Cluster Dynamics of Planetary Waves

The dynamics of nonlinear atmospheric planetary waves is determined by a small number of independent wave clusters consisting of a few connected resonant triads. We classified the different types of connections between neighboring triads that determine the general dynamics of a cluster. Each connection type corresponds to substantially different scenarios of energy flux among the modes. The general approach can be applied directly to various mesoscopic systems with 3-mode interactions, encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.Comment: 6 pages, 3 figs, EPL, publishe

Dynamical cascade generation as basic mechanism of Benjamin-Feir instability

A novel model of discretized energy cascade generated by Benjamin-Feir instability is presented. Conditions for appearance of direct and inverse cascades are given explicitly, as well as conditions for stabilization of the wave system due to cascade termination. These results can be used directly for explanation of available results of laboratory experiments and as basic forecast scenarios for planned experiments, depending on the frequency of an initially excited mode and steepness of its amplitude.Comment: Accepted to EP

Laminated Wave Turbulence: Generic Algorithms II

The model of laminated wave turbulence puts forth a novel computational problem - construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order $10^{12}$ and more. The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion. It is established that for the most common dispersion as an arbitrary function of a wave-vector length two different generic algorithms are necessary: (1) one-class-case algorithm for waves interacting through scales, and (2) two-class-case algorithm for waves interacting through phases. In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-class-case generic algorithm.Comment: to appear in J. "Communications in Computational Physics" (2006

Finite-Dimensional Turbulence of Planetary Waves

Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finite-dimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wave kinetic equations that account for interactions with overlapping quasi-resonances of finite amplitude waves. The present results are directly applicable to finite-dimensional wave turbulence in any wave system in finite domains with 3-mode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.Comment: 29 pages, 21 figures, submitted to PR

Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

Effect of the dynamical phases on the nonlinear amplitudes' evolution

In this Letter we show how the nonlinear evolution of a resonant triad depends on the special combination of the modes' phases chosen according to the resonance conditions. This phase combination is called dynamical phase. Its evolution is studied for two integrable cases: a triad and a cluster formed by two connected triads, using a numerical method which is fully validated by monitoring the conserved quantities known analytically. We show that dynamical phases, usually regarded as equal to zero or constants, play a substantial role in the dynamics of the clusters. Indeed, some effects are (i) to diminish the period of energy exchange $\tau$ within a cluster by 20$$ and more; (ii) to diminish, at time scale $\tau$, the variability of wave energies by 25$$ and more; (iii) to generate a new time scale, $T >> \tau$, in which we observe considerable energy exchange within a cluster, as well as a periodic behaviour (with period $T$) in the variability of modes' energies. These findings can be applied, for example, to the control of energy input, exchange and output in Tokamaks; for explanation of some experimental results; to guide and improve the performance of experiments; to interpret the results of numerical simulations, etc.Comment: 5 pages, 15 figures, submitted to EP

Gravity wave turbulence in a laboratory flume

We present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size 12×6  m. For a wide range of amplitudes the wave energy spectrum was found to scale as Eω∼ω-ν in a frequency range of up to one decade. However, ν appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4. We discuss our results in the context of existing theories and argue that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitudes the wave breaking effect dominates

Pseudomembranous colitis complicated by toxic megacolon in oncological patients

In recent years, information on the increase in the incidence of  infection associated with Clostridioides difficile (CDI) has appeared in the literature. It is known that C. difficile which causes pseudomembranous colitis (PMC) most often affects debilitated patients who receive treatment for the main pathology for a long time. That is why PMC is most common in cancer patients receiving long-term and aggressive anticancer treatment, which is often accompanied by the use of several courses of antibiotics. The result of the irrational use of antibiotics, incorrect PMC therapy may be the  formation of toxic megacolon, intestinal perforation, sepsis, which in turn is fraught with a fatal outcome. It is this state of affairs that aroused our interest in the study of this topic. The steady increase in the incidence of Clostridioides difficile infection makes it particularly relevant to study CDI problem in relation to cancer patients, since they most often have a wide range of risk factors for developing clostridial infection. The article presents an overview of domestic and foreign sources describing this pathology, discusses epidemiology, pathogenesis, clinical picture and current understanding of the CDI treatment. At the end of the review, we present a case of successful treatment of pseudomembranous colitis after stoma closure, which was complicated by the development of toxic megacolon. Colproctectomy was performed as part of the complex treatment of this pathology. The patient received respiratory, renal replacement, hepatoprotective, antibiotic and antifungal therapy and other treatments

Laplace Invariants for General Hyperbolic Systems

We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants

A Case of Successful Treatment of Gram-Negative Sepsis Associated with Toxic Myelosuppression in a Patient with HIV-Associated Non-Hodgkin’s Lymphoma

This article presents a clinical case of successful treatment of gram-negative sepsis in a patient with HIV-associated non-Hodgkin’s lymphoma. The patient was admitted to the intensive care unit in critical condition after the third course of polychemotherapy according to the ICE scheme. The severity of the condition was due to nosocomial pneumonia, septic shock, multiple organ failure, immunosuppression against the background of PCT and HIV infection, and the lack of specific treatment for HIV infection. Despite the absence of a positive blood culture throughout the entire treatment period, the diagnosis of sepsis was not in doubt, according to the criteria of the 2001 International Consensus Conference on Sepsis. The cause of the septic state was the combined effect of bacteria (Pseudomonas aeruginosa) and fungi (Candida albicans, Candida krusei) against the background of persistent HIV infection. The patient’s pneumonia was destructive and was twice aggravated by spontaneous pneumothorax. At the initial stage, intensive therapy led to positive dynamics. The severity of the systemic inflammatory response decreased, the acute respiratory insufficiency regressed, the X-ray pattern improved, and laboratory parameters stabilized. Despite the continued intensive therapy in the former volume on day 19, a sharply negative dynamics was noted, which led to a re-transfer of the patient to artificial ventilation of the lungs. The replacement of antibiotics and the specific treatment of HIV infection led to the patient’s recovery. In the future, chemotherapy was not carried out. Remission of the disease lasts six years