Bounded speed of propagation for solutions to radiative transfer equations

The Radiative Transfer Equation is the nonlinear transport equation

Generalized solutions of a class of nuclear-space-valued stochastic evolution equations

Generalized solutions are defined for stochastic evolution equations of the formdY _t =A ^* Y _t dt + dZ _t on the nuclear triplel(R ^d ) L²(R ^d ) l(R ^d ), whereA does not mapl(R ^d ) into itself. One case which is treated in detail involvesA = –(–) ^/2 ,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico.     

Self-assembled peptide tubelets with 7 A pores

Here we report the preparation and structural characteristics of self-assembling peptide tubelets composed of 32-membered rings formed of alternating alpha-amino acids and cis-3-aminocyclohexanecarboxylic acids. The tubelets possess a partial hydrophobic core environment, provided by the projection of the cyclohexane C2 methylene moiety into the lumen, and a Van der Waals pore diameter of about 7 A.     

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.     

Structural Determination of Bis-histidinopeptide Zinc Complexes by 15N NMR (HMBC) Spectra

Polynitrogen receptors such as bis-histidine peptides possess strong ability to bind metals, which play much important roles in medicinal, bioinorganic, bioorganic, biomimetic and supramolecular chemistry. In order to investigate the interaction of these hosts with a variety of neutral, cationic and anionic guests, several techniques, for example, NMR,potentiometric tirations and monocrystal X-ray diffraction have been employed. Among them NMR is a powerful technique for unraveling the structure of polynitrogen receptors as long as they are in solution where the rapid tumbling of molecules averages out the anisotropies such as chemical shift and dipole-dipole interactions. General 1H NMR approach has been widely used for the study of host-guest interaction, but it is difficult for the accurate measurement in complexes structures, particularly metal complexes structures in which how the polynitrogen receptors bind metal, and which nitrogen binds metal and so on.     

Supramolecular helical mesomorphic polymers. Chiral induction through H-bonding

The work described here concerns a challenge of general interest in supramolecular chemistry: the achievement of chiral helical organizations with controlled structures. This work provides a strategy to obtain supramolecular polymers in which a chiral helical conformation has been induced by a noncovalent association, that is, through hydrogen bonding. Polycatenar 2,4,6-triarylamino-1,3,5-triazines, which organize into columnar mesophases and are susceptible to H-bonding interactions, were chosen as a starting point to build up the chiral supramolecular structure. The stacking of these mesogens has been forced to wind in a helical way by means of H-bond association with (R)-3-methyladipic acid, within the mesophase. The optically active columnar organization has been studied in depth by optical microscopy, differential scanning calorimetry (DSC), X-ray diffraction, and circular dichroism. Formation of stable complexes between the triazine units and (R)-3-methyladipic acid has also been investigated by means of NMR diffusion-ordered spectroscopy (DOSY) experiments in chloroform.     

Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9–10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the ‘1’ and ‘0’ basis states. For lower magnetic fields (B < 0.1 T), and lower frequencies (<2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.

We show that a sizeable electronuclear entanglement of the S = 1/2 and I = 7/2 spins of a vanadyl porphyrin provides the conditions to act as a universal 4-qubit processor, and thus implement quantum error correction at the molecular level.     

Chemical, structural, and thermal properties of Zn(II)-Cr(III) layered double hydroxides intercalated with sulfated and sulfonated surfactants

Zn(II)-Cr(III)-LDHs (layered double hydroxides) containing sulfated or sulfonated surfactants as the interlamellar anion were synthesized by the coprecipitation method. The syntheses were conducted under various different experimental conditions, such as the Zn : Cr ratio, pH, and aging time. In each of the prepared materials, unlike previously reported data, the interlayer anion arrangement did not change, being consistent with a perpendicular monolayer. The thermal decomposition process of the prepared materials was studied by a set of analysis methods, such as TG/DTA, TG/MS, PXRD, and FT-IR. From the results obtained it was possible to conclude that, in an air atmosphere, the anions decomposed by a partial combustion, leading to the formation of sulfide. The results also showed that sulfonated surfactants containing LDHs are much more stable than those containing sulfated surfactants. A mechanism was proposed for the thermal decomposition of such LDHs based on the experimental results.     

A study of two-electron quantum dot spectrum using discrete variable representation method

A variational method called discrete variable representation is applied to study the energy spectra of two interacting electrons in a quantum dot with a three-dimensional anisotropic harmonic confinement potential. This method, applied originally to problems in molecular physics and theoretical chemistry, is here used to solve the eigenvalue equation to relative motion between the electrons. The two-electron quantum dot spectrum is determined then with a precision of at least six digits. Moreover, the electron correlation energies for various potential confinement parameters are investigated for singlet and triplet states. When possible, the present results are compared with the available theoretical values.