Smectic membranes in motion: approaching the fast limits of x-ray photon correlation spectroscopy

The dynamics of the layer-displacement fluctuations in smectic membranes have been studied by x-ray photon correlation spectroscopy (XPCS). We report transitions from an oscillatory damping regime to simple exponential decay of the fluctuations, both as a function of membrane thickness and upon changing from specular to off-specular scattering. This behavior is in agreement with recent theories. Employing avalanche photodiode detectors and the uniform filling mode of the synchrotron storage ring, the fast limits of XPCS have been explored down to 50 ns.     

Effects of feedback from collimating, focusing, and spot-array generating outcoupler gratings in surface-emitting semiconductor lasers

We experimentally demonstrate that a grating outcoupler used for complex beam shaping (spot-array generation) can produce unintentional optical feedback that severely disturbs the integrated in-plane laser that illuminates the coupler. Simulations show that these outcouplers, in contrast to conventional collimating or focusing outcouplers, tend to produce high levels of feedback in spite of the detuning used to suppress feedback. Further, this feedback is focused to high intensity in the laser gain medium. This focused light acts as a seed for the nonlinear self-focusing that causes wave-front distortion and filamentation, which degrades the beam quality.     

Changes in orcine muscle water characteristics during growth--an in vitro low-field NMR relaxation study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field (1)H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T(2) relaxation data imparted the existence of three distinct water populations, T(2b), T(21), and T(22), with relaxation times of approximately 1-10, 45-120, and 200-500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T(21). It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T(21), during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T(21) time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

Heterocyclization of compounds containing diazo and cyano groups. 6. Theoretical and experimental investigations of cyclization of 2-cyano-2-diazoacetamides to 5-hydroxy-1,2,3-triazole-4-carbonitriles

A series of N-alkyl- and N-aryl-2-cyano-2-diazoacetamides was synthesized by the reaction of 2-amino-2-cyanoacetamides with sodium nitrite in hydrochloric acid. The mechanism of their heteroclectrocyclization to 5-hydroxy-1,2,3-triazoles was investigated kinetically and theoretically by the B3LYP/6-31+G^* method. The conclusion was made on the basis of the determined activation energy of the cyclization process. reaction parameters , and kinetic isotope effects, that there is a difference between the mechanisms of cyclization of the N-alkyl and N-aryl derivatives of 2-cyano-2-diazoacetamide; cyclization of the N-alkyl derivatives takes place by a monorotatory mechanism, while cyclization of the N-aryl derivatives takes place by a mechanism where one of the stages is heteroelectrocyclization of 2-diazoacetimidates.For Communication 5, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 26–41, January, 2000.     

These are the differentials of order

We answer P.-A. Meyer's question ``Qu'est ce qu'une différentielle d'ordre ?'. In fact, we present a general theory of higher order differentials based upon a construction of universal objects for higher order differentials. Applied to successive tangent spaces on a differentiable manifold, our theory gives the higher order differentials of Meyer as well as several new results on differentials on differentiable manifolds. In addition our approach gives a natural explanation of the quite mysterious multiplicative structure on higher order differentials observed by Meyer. Applied to iterations of the first order Kähler differentials our theory gives an algebra of higher order differentials for any smooth scheme. We also observe that much of the recent work on higher order osculation spaces of varieties fits well into the framework of our theory.

     

Trace distributions associated to the Schrödinger operator

Dedicated to Professor Shmuel Agmon     

Performance bounds on multiprocessor scheduling strategies for statically allocated programs

In multiprocessors with static allocation of processes to processors, scheduling can be done locally for each processor. The scheduling strategy may have dramatic effect on the execution time of a parallel program. It is an NP-hard problem to find an optimal schedule, and very little is known of how close the heuristic solutions get.The major result here is a theorem stating that if certain program parameters, which can be obtained from an execution of the program on a single-processor, are known, the execution time of the optimal schedule can be calculated within a factor equal to the largest number of border processes on one processor. Border processes are processes which communicate with other processors. The program parameters are obtained using a previously developed tool.Due to the generality of this theorem, the proof is rather complex because it has to cover a large range of situations. The theorem itself, however, is easy to apply, making it possible to compare the performance of different scheduling strategies with the optimal case. The proof also gives important hints on how to design efficient scheduling algorithms for statically allocated programs.     

On the spontaneous magnetization in the Ising model

The equality between the spontaneous magnetization and the long range order is established for the Ising model with nearest neighbour interactions for low and high temperatures. The proof is presented for the two-dimensional lattice but works also in higher dimensions. The result verifies that the valuem*=(1–(Sh)^–4)^1/8 of the spontaneous magnetization below the critical point calculated by Onsager and Yang is the true value, which has been a long standing open question.     

Diffusion and solubility of methane in polyisobutylene

Diffusion coefficients and solubilities of methane in polyisobutylene have been measured at four temperatures between 102 and 188°C. in the pressure range 23–341 atm. Diffusion coefficients extrapolated to atmospheric pressure range from 1.72 × 10^?6 cm.²/sec. at 102°C. to 1.5 × 10^?5 cm.²/sec. at 188°C. corresponding to an activation energy for diffusion of 8.7 ± 0.4 kcal./mole. Solubilities are small, about one molecule of methane for every forty carbon atoms in the polyisobutylene at 300 atm. partial pressure of methane. Solubilities vary little with temperature, but show an apparent minimum between 127 and 188°C. With improved methods of data analysis, diffusion coefficients and solubilities have been recalculated from previously reported studies on nitrogen in branched polyethylene and methane in branched polyethylene, linear polyethylene, and polystyrene. Recalculated diffusion coefficients are essentially the same as those reported previously, but the recalculated solubilities are decreased from 2 to 30%. The solubilities of all five systems show strong deviations from Henry's law, i.e., increases in partial pressure of methane and nitrogen with respect to solubility exceed linearity. The partial pressure (or fugacity)—solubility data may be interpreted in terms of a sorption model in which sorbed molecules are accommodated in widely dispersed, unoccupied volumes or sites in the polymer. An almost equivalent, solution model in which the first sorbed molecules to enter the polymer are accommodated to a large extent in existing volumes in the polymer, with successively sorbed molecules swelling the polymer to a greater extent (i.e., partial molal volume of sorbed molecules, V ₁, increasing with concentration) can also account for these data.