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The authors describe their experience in a successful treatment of a patient with necrotizing infection of lower limb soft tissues complicated by sepsis. Their comprehensive approach included two-stage surgical intervention and medicamentous therapy. As a result, the patient has completely recovered.

We reconsider a recently proposed design for smart responsive brushes, which is based on a conformational transition in very dilutely embedded block copolymers with a surface active block (Qi et al., Macromolecules 53, 5326, 2020). Under certain conditions, the transition acquires an unusual character: it remains very sharp, but the barrier separating the adsorbed and desorbed states disappears completely. We show that these features are very robust with respect to changing almost all system parameters: the lengths of the inert and active blocks of the minority chain, the brush length, its density, and its polydispersity. The only relevant condition is that the inert block of the minority chain is long enough to extend outside the brush density profile. We develop an analytical theory that predicts the relevant characteristics of the transition and verify it with Monte Carlo simulations. We also show that the surprising universality of the transition properties is rooted in an underlying connection to the force-induced desorption transition, which is known to combine the features of the first- and second-order transitions with a pretransition fluctuation growth accompanied by phase coexistence.

The article presents the clinical case of successful treatment of a patient with heel plantar trophic ulcer. The results of plastics a neuropathy heel ulcer by medial plantar island flap are demonstrated.

The paper considers the construction of adaptive methods based on the explicit Runge–Kutta stages. The coefficients of these methods are adjusted to the problem being solved, using component-wise estimates of the eigenvalues of the Jacobi matrix with the maximum absolute values. Such estimates can be easily obtained at the stages of the explicit method, which practically does not require additional calculations. The effect of computational errors and stiffness of the problem on the stability and accuracy of the numerical solution is studied. The analysis allows one to construct efficient explicit methods that are not inferior to implicit methods in solving many stiff problems. New nested pairs of adaptive methods are proposed, and the results of numerical experiments are presented.

Recently, a new design for switch sensors has been proposed that exploits a conformational transition of end-grafted minority adsorption-active homopolymers in a monodisperse polymer brush [Klushin...

Recently a novel class of responsive uncharged polymer brushes has been proposed [Klushin et al, J. Chem. Phys. 154, 074904 (2021)] where the brush-forming chains have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush with a reduced grafting density. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly as a response to changes in environmental parameters. In this paper we use numerical self-consistent field calculations and theoretical considerations to study this phenomenon in polydisperse brushes. Our results reveal an unexpected effect: Although all chains are chemically identical, shorter chains are adsorbed preferentially. Hence, with the increase in the surface affinity parameter, a reduction in the surface grafting density of the residual brush is accompanied by a change in the shape of its molecular mass distribution. In particular, an originally bidisperse brush can be effectively transformed into a nearly monodisperse one containing only the longer chain fraction., 14 pages, 19 figures, submitted to J. Chem. Phys

We study the effect of polydispersity on the compression and interpenetration properties of two opposing polymer brushes by numerical self-consistent field approach and by analytical theory. Polydispersity is represented by an experimentally relevant Schulz–Zimm chain-length distribution. We focus on three different polydispersities representing sharp, moderate, and extremely wide chain length distributions and derive approximate analytical expressions for the pressure–separation curves, Π(D). We study the brush interpenetration and quantify it in terms of the overlap integral, Γ, representing the number of interbrush contacts, and interpenetration length, δ. For the case of moderate densities where the equation of state is dominated by the second virial term with coefficient υ, we demonstrate that the pressure, the overlap integral, and the interpenetration length are related by a simple equation, Π/kBT = υΓ/δ, where kBT represents the thermal energy. We propose a scaling form for δ(D) for the three poly...

We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical SCF calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters., Comment: To appear in J. Chem. Phys

The main computational costs of implicit Runge–Kutta methods are caused by solving a system of algebraic equations at every step. By introducing explicit stages, it is possible to increase the stage (or pseudo-stage) order of the method, which makes it possible to increase the accuracy and avoid reducing the order in solving stiff problems, without additional costs of solving algebraic equations. The paper presents implicit methods with an explicit first stage and one or two explicit internal stages. The results of solving test problems are compared with similar methods having no explicit internal stages.

We consider methods that are the inverse of the explicit Runge–Kutta methods. Such methods have some advantages, while their disadvantage is the low (first) stage order. This reduces the accuracy and the real order in solving stiff and differential-algebraic equations. New methods possessing properties of methods of a higher stage order are proposed. The results of the numerical experiments show that the proposed methods allow us to avoid reducing the order.

The solution of stiff problems is frequently accompanied by a phenomenon known as order reduction. The reduction in the actual order can be avoided by applying methods with a fairly high stage order, ideally coinciding with the classical order. However, the stage order sometimes fails to be increased; moreover, this is not possible for explicit and diagonally implicit Runge–Kutta methods. An alternative approach is proposed that yields an effect similar to an increase in the stage order. New implicit and stabilized explicit Runge–Kutta methods are constructed that preserve their order when applied to stiff problems.

Products formed in laser ablation of single-crystal silicon beneath a water layer under irradiation with nanosecond pulses from a fiber-optic ytterbium laser have been studied. SEM images of structures deposited by dewatering of the colloid solution formed in the course of the ablation are presented. IR spectroscopy and Raman spectroscopy were used to determine their chemical composition and structural features.

The features and basic functionality of the MVTU software package are considered. The software is intended for the research and design of a wide range of systems described by differential, algebraic, and difference equations. Examples of the solutions of the research and applied problems are given.

We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force $F$ applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition, and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static and the dynamic behavior of chains with different length $N$ are very well described by a scaling Ansatz with the scaling parameters $(\varepsilon - \varepsilon^*) N^\phi$ (adsorption transition) and $(F-F^*) N^\nu$ (loop-stretch transition), respectively, where $\phi$ is the crossover exponent of the adsorption transition, and $\nu$ the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the Ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes., Comment: 14 pages, 10 figures

We consider the synthesis problem for low order controllers that provide given properties for a linear continuous system under uncertainty in object parameters. The synthesis is done with stability and quality criteria that have a simple dependence on the coefficients of the characteristic polynomial. We give examples of synthesizing controllers with given requirements to transition process quality, performance, and tracking accuracy.

We have studied the process of destruction of the surface of a single-crystalline silicon wafer scanned by the beam of a pulsed ytterbium-doped fiber laser radiation with a wavelength of λ = 1062 nm. It is established that the laser ablation can proceed without melting of silicon and the formation of a plasma plume. Under certain parameters of the process (radiation power, beam scan velocity, and beam overlap density), pronounced oxidation of silicon microparticles with the formation of a characteristic loose layer of fine powdered silicon dioxide has been observed for the first time. The range of lasing and beam scanning regimes in which the growth of SiO2 layer takes place is determined.

An implicit two-step Runge-Kutta method of fifth order is proposed for the numerical solution of differential and differential-algebraic equations. The location of nodes in this method makes it possible to estimate the values of higher derivatives at the initial and terminal points of an integration step. Consequently, the proposed method can be regarded as a finite-difference analog of the Obrechkoff method. Numerical results, some of which are presented in this paper, show that our method preserves its order while solving stiff equations and equations of indices two and three. This is the main advantage of the proposed method as compared with the available ones.

Efficient schemes for the implementation of diagonally implicit Runge-Kutta methods are considered. Methods of the 3rd and 4th orders are implemented. They are compared with known implicit solvers as applied to the solution of stiff and differential-algebraic equations.

Singly implicit diagonally extended Runge-Kutta methods make it possible to combine the merits of diagonally implicit methods (namely, the simplicity of implementation) and fully implicit ones (high stage order). Due to this combination, they can be very efficient at solving stiff and differential-algebraic problems. In this paper, fourth-order methods with an explicit first stage are examined. The methods have the third or fourth stage order. Consideration is given to an efficient implementation of these methods. The results of tests in which the proposed methods were compared with the fifth-order RADAU IIA method are presented.

Implementation schemes for second-order implicit Runge-Kutta methods are considered. The schemes allow one to reduce computational costs when solving stiff problems with low accuracy. The results of the comparison with implicit MATLAB solvers are presented.

We study the effect of polydispersity on the structure of polymer brushes by analytical theory, a numerical self-consistent field approach, and Monte Carlo simulations. The polydispersity is represented by the Schulz-Zimm chain-length distribution. We specifically focus on three different polydispersities representing sharp, moderate and extremely wide chain length distributions and derive explicit analytical expressions for the chain end distributions in these brushes. The results are in very good agreement with numerical data obtained with self-consistent field calculations and Monte Carlo simulations. With increasing polydispersity, the brush density profile changes from convex to concave, and for given average chain length $N_n$ and grafting density $\sigma$, the brush height $H$ is found to scale as $(H/H_{\mathrm{mono}}-1)\propto(N_w/N_n-1)^{1/2}$ over a wide range of polydispersity indices $N_w/N_n$ (here $H_{\mathrm{mono}}$ is the height of the corresponding monodisperse brush. Chain end fluctuations are found to be strongly suppressed already at very small polydispersity. Based on this observation, we introduce the concept of the brush as a near-critical system with two parameters (scaling variables), $(N_{n}\sigma^{2/3})^{-1}$ and $(N_w/N_n-1)^{1/2}$, controlling the distance from the critical point. This approach provides a good description of the simulation data. Finally we study the hydrodynamic penetration length $l_\mathrm{p}$ for brush-coated surfaces in flow. We find that it generally increases with polydispersity. The scaling behavior crosses over from $l_\mathrm{p}\sim N_\mathrm{n}^{1/2}\sigma^{-1/6}$ for monodisperse and weakly polydisperse brushes to $l_\mathrm{p}\sim N_{n}^{2/3}$ for strongly polydisperse brushes., Comment: 21pages, 9 figures. Accepted for publication in Macromolecues

Using molecular dynamics simulations, we study and compare the pressure, P, and the surface tension, γ, of linear chains and of ring polymers at the hard walls confining both melts into a slit. We examine the dependence of P and γ on the length (i.e., molecular weight) N of the macromolecules. For linear chains, we find that both pressure and surface tension are inversely proportional to the chain length, P(N)−P(N→∞)∝N−1,γ(N)−γ(N→∞)∝N−1, irrespective of whether the confining planes attract or repel the monomers. In contrast, for melts comprised of cyclic (ring) polymers, neither the pressure nor the surface tension is found to depend on molecular weight N for both kinds of wall-monomer interactions. While other structural properties as, e.g., the probability distributions of trains and loops at impenetrable walls appear quantitatively indistinguishable, we observe an amazing dissimilarity in the probability to find a chain end or a tagged monomer of a ring at a given distance from the wall in both kinds o...

Stiffly accurate Runge-Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge-Kutta methods.

In this paper, we discuss the elastic behavior of an isolated macromolecule in conjugated and non-conjugated ensembles during different modes of applying a mechanical force to the chain ends, namely, the mechanical effects corresponding to the methods of atomic force microscopy, magnetic levitation, and stretching of a macromolecule in an isotropic force field. Recently published results on the Langevin dynamics computer simulation of the stretching of a Gaussian polymer chain in different ensembles are analyzed. An analytical description of all the results of this simulation is given to show that the conclusion made by the authors of those studies about the nonequivalence of conjugated ensembles for Gaussian chains is not quite correct. A theoretical examination of the stretching of individual semirigid chains, which exhibit interesting behavior because of manipulations with actin molecules and microtubules, which are components of the cytoskeleton of most cells, is performed. We present rigorous analytical results about the stretching of chains composed of two or three freely jointed rods of equal length without consideration for excluded-volume inter-actions. It is shown that the stress-strain curves of these chains differ not only quantitatively but also qualitatively in different ensembles and that these curves for a chain of two freely jointed rods have an anomalous shape. These results on the different behavior of stress-strain for different modes of external mechanical impacts can be useful for interpreting experiments on the stretching of individual polymer molecules with different structures obtained via different methods, such as atomic-force microscopy and magnetic levitation.

When solving stiff problems the efficiency of the Runge-Kutta methods can be substantially improved if the parameters of the integration formula are adjusted to the problem at hand. The construction of such methods called adaptive is considered. The results obtained on test problems are compared with those obtained by known methods.

Explicit Runge-Kutta methods with the coefficients tuned to the problem of interest are examined. The tuning is based on estimates for the dominant eigenvalues of the Jacobian matrix obtained from the results of the preliminary stages. Test examples demonstrate that methods of this type can be efficient in solving stiff and oscillation problems.

Explicit Runge-Kutta methods with the stability domains extended along the real axis are examined. For these methods, a simple and efficient procedure for calculating the stability polynomials is proposed. Three techniques for constructing methods with given stability polynomials are considered. Methods of the second and third orders are constructed, and their accuracy as applied to solving the Prothero-Robinson equation is examined. A comparison of the above methods on some test problems is performed.

The simplest equations are considered that simulate the behavior of various error components of Runge-Kutta methods. The expressions for the local and global errors are obtained. The minimization of these errors allows one to construct explicit and implicit methods that have an improved accuracy when solving stiff and differential-algebraic problems.

Explicit multistep methods for solving Cauchy problems are examined. The proposed methods have their stability domains extended along the real axis and can be an alternative to one-step Runge-Kutta-Chebyshev methods when stiff problems are solved.

Diagonally implicit Runge-Kutta methods satisfying additional order conditions are examined. These conditions make it possible to solve differential algebraic equations of indices two and three to higher accuracy. Advantages of the proposed methods over other known techniques are demonstrated using test problems.

Explicit two-step Runge-Kutta methods with extended stability regions are considered as well as similar methods with an increased stage order. The advantage of two-step methods over the traditional one-step Runge-Kutta methods is shown.

The Runge-Kutta methods possessing the interpolation property, i.e., methods in which all coefficients belong to the interval [0, 1] are studied. Explicit and implicit methods of up to the fifth order inclusive that satisfy or almost satisfy the interpolation condition are considered.

A technique is proposed for constructing two-step Runge-Kutta methods on the basis of one-step methods. Explicit and diagonally implicit two-step methods with the second or third stage order are examined. Test problems are presented showing that the proposed methods are superior to conventional one-step techniques.

The IR spectra in the hydroxyl group stretching vibration region of the simplest hydroxyalkylpyrrolizidines have been examined. The spectra were taken in the form of pure liquids, dilute solutions in carbon tetrachloride, and for individual bases in the gas phase. It was shown that in dilute solutions ΔνOH depends on the geometric parameters of the intramolecular hydrogen bond (IMHB). The energy of the IMHB of 3-(2-hydroxyethyl)pyrrolizidine was measured in dilute solution and in the gas phase.

This review is concerned with the response of an isolated polymer chain subjected to the action of the two different modes of the mechanical impact on the chain ends. In one mode, the end-to-end distance is changed in a controlled fashion and the fluctuating response force is measured; in the second case, an external stress field is applied to the chain end, and the measured response of the system is the fluctuating end-to-end distance. The main attention is focused on the results of the computer-aided simulation experiments and theoretical results. Upon stretching of an ideal chain, a real chain in a good solvent, or a globule, the resultant strain-force and force-strain dependences are shown to be different for chains with finite length L; however, this difference diminishes with an increase in the length of a molecule. When the anchored Gaussian chain is separated from the adsorbing surface, this difference disappears in the limit of high L; however, in the neighborhood of the phase transition, some characteristics (fluctuations, distribution functions) appear to be critically different under different impact modes even in the thermodynamic limit. The example of an abnormal system is discussed: The behavior of a polymer chain compressed by a small piston is different in the conjugated ensembles, and, as the system increases in size, this difference becomes even more pronounced.

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes., Comment: 13pages, 14figures

The reaction mixture from detoxication of technical-grade yperite with monoethanolamine was fractionated, and its composition was determined. The structures of the free thiomorpholine bases formed in the process were determined by gas chromatography—mass spectrometry.

An explicit multistep method of variable order for integrating stiff systems with high accuracy and low computational costs is examined. To stabilize the computational scheme, componentwise estimates are used for the eigenvalues of the Jacobian matrix having the greatest moduli. These estimates are obtained at preliminary stages of the integration step. Examples are given to demonstrate that, for certain stiff problems, the method proposed is as efficient as the best implicit methods.