Maximum Caliber: a variational approach applied to two-state dynamics

We show how to apply a general theoretical approach to nonequilibrium statistical mechanics, called Maximum Caliber, originally suggested by E. T. Jaynes [Annu. Rev. Phys. Chem. 31, 579 (1980)], to a problem of two-state dynamics. Maximum Caliber is a variational principle for dynamics in the same spirit that Maximum Entropy is a variational principle for equilibrium statistical mechanics. The central idea is to compute a dynamical partition function, a sum of weights over all microscopic paths, rather than over microstates. We illustrate the method on the simple problem of two-state dynamics, A<-->B, first for a single particle, then for M particles. Maximum Caliber gives a unified framework for deriving all the relevant dynamical properties, including the microtrajectories and all the moments of the time-dependent probability density. While it can readily be used to derive the traditional master equation and the Langevin results, it goes beyond them in also giving trajectory information. For example, we derive the Langevin noise distribution rather than assuming it. As a general approach to solving nonequilibrium statistical mechanics dynamical problems, Maximum Caliber has some advantages: (1) It is partition-function-based, so we can draw insights from similarities to equilibrium statistical mechanics. (2) It is trajectory-based, so it gives more dynamical information than population-based approaches like master equations; this is particularly important for few-particle and single-molecule systems. (3) It gives an unambiguous way to relate flows to forces, which has traditionally posed challenges. (4) Like Maximum Entropy, it may be useful for data analysis, specifically for time-dependent phenomena.     

Nitrido-Sodalithe. II. Synthese,Struktur und Eigenschaften von M(6+(y/2)–x)H2x[P12N24]Zy mit M = Fe,Co, Ni,Mn; Z = Cl,Br, I; 0 ≤ x ≤ 4; y ≤ 2

Nitrido-Sodalites. II. Synthesis, Crystal Structure, and Properties of M_{(6+(y/2)–x)}H_2x[P₁₂N₂₄]Z_y with M = Fe, Co, Ni, Mn; Z = Cl, Br, I; 0 ≤ x ≤ 4; y ≤ 2 The nitrido sodalites M_{(6+(y/2)–x)}H_2x[P₁₂N₂₄]Z_y with M = Fe, Co, Ni, Mn; Z = Cl, Br, I; 0 ≤ x ≤ 4; y ≤ 2 are obtained by the reaction of HPN₂ or [PN(NH₂)₂]₃ with the metal halogenide MZ₂ (T = 700°C). The compounds are isotypic to Zn_(7–x)H_2x[P₁₂N₂₄]Cl₂. An increase of the ionic radii of the cations or anions results in an expansion of the lattice which is caused by an increase of the P? N? P angle. The influence of the cation is more dominant than that of the anion. By reacting [PN(NH₂)₂]₃ with metal halogenide (MZ₂) hydrogen free, X-ray amorphous products are obtained. The formation of the chloride-containing P? N-sodalite in this reaction begins at temperatures below 450°C.     

Bismuth Tri‐ and Tetraarylcarboxylates: Crystal Structures,In Situ X‐ray Diffraction,Intermediates and Luminescence

A systematic investigation of the systems Bi³⁺/carboxylic acid/HNO₃ for the tri‐ and tetracarboxylic acids pyromellitic acid (H₄Pyr), trimellitic acid (H₃Tri) and trimesic acid (H₃BTC) acid led to the discovery of five new bismuth carboxylates. Structural characterisation allowed the influence of the linker geometry and the Bi³⁺:linker molar ratio in the starting solution on the crystal structure to be determined. The crystallisation of three selected compounds was investigated by in situ energy‐dispersive X‐ray diffraction. Three new crystalline intermediates were observed within minutes, and two of them could be isolated by quenching of the reaction mixture. Their crystal structures were determined from laboratory and synchrotron X‐ray powder diffraction data and allowed a possible reaction pathway to be established. In depth characterisation of the luminescence properties of the three bismuth pyromellate compounds was carried out. Fluorescence and phosphorescence could be assigned to (mainly) ligand‐ and metal‐based transitions. The polymorphs of Bi(HPyr) exhibit different luminescence properties, although their structures are very similar. Surprisingly, doping of the three host structures with Eu³⁺ and Tb³⁺ ions was only successful for one of the polymorphs.     

Observation of phase defects in quasi-two-dimensional Bose-Einstein condensates

We have observed phase defects in quasi-2D Bose-Einstein condensates close to the condensation temperature. Either a single or several equally spaced condensates are produced by selectively evaporating the sites of a 1D optical lattice. When several clouds are released from the lattice and allowed to overlap, dislocation lines in the interference patterns reveal nontrivial phase defects.     

Comparison of speech production in upright and supine position

Speech is usually produced in an upright sitting or standing posture. Measurements and judgments of speech may be made in conditions requiring a supine position, however. These conditions include MRI recordings, and oral procedures, such as, adjustments to dental appliances, medical and surgical procedures. It is of interest, therefore, to see whether gravity has strong or systematic effects on tongue behavior. In the present study, 13 subjects repeated several words, which contained extreme consonant and vowel tongue positions, during upright and supine condition. Ultrasound imaging provided midsagittal tongue contours, in each condition, for comparison. A neck brace was used to stabilize transducer placement and the palate was used as a physiological reference to register the data sets. Results showed a significant subject effect. In supine position the tongue was more posterior than upright for seven subjects, more anterior for two subjects and varied by phoneme for four subjects. However, there was no significant phoneme effect. The direction of change and the amount of change were not directly related. Most subjects had small upright-supine differences. The largest differences, less than 3 mm on average, were in the posterior tongue.     

A comparative study of the electric giant dipole resonance of 24−26Mg

The electric giant dipole resonance of ^24?26Mg has been explored up to 30 MeV excitation energy with bremsstrahlung. ΔE, E spectra of charged photo-particles and spectra of prompt deexcitation γ-rays from excited residual nuclear states were obtained at various bremsstrahlung endpoint energies. The ²⁵Mg(γ, p₀), (γ, d), ^24,25Mg(γ, α) differential cross sections as well as ^24?26Mg(γ, xγ′) integrated cross sections are presented. The results are discussed in terms of one-particle, one-hole excitations and isospin composition of giant resonance states. A comparison with calculations for ²⁴Mg gives poor agreement. Excitations from deeper shells were found in the giant dipole resonance of ²⁴Mg, but do not seem to be concentrated at higher energies. In ²⁵Mg, only weak excitations of this kind were found, and they are completely absent in ²⁶Mg.