Brownian dynamics simulation of electrostatically interacting proteins

Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.     

Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space

Diffraction microtomography in coherent light is foreseen as a promising technique to image transparent living samples in three dimensions without staining. Contrary to conventional microscopy with incoherent light, which gives morphological information only, diffraction microtomography makes it possible to obtain the complex optical refractive index of the observed sample by mapping a three-dimensional support in the spatial frequency domain. The technique can be implemented in two configurations, namely, by varying the sample illumination with a fixed sample or by rotating the sample using a fixed illumination. In the literature, only the former method was described in detail. In this report, we precisely derive the three-dimensional frequency support that can be mapped by the sample rotation configuration. We found that, within the first-order Born approximation, the volume of the frequency domain that can be mapped exhibits a missing part, the shape of which resembles that of an apple core. The projection of the diffracted waves in the frequency space onto the set of sphere caps covered by the sample rotation does not allow for a complete mapping of the frequency along the axis of rotation due to the finite radius of the sphere caps. We present simulations of the effects of this missing information on the reconstruction of ideal objects.      

Equations governing the oscillations of a self-gravitating elastic sphere under the influence of gravitational waves

We consider the influence of a plane gravitational wave on the following Newtonian system: a self-gravitating elastic sphere without rotation. We determine the equation governing the elastic oscillations within the framework of the general relativity. We include dissipative processes by using a simple relativistic model of viscoelasticity. If the wavelength is much larger than the dimension of the elastic sphere, we transform these equations into the form derived by Ashby and Dreitlein previously. We also determine the equations governing the elastic oscillations within the framework of the Brans-Dicke scalar-tensor theory of gravitation.     

Effects of rotation on Landau states of electrons on a spherical shell

Based on a previously observed analogy between electromagnetic and non-inertial effects, we investigate the competition between magnetic field and rotation in the quantum motion of an electron constrained to the surface of a sphere. We solve numerically the Schrödinger equation of the problem for the energy eigenvalues and the eigenfunctions and compare the effects of the magnetic field and rotation. We obtain that, for a weak magnetic field, an electron can not distinguish between magnetic field and rotation, since they lead to equivalent behavior. But this is no longer true for strong magnetic fields. However, surprisingly, even though the rotation and magnetic fields play different roles in the electronic properties of the system, when together, each influence of the magnetic field on the energy levels can be separately balanced by rotation. We also show that no matter the intensity of the magnetic field, it is always possible to destroy the Landau levels in the sphere by rotation.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

Accommodation mechanisms for grain boundary sliding as inferred from texture evolution during superplastic deformation

To gain insight into accommodation mechanisms for local stress concentrations produced by grain boundary sliding (GBS), we systematically examined texture evolution within a superplastic magnesium alloy undergoing deformation at a relatively low deformation temperature (at which basal slip is known to be the preferred slip system in magnesium). Although we did observe an overall weakening of the initial basal texture during superplastic deformation, we also observed within the interior of the specimen a convergent evolution that depends on loading direction. We attribute this texture evolution within the bulk to the competing effects of (a) orientation divergence due to grain rotation accompanied by GBS and (b) convergent evolution due to slip, which acts primarily as an accommodation mechanism for GBS. In contrast, at the near-surface, we found the initial orientation to be preserved, indicating that slip accommodation is less important near the surface than within the bulk.     

铵根离子在水和甲醇溶液中的转动机制

Dynamics of ammonium and ammonia in solutions is closely related to the metabolism of ammoniac compounds, therefore plays an important role in various biological processes. NMR measurements indicated that the reorientation dynamics of NH₄⁺ is faster in its aqueous solution than in methanol, which deviates from the Stokes-Einstein-Debye rule since water has higher viscosity than methanol. To address this intriguing issue, we herein study the reorientation dynamics of ammonium ion in both solutions using numerical simulation and an extended cyclic Markov chain model. An evident decoupling between translation and rotation of methanol is observed in simulation, which results in the deviation of reorientation from the Stokes-Einstein-Debye rule. Slower hydrogen bond (HB) switchings of ammonium with methanol comparing to that with water, due to the steric effect of the methyl group, remarkably retards the jump rotation of ammonium. The observations herein provide useful insights into the dynamic behavior of ammonium in the heterogeneous environments including the protein surface or protein channels.     

Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field

An analytic solution is given for classical magnetohydrodynamic (MHD) problem of almost rigid-body rotation of a viscous, conducting spherical layer of liquid in an axisymmetric potential magnetic field. Large-scale flows bounded by rigid spheres are described for the first time in a new approximation. Two problems are solved: (1) in which both spheres are insulators and (2) in which the outer sphere is an insulator and the inner sphere a conductor. Axially symmetric flows and azimuthal magnetic fields are maintained by a slightly faster rotation of the inner sphere. The primary regeneration takes place in the boundary and shear MHD layers. The shear layers, described here for the first time, smooth out the large gradients at the boundaries of the MHD structures encompassed by them. There is essentially no azimuthal magnetic field inside these original structures, which are bounded by potential contours tangent to the spheres. An applied constant magnetic field creates a rigid MHD structure outside an axial cylinder tangent to the inner sphere. Inside the cylinder the rotation is faster and the meridional flux depends on height. A magnetic dipole forms a structure tangent to the outer equator. Outside the structure, the rotation is also rigid-body when both spheres are insulators. When a conducting sphere is present, the liquid rotates differentially everywhere, while near the axis and inside the MHD structure, it rotates even faster than the inner sphere. The last example of a general solution is a quadrupole magnetic field. In this case, two equatorially symmetric MHD structures are formed which rotate together with the inner sphere. Outside the structures, as in the most general case, the rotation is differential, the azimuthal magnetic field falls off as the first power of the applied field, and the meridional flux falls off as the square of the field in the first problem, and as the cube in the second. Zh. éksp. Teor. Fiz. 112, 2056–2078 (December 1997)     

Reduction of energy-loss “ghost structures” observed in electrostatic deflection type electron analysers

Ghost lines due to electron reflections occurring on the wall plates of an electrostatic deflection type electron analyser are observed and studied as a function of electron intensity and energy, in the kinetic energy range 25–40keV. The model by Froitzheim et al. [3] is found to be in good agreement with our measurements. A new method, based on the angular separation of the ghost beam from the analysed beam, is used to reduce the ghost structure intensity by a factor of about 300.     

Thomas rotation and polarized light: A non-abelian geometric phase in optics

We describe anon-abelian Berry phase in polarization optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarized light. The analogy permits a simple optical realization of the non-abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.     

A Geometrical Representation of Entanglement as Internal Constraint

We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a “rotation” and “stretching” of the sphere representing the states of the second particle as measurements are performed on the first particle. In the case of the singlet state entanglement can be represented by a real physical constraint, namely by means of a rigid rod.     

Application of the electrostatic mean value theorem to electrostatic sensor electrodes

We present a method for approximating the potential of conducting objects due to a known electrostatic source. The method involves averaging the incident potential over the conductor surface or volume region, which is known to give the exact value for a perfectly conducting sphere. The method is extended to spheroidal geometries, both prolate and oblate, to study the error incurred for deviations from the spherical case. Exact values for the spheroid potentials are derived and compared with those obtained by the mean value approximations. The result for the oblate spheroid is extended to the case of a two-dimensional electrostatic disk. The approximations are proposed as a method for predicting the potential of conducting electrodes used with electrostatic sensors for the measurement of electrostatic field disturbances. In this regard, the mean value approximation is applied to determine the source to electrode mutual capacitance, which is implemented in the model for the sensor system. Electrostatic disk electrodes are used with an electrostatic disturbance sensor to experimentally validate the application of the mean value approximation.     

Nucleation and Growth of Magnetron-Sputtered Ag Nanoparticles as Witnessed by Time-Resolved Small Angle X-Ray Scattering

Kinetic aspects of the synthesis of Ag nanoparticles (NPs) by magnetron sputtering are studied by in situ and time-resolved small angle X-ray scattering (SAXS). Part of the NPs are found to become confined within a capture zone at 1–10 mm from the surface of the target and circumscribed by the plasma ring. Three regimes of the NP growth are identified: 1) early growth at which the average NP diameter rapidly increases to 90 nm; 2) cycling instabilities at which the SAXS signal periodically fluctuates either due to expelling of large NPs from the capture zone or due to the axial rotation of the NP cloud; and 3) steady-state synthesis at which stable synthesis of the NPs is achieved. The NP confinement within the capture zone is driven by the balance of forces, the electrostatic force being dominant. On reaching the critical size, large NPs acquire an excessive charge and become expelled from the capture zone via the electrostatic interactions. As a result, significant NP deposits are formed on the inner walls of the aggregation chamber as well as in the central area of the target.     

Time-domain observation of optical pulse propagation in whispering-gallery modes of glass spheres

We report picosecond time-resolved measurements of optical pulse propagation in dielectric spheres (8, 10, and 26 mm in diameter) for which the pulse duration ( approximately 2 ps) was short compared with the equatorial round-trip time within the sphere. A size-independent buildup of the leakage intensity in terms of the number of round trips was observed for each of the spheres, as were damped low-frequency oscillations superimposed upon the pulse ringdown envelope. These features of the data are interpreted as resulting from perturbative coupling of eigenmodes of the sphere and trajectory precession near the observation region.     

Structure, dsingle-particle and many-particle coefficients of Lennard—Jones liquid Al

We investigate the effects of temperature and density on the single-particle and many-particle coefficients as well as on the structures of homogenous systems in which the particles are assumed to interact via a continuous soft sphere potential in the microcanonical ensemble. The pair distribution function and therefore the structures of the systems studied are affected by temperature close to and above the melting point through migrations of atoms from the first shell in the pair distribution function. The dynamics of atomic pairs in the short-time regime in liquid aluminium may be said to be governed by the potential of mean force, which depends on the static structure of liquid Al at all investigated temperatures. A polynomial dependence ofD on density and temperature was observed in contradiction to Arrhenius law. The shear viscosities of the systems studied are largely nonlinear. It was observed that the soft sphere potential used in our calculations overestimates the Stoke-Einstein relation.     

Time-dependent interaction across two conducting spheres in an applied electrostatic field

Charged particles exist widely in variety of technological areas as well as in nature. Even a weak charge on the particles can significantly influence their electric interaction. We investigated the phenomenon of time-dependent electric interaction between two conducting spheres in an electrostatic field. A mirror-image method was developed to analyze this system, and the fundamental role of the charges on the spheres was studied. We concluded that charges conducted to the lower sphere through the alumina tube used in our system play a main role in determining the time-dependent interaction, whereas the influence from air ions is negligible.     

Circular dichroism and viscosity studies of gelatin with anionic surfactant,SDBS

The interaction of SDBS in aqueous gelatin solutions is studied above the gelation temperature by viscosity and circular dichroism (CD) measurements. The steep rise in the relative viscosity of the system could be due the structural transitions leading to micellar growth of higher orders, which is supported by CD measurements. The circular dichroism spectra indicated that gelatin helped in inducing the sphere → rod transition, without suffering any conformational changes within it. The large changes in viscosity over the concentration range studied points to the strong molecular interactions in gelatin–SDBS system and its dependence on [SDBS]. CD spectra showed an increase in ellipticity, suggesting that the micelle can either bind intra molecularly, i.e. within a gelatin molecule, or it can bind cooperatively with two or more molecules to form a large complex. The findings are particularly significant in terms of the head group contribution, hydrophobic interaction and formation of formulated complexes.     

Polymer and surface roughness effects on the drag crisis for falling spheres

We make time resolved velocity measurements of steel spheres in free fall through liquid using a continuous ultrasound technique. We explore two different ways to induce large changes in drag on the spheres: 1) a small quantity of viscoelastic polymer added to water and 2) altering the surface of the sphere. Low concentration polymer solutions and/or a pattern of grooves in the sphere surface induce an early drag crisis, which may reduce drag by more than 50% compared to smooth spheres in pure water. On the other hand, random surface roughness and/or high concentration polymer solutions reduce drag progressively and suppress the drag crisis. We also present a qualititative argument which ties the drag reduction observed in low concentration polymer solutions to the Weissenberg number and normal stress difference.     

Thermoelectric detection of ferromagnetic resonance of a nanoscale ferromagnet

We present thermoelectric measurements of the heat dissipated due to ferromagnetic resonance of a Permalloy strip. A microwave magnetic field, produced by an on-chip coplanar strip waveguide, is used to drive the magnetization precession. The generated heat is detected via Seebeck measurements on a thermocouple connected to the ferromagnet. The observed resonance peak shape is in agreement with the Landau-Lifshitz-Gilbert equation and is compared with thermoelectric finite-element modeling. Unlike other methods, this technique is not restricted to electrically conductive media and is therefore also applicable to for instance ferromagnetic insulators.     

Extending the Fast Multipole Method for Charges inside a Dielectric Sphere in an Ionic Solvent: High Order Image Approximations for Reaction Fields

As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa < 1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10⁻⁴ relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.