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We investigate a well-known phenomenon of the appearance of the crossover points, corresponding to the
intersections of the solubility isotherms of the solid compound in supercritical fluid. Opposed to
the accepted understanding of the existence of two fixed crossover points, which confine the region of
the inverse isobaric temperature dependence of the solubility, we have found that these points tend to shift
with the change of the temperature and in the limit of the certain threshold value they converge to a single
point. We demonstrate this analyzing the solubility data of a set of poorly soluble drug compounds, which
have been computed in a wide area of the phase diagram via the approach, based on the classical density
functional theory. Thorough analysis of the available in the literature experimental solubility data is found
to be in an agreement with our conclusions, as one can find that the wider temperature region of the experimental
study is, the more pronounced effect of the crossover points drift can be observed.
We explore connected ane algebraic groups G, which enjoy the following finiteness property (F): for every algebraic action of G, the closure of every G-orbit contains only nitely many G-orbits. We obtain two main results. First, we classify such groups. Namely, we prove that a connected affine algebraic group G enjoys property (F) if and only if G is either a torus or a product of a torus and a one-dimensional connected unipotent algebraic group. Secondly, we obtain a characterization of such groups in terms of the modality of action in the sense of V. Arnol'd. Namely, we prove that a connected affine algebraic group G enjoys property (F) if and only if for every irreducible algebraic
variety X endowed with an algebraic action of G, the modality of X is equal to the minimum of codimensions of G-orbits in X.
We propose a novel algorithm for the construction of the sparse, nonetheless, the massive and rigid structure. The generated structures possess two significant properties reminiscent of the metallic foams. Firstly, the weight of the structures can be as low as the percent of the bulk one. Secondly, the structures are mechanically rigid. The structures are necessary for the simulation of the physical models of the foam properties.
The population annealing method is a promising approach for large-scale simulations because it is potentially scalable on any parallel architecture. We present an implementation of the algorithm on a hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible by efficiently redistributing replicas. We provide details of testing on hardware based the Intel Skylake/Nvidia V100 running more than two million replicas of the Ising model sample in parallel. The results are quite encouraging because the acceleration grows toward the perfect line as the complexity of the simulated system increases.
The process of poly(methyl methacrylate) (PMMA) matrix impregnation with mefenamic acid (MFA) in a supercritical carbon dioxide medium has been studied by the full atomistic classical molecular dynamics method. Simulations have been performed for two systems that differ in the polymer sample size (≈270 kDa and ≈1080 kDa) at 333 K and 40 MPa. The characteristics of the systems, such as the radius of gyration, end-to-end distance, mean squared displacement, radial distribution functions, average number of hydrogen bonds, and number of close contacts, have been analyzed and discussed. It has been found that by the end of the simulation (15 ns), the MFA loadings reach about 1.43 w/w % and 1.14 w/w % for the small and big PMMA samples, respectively. It was shown that the solute was distributed in the molecular form inside the polymer matrix. At the same time, when the CO2 molecules were removed from the systems and the simulation was performed in a canonical ensemble with the same cell length as in the previous isobaric-isothermal ensemble, the MFA molecules began to self-associate and get adsorbed on the polymer surface as hydrogen-bonded aggregates. In order to estimate the strength of the intermolecular interaction between the system components, ab initio calculations were performed. The calculated energies of the electron donor–acceptor (EDA) and hydrogen-bonded (HB) complexes can be arranged in the following order (in absolute value): ΔEEDA(PMMA-CO2)≈ΔEHB(MFA-CO2) < ΔEHB(PMMA-MFA) < ΔEHB(MFA-MFA).
We consider an interesting class of composite optimization problems with a gradient dominance condition and introduce corresponding analogue of the recently proposed concept of an inexact oracle. This concept is applied to some classes of smooth functional.
We analyzed the impacts of data span on trend estimates using Earth’s long-term polar motion time series, 1846-present, and using methodologies including singular spectrum analysis, and Panteleev’s filter to mitigate the time series containing transient signals. Our results show that the fluctuations of the mean rotational pole position, the Markowitz wobble, cannot be fully explained by the oceanic and atmospheric excitations. However, there exists plausible similarity with the variations of amplitudes of the Chandler wobble. To explain the abrupt deviation of the mean pole from the previous state after year 2000, we first compute Earth rotation excitations, using the temporal variations of the second-degree Stokes coefficients, , estimated from GRACE, GRACE Follow-On and Satellite Laser Ranging (SLR), 2002–2021. We then compare their trend estimates with that of the Earth’s polar motion, and conclude that the drift of the pole is consistent with the climate-induced mass redistributions within the Earth system during the past two decades. However, the observed trend is not in exact agreement with the prediction values using contemporary glacial isostatic adjustment (GIA) process forward models. The analysis of the variations since 1976 from SLR and the corresponding length of day (LOD) changes, reveals a clear trend reversal around the year 2000. However, the observed variations can only explain of the long-term LOD changes. The remaining decadal signal in the LOD, usually accounted for by the angular momentum exchange at the core-mantle boundary, is observed to be anti-correlated with the Earth surface temperature anomaly. The geophysical explanation on these relationships remains elusive, and necessitates future studies.
We study correlations between the structure and properties of a free association network of the English language, and solutions of psycholinguistic Remote Association Tests (RATs). We show that average hardness of individual RATs is largely determined by relative positions of test words (stimuli and response) on the free association network. We argue that the solution of RATs can be interpreted as a first passage search problem on a network whose vertices are words and links are associations between words. We propose different heuristic search algorithms and demonstrate that in “easily-solving” RATs (those that are solved in 15 seconds by more than 64% subjects) the solution is governed by “strong” network links (i.e. strong associations) directly connecting stimuli and response, and thus the efficient strategy consist in activating such strong links. In turn, the most efficient mechanism of solving medium and hard RATs consists of preferentially following sequence of “moderately weak” associations.
A model for deep bed filtration of a polydisperse suspension with small
impurities in a porous medium is considered. Different suspended particles move with
the same velocity as the carrier water and get blocked in the pore throats due to the
size-exclusion mechanism of particle retention. A solution of the model in the form of a
traveling wave is obtained. The global exact solution for a multiparticle filtration with
one high concentration and several low concentrations of suspended particles is obtained
in an explicit form. The analytic solutions for a bidisperse suspension with large and small
particles are constructed. The profiles of the retained small particles change monotony
with time. The global asymptotics for the filtration of a polydisperse suspension with
small kinetic rates is constructed in the whole filtration zone.
Filtration problems arise in the design of tunnels and underground structures. A onedimensional
filtration model of a monodisperse suspension in a homogeneous porous medium
is considered. For a general nonlinear filtration function, an asymptotic solution is constructed
behind the concentrations front of suspended and retained particles. It is shown that the
asymptotics is close to the numerical solution. Comparison of the asymptotics with the
suspended particles concentration at the outlet of the porous medium allows solving the inverse
filtration problem on finding the nonlinear filtration function. The proposed method allows to
obtain the filtration function based on the results of standard laboratory experiments.
During the construction of hydraulic and underground structures, a grout solution is pumped into the ground
to create waterproof partitions. The liquid grout is filtered in the porous rock and clogs the pores when hardened. The
mathematical model of deep bed filtration describes the transfer of suspension particles and colloids by a fluid flow through
the pores of a rock. For a one-dimensional filtration problem in a homogeneous porous medium with almost constant
coefficients, an asymptotic solution is constructed. The asymptotics is compared with the numerical solution.
In the framework of creating a digital ecosystem of commercial real estate objects, the main problem is the formation of a digital environment for managing all components of engineering systems that ensure the vital activity of the real estate object. The aim of this work is to develop a system for accounting for mutual settlements for electricity consumed on the basis of a distributed ledger using blockchain technology. To assess the effectiveness of the system a simulation model was built using AnyLogic system. Based on the model the system architecture was designed and a software application of the distributed ledger was developed.
We study the process of the destruction of synchronous oscillations in a model of two interacting microbubble contrast agents exposed to an external ultrasound field. Completely synchronous oscillations in this model are possible in the case of identical bubbles when the governing system of equations possess a symmetry leading to the existence of a synchronization manifold. Such synchronous oscillations can be destructed without breaking the corresponding symmetry of the governing dynamical system. Here, we describe the phenomenological mechanism responsible for such destruction of synchronization and demonstrate its implementation in the studied model. We show that the appearance and expansion of transversally unstable areas in the synchronization manifold leads to the transformation of a synchronous chaotic attractor into a hyperchaotic one. We also demonstrate that this bifurcation sequence is stable with respect to symmetry breaking perturbations.
This study investigates possibilities for extension and improvement of algorithms for generation of libration point orbits in the framework of the circular restricted three body problem. Two algorithms for orbit generation based on bisection approach using different ways for evaluation of unstable component of motion are considered. The spacecraft's state vector is periodically adjusted in such a way that unstable component of motion is neutralized and the trajectory corresponding to the corrected state vector belongs to the central manifold associated with libration point. The first algorithm uses expression for unstable component derived from linearized equations of motion. The second one is based on the procedure of reduction to central manifold, utilizing canonical coordinate transformations to nullify high order monomials in the expansion of Hamiltonian of the system in terms of Legendre polynomials. This allows expressing unstable component as one of generalized coordinates of Hamiltonian system obtained as the result of aforementioned transformation. Evaluation of these techniques proved their applicability for orbit generation. However, the second approach allows generating orbits in greater vicinity of libration point.
Recently discussed topological materials Weyl-semimetals (WSs) combine both: high electron mobility comparable with graphene and unique topological protection of Dirac points. We present novel results related to electromagnetic field propagation through WSs. It is predicted that transmission of the normally incident polarized electromagnetic wave (EMW) through the magnetic WS strongly depends on the orientation of polarization with respect to a gyration vector g. The latter is related to the vector-parameter b, which represents the separation between the Weyl nodes of opposite chirality in the first Brillouin zone. By changing the polarization of the incident EMW with respect to the gyration vector g the system undergoes the transition from the isotropic dielectric to the medium with Kerr-or Faraday-like rotation of polarization and finally to the system with chiral selective electromagnetic field. It is shown that WSs can be applied as the polarization filters.
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms
for short, which are certain bipartite graphs decorated withwords in a given alphabet, generalizing linear logic proof-nets.
We also introduce and study linear logic grammars, directly based on cobordisms and using classical multiplicative linear logic
as a typing system.
Despite the modern level of development of computational chemistry methods and technological progress, fast and accurate determination of solvation free energy remains a huge problem for physical chemists. In this paper, we describe two computational schemes that can potentially solve this problem. We consider systems of poorly soluble drug compounds in supercritical carbon dioxide. Considering that the biggest contribution among all intermolecular interactions is made by van der Waals interactions, we model solute and solvent particles as coarse-grained ones interacting via the effective Lennard-Jones potential. The first proposed approach is based on the classical density functional theory and the second one relies on molecular dynamics simulation of the Lennard-Jones fluid. Sacrificing the precision of the molecular structure description while capturing the phase behavior of the fluid with sufficient accuracy, we propose computationally advantageous paths to obtaining the solvation free energy values with the accuracy satisfactory for engineering applications. The agreement reached between the results of such coarse-graining models and the experimental data indicates that the use of the all-atom molecular dynamic simulations for the studied systems seems to be excessive.
Halo orbits of Sun-Earth system are utilized in space missions as they allow to maintain the spacecraft in an area that is stationary relative to Sun and Earth. The advantage of halo orbits is their periodicity and their form allowing the spacecraft to avoid the zones of solar interference and the Earth shadow. The transfer between a low-Earth orbit and a halo orbit around a libration point can be realized by a single-burn maneuver, which transfers the spacecraft to an orbit of stable manifold resulting in a halo orbit. An amplitude of halo orbit depends on the altitude of the parking low-Earth orbit at which the transfer maneuver is performed. This work is aimed to explore and systemize the single burn transfer options utilizing single and multiple Earth passing trajectories in the framework of the circular restricted three body problem. The algorithms providing transfer options for the desired halo orbit and the parking orbit altitude are developed. The transfer trajectories for the Sun-Earth L1 and L2 halo orbits in a wide range of out-of-plane amplitudes were constructed and studied. The constructed trajectories were clustered based on the transfer time and the halo orbit amplitude.
Superplasticity is an ability of polycrystalline materials to archive extremely large deformations, which is utilized in advanced forming technologies demanded mainly in the aerospace industry. Design of such technologies needs an information of the material flow behaviour, which describes the relation of the effective stress on the strain and strain rate taking place during deformation. The most popular experimental method for investigation of the flow behaviour of superplastic materials is tensile testing. The procedure of superplastic tensile testing and interpretation of its results is described by several international standards. At the same time, it is known that the due to flow inhomogeneity in the specimen volume the accuracy of such tests may be violated. Moreover, different standards provide different ratio between the width and the height of the gauge area of a specimen. This work provides the numerical analysis aimed to study how the initial specimen geometry affects the results of tensile tests. A computer program implementing finite element method (FEM) was developed to predict the specimen deformation during the test. A flat specimen is discretized using prismatic elements with specific geometrical constraints reducing the degree of freedom to the order of a plane stressed task. The output stress and strain values were calculated as specified in the ASTM E2448 standard. The effect of the gauge length was studied focusing on the output stress strain curves. The results were compared with the experimental results available in the literature.