Microscopic theory of quantum fluid at nonzero temperature. The momentum distribution,liquid-structure factor and ground-state energy of liquid4He

Summary Employing theU-matrix theory in the present form we have presented a microscopic theory of an interactingN-boson system at nonzero temperature. The Hamiltonian includes a term describing the external influence, a term for a two-particle interaction and one pertaining to the dipole-type interaction. To study the ground state of liquid⁴He, only the two-particle interaction is included. Based on scattering data, we have deduced the two-particle potential function. With that we calculate numerically the momentum atT=1.1 K for several sets of parameters. It is shown that the theoretical curves agree well with the observed results. The corresponding liquid-structure-factor curves fit the measured data very well and the best result for the ground-state energy is −7.12K.

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Riassunto Impiegando la teoria della matriceU nella forma presente, abbiamo presentato una teoria microscopica di un sistema interagente diN bosoni a temperatura non nulla. L'hamiltoniana include un termine che descrive l'influenza esterna, un termine per un'interazione a 2 particelle e une che riguarda l'interazione di tipo dipolare. Per studiare lo stato fondamentale dell'⁴He liquido s'include solo l'interazione a 2 particelle. Basandoci su dati di scattering, abbiamo dedotto la funzione potenziale a 2 particelle. Con quella, calcoliamo numericamente la distribuzione dell'impulso aT=1.1K per diversi gruppi di parametri. Si mostra che le curve teoriche sono in buon accordo con i risultati osservati. Le corrispondenti curve del fattore di struttura del liquido si adattano benissimo ai dati misurati e il risultato migliore per l'energia dello stato fondamentale è − 7.12K.

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Резюме Используь теориюU-матрицы, мы предлагаем микроскопическую теорию взаимодеюствующейN-бозонной системы при ненулевых температурах. Гамильтониан включает член, описывающий внешнее влияние, член двух-частичного взаимодействия и член, относящийся к дипольному типу взаимодействия. При исследовании основного состояния шидкого⁴He учитяватся только двух-частичное взаимодействие. Основываясь на данных по рассеянию, мы выводим двух-частичную потенциальную функцию. Мы численно определяем распределение по импульсам приT=1.1K для некоторых систем параметров. Показывается, что теоретические кривые согласуются с наблюденными результатами. Соответст вующий структурный фактор зидкости хорошо согласуется с экспериментальными данными. Полученная величина энергии основного состояния составляет −7.12 K.

     

On orthogonal matrices with constant diagonal

In connection with the problem of finding the best projections of k-dimensional spaces embedded in n-dimensional spaces Hermann König asked: Given m∈$\text{R}$ and n∈$\text{N}$, are there n×n matrices C=(c_ij), i, j=1,…,n, such that c_ii=m for all i, |c_ij|=1 for i≠j, and C²=(m²+n?1)I_n? König was especially interested in symmetric C, and we find some families of matrices satisfying this condition. We also find some families of matrices satisfying the less restrictive condition CC^T=(m²+n?1)I_n.     

Non-skew symmetric orthogonal matrices with constant diagonals

A matrix C of order n is orthogonal if CC^T=dI. In this paper, we restrict the study to orthogonal matrices with a constant m > 1 on the diagonal and ±1's off the diagonal. It is observed that all skew symmetric orthogonal matrices of this type are constructed from skew symmetric Hadamard matrices and vice versa. Some simple necessary conditions for the existence of non-skew orthogonal matrices are derived. Two basic construction techniques for non-skew orthogonal matrices are given. Several families of non-skew orthogonal matrices are constructed by applying the basic techniques to well-known combinatorial objects like balanced incomplete block designs. It is also shown that if m is even and n=0 (mod 4), then an orthogonal matrix must be skew symmetric. The structure of a non-skew orthogonal matrix in the special case of m odd,n=2 (mod 4) and m?1/6n is also studied in detail. Finally, a list of cases with n?50 is given where the existence of non-skew orthogonal matrices are unknown.     

Transverse momentum distribution of partons in QCD

The renormalization group approach is applied to the study of transverse momentum distribution of partons in QCD. We generalize the method of Altarelli and Parisi to obtain a formula for the mean squared average transverse momentum as a function of Q² and x, the virtual photon mass squared and the longitudinal momentum fraction of the parton. For large Q², it decreases with x in addition to the expected increase with Q². This x-dependence reduces substantially the transverse momentum of massive μ-pairs produced by hadronic collisions from its linear dependence on $\text{(}\text{Q}{}^2\text{ln}\text{Q}{}^2\text{)}\text{1}\text{2}$.     

Structural study of DNA condensation induced by novel phosphorylcholine-based copolymers for gene delivery and relevance to DNA protection

Poly[2-(dimethylamino)ethyl methacrylate-b-2-methacryloyloxyethyl phosphorylcholine] (DMA-MPC) is currently under investigation as a new vector candidate for gene therapy. The DMA block has been previously demonstrated to condense DNA effectively. The MPC block contains a phosphorylcholine (PC) headgroup, which can be found naturally in the outside of the cell membrane. This PC-based polymer is extremely hydrophilic and acts as a biocompatible steric stabilizer. In this study, we assess in detail the morphologies of DNA complexes obtained using the diblock copolymer series DMA(x)MPC30 (where the mean degree of polymerization of the MPC block was fixed at 30 and the DMA block length was systematically varied) using transmission electron microscopy (TEM) and liquid atomic force microscopy (AFM). Both techniques indicate more compact complex morphologies (more efficient condensation) as the length of the cationic DMA block increases. However, the detailed morphologies of the DMA(x)MPC30-DNA complexes observed by TEM in vacuo and by AFM in aqueous medium are different. This phenomena is believed to be related to the highly hydrophilic nature of the MPC block. TEM studies revealed that the morphology of the complexes changes from loosely condensed structures to highly condensed rods, toroids, and oval-shaped particles as the DMA moiety increases. In contrast, morphological changes from plectonemic loops to flower-like and rectangular block-like structures, with an increase in highly condensed central regions, are observed by in situ AFM studies. The relative population of each structure is clearly dependent on the polymer molecular composition. Enzymatic degradation assays revealed that only the DMA homopolymer provided effective DNA protection against DNase I degradation, while other highly condensed copolymer complexes, as judged from TEM and gel electrophoresis, only partially protected the DNA. However, AFM images indicated that the same highly condensed complexes have less condensed regions, which we believe to be the initiation sites for enzymatic attack. This indicates that the open structures observed by AFM of the DNA complexation by the DMA(x)MPC30 copolymer series are closer to in vivo morphology when compared to TEM.     

Hydrogen-bonded anionic rosette networks assembled with guanidinium and C3-symmetric oxoanion building blocks

Two premeditated anionic rosette-layer architectures have been constructed using guanidinium and ubiquitous C3-symmetric oxoanions that carry unequal charges, employing bulky organic cations as interlayer templates. The undulate guanidinium-carbonate network occurs in 4[(C2H5)4N+].8[C(NH2)3+].3(CO3)2-.3(C2O4)2-.2H2O, in which the disordered (C2H5)4N+ guests are accommodated in pouches and channels within a complex three-dimensional hydrogen-bonded host framework. In [(C2H5)4N+]2.[C(NH2)3+].[1,3,5-C3H3(COO-)3].6H2O, ordered (C2H5)4N+ cations are sandwiched between planar guanidinium-trimesate host layers whose honeycomb cavities are tightly fitted with flattened-chair (H2O)6 clusters of symmetry 2.     

Anharmonic phonons and structural phase transitions

Exact results for the order parameter and the meansquare displacement as functions of temperature are given for a quantum interacting phonon Hamiltonian with quartic anharmonicities. Upper bounds for the transition temperature are also derived. Approximate theories including the mean field approximation, the random phase approximation (or quasiharmonic approximation) and the self consistent approach (using Blume-Hubbard scheme) are compared with our exact results. The mean field approximation for the meansquare displacement is found to violate our bounds.The classical value is shown to form a lower bound for the kinetic energy. Upper bounds for the kinetic energy are obtained showing the region of temperature in which the use of the high temperature expansion of the fluctuation-dissipation theorem is justified. Comparison of the Hamiltonian and our results with electron-paramagnetic-resonance measurements are discussed.     

Fatty acids. IV. Synthesis of all the dimethylene-interrupted methyl octadecadiynoates and a study of their gas-liquid chromatographic properties.

All the dimethylene-interrupted methyl octadecadiynoates have been synthesised and the gas-liquid chromatographic behaviour of these isomers was studied on polar [Carbowax 20M, FFAP, DEGA, DEGS and Silar 10C (recently renamed as Apolar 10C)], semi-polar (XE-60) and non-polar (SE-30, OV-101 and Apiezon L) stationary phases. The possibility of identification and separation of these isomers is discussed. The delta3a,7a isomer was found to decompose on most polar phases and the delta2a,6a isomer could not be eluted from the Carbowax 20M phase.