Magnetohydrodynamics with Applications to the Study of Electrolysis and Turbulence

The equations of magnetohydrodynamics (MHD) are presented as continual modeling for slow motions. The original equations of the MHD environment are linearized, reduced, and applied to the analysis of environments characterized by the phenomena of electrolysis and turbulence. A continual approach for electrolysis and turbulence is presented, and the real-life ongoing studies are considering local models. The formulation of the problem and its analysis are presented as the density of the MHD-field decreases from a flat wall. Experimental studies with respect to propulsion devices in sea water are characterized.

Deuteron Chemical Exchange Saturation Transfer for the Detection of Slow Motions in Rotating Solids

We utilized the 2H Chemical Exchange Saturation Transfer (CEST) technique under magic angle spinning (MAS) conditions to demonstrate the feasibility of the method for studies of slow motions in the solid state. For the quadrupolar anisotropic interaction, the essence of CEST is to scan the saturation pattern over a range of offsets corresponding to the entire spectral region(s) for all conformational states involved, which translates into a range of −60–+ 60 kHz for methyl groups. Rotary resonances occur when the offsets are at half-and full-integer of the MAS rates. The choice of the optimal MAS rate is governed by the condition to reduce the number of rotary resonances in the CEST profile patterns and retain a sufficiently large quadrupolar interaction active under MAS to maintain sensitivity to motions. As examples, we applied this technique to a well-known model compound dimethyl-sulfone (DMS) as well as amyloid-β fibrils selectively deuterated at a single methyl group of A2 belonging to the disordered domain. It is demonstrated that the obtained exchange rate between the two rotameric states of DMS at elevated temperatures fell within known ranges and the fitted model parameters for the fibrils agree well with the previously obtained value using static 2H NMR techniques. Additionally, for the fibrils we have observed characteristic broadening of rotary resonances in the presence of conformational exchange, which provides implications for model selection and refinement. This work sets the stage for future potential extensions of the 2H CEST under MAS technique to multiple-labeled samples in small molecules and proteins.

Slow Motions of A Circular Cylinder in a Liquid after a Separation Impact

The plane problem of the separation impact of a circular cylinder completely immersed in an ideal incompressible heavy liquid is considered. It is assumed that after the impact, the cylinder moves horizontally at a constant speed. An attached cavity is formed behind the body, the shape of which depends on the physical and geometric parameters of the problem. It is required to study the process of collapse of the cavity at low velocities of the cylinder, which correspond to small Froude numbers. The solution to the problem is constructed using asymptotic expansions in a small parameter, which is the dimensionless speed of the cylinder. In this case, as the characteristic speed of the problem, a value is chosen equal to the square root of the product of the radius of the cylinder and the acceleration of gravity. As a result of this choice, the indicated small parameter coincides with the Froude number, and therefore, we can assume that the asymptotics of the problem is constructed for small Froude numbers. In the leading asymptotic approximation, a mixed problem of potential theory with one-sided constraints on the surface of the body is formulated. With its help, the position of the separation points at each moment of time is determined and the time of collapse of a thin cavity is found. The results obtained can be used to solve practical problems of ship hydrodynamics, in which it is necessary to take into account the phenomenon of cavitation.

RESEARCH OF VIBROREOLOGICAL MODELS OF LAYER OF BULK ENVIRONMENT

Vibration mechanics and vibroreology play an important role in the new section of applied vibration theory formed in recent years - the theory of vibration processes and devices. This theory studies the patterns of excitation and vibration in different mechanical systems; it also includes the theory of machines in which vibration is used to achieve useful goals. Based on the considered models, it was possible to describe the chaotic motion of the bulk medium layer over the vibrating plane. Such movements, well known for liquids, have indeed been observed in the case of a bulk medium, which serves as another confirmation of the possibility of modeling slow motions of a bulk medium during vibration in the form of viscous fluid motions (of course, with the above caveats and additions). When studying the described simplest models, motion (including we are interested in slow motion) can be found by directly using the solution of the problem of vibrotransportation of the body (particles). The value of this approach is determined, however, by the possibility of its application for an approximate solution in more complex cases. In the study of slow motions of bodies interacting with both the forces of dry friction and collisions, these interactions can be modeled by the forces of viscous friction, taking into account the driving vibration force. This leads to the following vibroreological approach to modeling the behavior of the bulk medium in vibrating trays and vessels. Of all the considered models, the most promising is the model of the behavior of the bulk medium under the influence of vibration in the form of a viscous medium.The described models can be used when considering a practically important task of vibration penetration into a free medium.

Slow, heterogeneous NFκB single molecule conformational dynamics and implications for function

The transcription factor NFκB (RelA-p50) is a multidomain protein that binds DNA and its inhibitor, IκBα with apparently different conformations. We used single-molecule FRET to characterize the interdomain motions of the N-terminal DNA-binding domains in the free protein and also in various bound states. Several surprising results emerged from this study. First, the domains moved with respect to each other on several widely different timescales from hundreds of milliseconds to minutes. The free NFκB displayed stochastic motions leading to a broad distribution of states, ranging from very low-FRET states to high-FRET states. Varying the ionic strength altered the slow motions suggesting that they may be due to different weak electrostatic interactions between the domains creating a rugged energy landscape. Third, the DNA-binding domains continued to be mobile even when the protein was bound to its cognate DNA, but in this case the majority of the states were either high-FRET, a state expected from the available x-ray structures, or low-FRET, a state consistent with one of the DNA-binding domains dissociated. The fluctuations of the DNA-bound states were of lower amplitude and slightly faster frequency. Fourth, the inhibitor, IκBα freezes the domains into a low-FRET state, expected to be incapable of binding DNA. Neutralization of five acidic residues in the IκBα PEST sequence, which was previously shown to impair IκBαs ability to strip NFκB from the DNA, also impaired its ability to freeze the domains into a low-FRET state indicating that the freezing of motions of the DNA-binding domains is essential for efficient molecular stripping.

On New Modifications of Some Perturbation Procedures

In this paper, we present new modifications for some perturbation procedures used in mathematics, physics, astronomy, and engineering. These modifications will help us to solve the previous problems in different sciences under new conditions. As problems, we have, for example, the rotary rigid body problem, the gyroscopic problem, the pendulum motion problem, and other ones. These problems will be solved in a new manner different from the previous treatments. We solve some of the previous problems in the presence of new conditions, new analysis, and new domains. We let complementary conditions of such studied previously. We solve these problems by applying the large parameter technique used by assuming a large parameter which inversely proportional to a small quantity. For example, in rigid body dynamic problems, we take such quantity to be one of the components of the angular velocity vector in the initial instant of the rotary body about a fixed point. The domain of our solutions will be depending on the choice of a large parameter. The problem of slow (weak) oscillations is considered. So, we obtain slow motions of the bodies instead of fast motions and find the solutions of the problem in present new conditions on both of center of gravity, moments of inertia, and the angular velocity vector or one of these parameters of the body. This study is important for aerospace engineering, gyroscopic motions, satellite motion which has the correspondence of inertia moments, antennas, and navigations.

On the regularity of solution to the time-dependent p-Stokes system

In this paper we consider the time evolutionary \(p\)-Stokes problem in a smooth and bounded domain. This system models the unsteady motion or certain non-Newtonian incompressible fluids in the regime of slow motions, when the convective term is negligible. We prove results of space/time regularity, showing that first-order time-derivatives and second-order space-derivatives of the velocity and first-order space-derivatives of the pressure belong to rather natural Lebesgue spaces.

Analysis of Nanoconfined Protein Dielectric Signals Using Charged Amino Acid Network Models

Protein slow motions involving collective molecular fluctuations on the timescale of microseconds to seconds are difficult to measure and not well understood despite being essential to sustain protein folding and protein function. Broadband dielectric spectroscopy (BDS) is one of the most powerful experimental techniques to monitor, over a broad frequency and temperature range, the molecular dynamics of soft matter through the orientational polarisation of permanent dipole moments that are generated by the chemical structure and morphological organisation of matter. Its typical frequency range goes from 107 Hz down to 10−3 Hz, being thus suitable for investigations on slow motions in proteins. Moreover, BDS has the advantage of providing direct experimental access to molecular fluctuations taking place on different length-scales, from local to cooperative dipolar motions. The unfolding of the cholera toxin B pentamer (CtxB5) after thermal treatment for 3h at 80°C is investigated by BDS under nanoconfined and dehydrated conditions. From the X-ray structure of the toxin pentamer, network-based models are used to infer the toxin dipoles present in the native state and to compute their stability and dielectric properties. Network analyses highlight three domains with distinct dielectric and stability properties that support a model where the toxin unfolds into three conformations after the treatment at 80°C. This novel integrative approach offers some perspective into the investigation of the relation between local perturbations (e.g. mutation, thermal treatment) and larger scale protein conformational changes. It might help ranking protein sequence variants according to their respective scale of dynamics perturbations.