT, the Nyquist-OTDM signal with its characteristic sinc-shaped time-domain trace is converted into an orthogonal frequency division multiplexing (OFDM) signal with sinc-shaped spectra for each subcarrier. The subcarrier frequency spacing of the converted OFDM signal is designed to be larger than the transform-limited case, here 10 times greater than the symbol rate of each subcarrier. Therefore, only passive filtering is needed to extract the subcarriers of the converted OFDM signal. In addition, a polarization diversity scheme is used in the four-wave mixing (FWM) based TD-OFT, and less than 0.5 dB polarization sensitivity is demonstrated in the OTDM receiver.</p