Source and coefficient identification problems for the wave equation on graphs

Avdonin and Kurasov proposed a leaf peeling method based on the boundary control to recover a potential for the wave equation on a tree. Avdonin and Nicaise considered a source identification problem for the wave equation on a tree. This paper extends the methodology to the wave equation with unknown potential and source distributed parameters defined on a general tree graph.     

Molecular dynamics investigation of soliton propagation in a two-dimensional Yukawa liquid

We investigate via molecular dynamics simulations the propagation of solitons in a two-dimensional many-body system characterized by Yukawa interaction potential. The solitons are created in an equilibrated system by the application of electric field pulses. Such pulses generate pairs of solitons, which are characterized by a positive and negative density peak, respectively, and which propagate into opposite directions. At small perturbation, the features propagate with the longitudinal sound speed, from which an increasing deviation is found at higher density perturbations. An external magnetic field is found to block the propagation of the solitons, which can, however, be released upon the termination of the magnetic field and can propagate further into directions that depend on the time of trapping and the magnetic field strength.     

Phytochemical Fingerprinting and In Vitro Antimicrobial and Antioxidant Activity of the Aerial Parts of Thymus marschallianus Willd. and Thymus seravschanicus Klokov Growing Widely in Southern Kazakhstan

The chemical composition of the hydroethanolic extracts (60% v/v) from the aerial parts of Thymus marschallianus Willd (TM) and Thymus seravschanicus Klokov (TS) from Southern Kazakhstan flora was analyzed together with their hexane fractions. Determination of antibacterial, antifungal and antioxidant activities of both extracts was also performed. RP-HPLC/PDA and HPLC/ESI-QTOF-MS showed that there were some differences between the composition of both extracts. The most characteristic components of TM were rosmarinic acid, protocatechuic acid, luteolin 7-O-glucoside, and apigenin 7-O-glucuronide, while protocatechuic acid, luteolin 7-O-glucoside, luteolin 7-O-glucuronide, and eriodictyol predominated in TS. The content of polyplenols was higher in TS than in TM. The GC-MS analysis of the volatile fraction of both examined extracts revealed the presence of thymol and carvacrol. Additionally, sesquiterpenoids, fatty acids, and their ethyl esters were found in TM, and fatty acid methyl esters in TS. The antioxidant activity of both extracts was similar. The antibacterial activity of TS extract was somewhat higher than TM, while antifungal activity was the same. TS extract was the most active against Helicobacter pylori ATCC 43504 with MIC (minimal inhibitory concentration) = 0.625 mg/mL, exerting a bactericidal effect. The obtained data provide novel information about the phytochemistry of both thyme species and suggest new potential application of TS as a source of bioactive compounds, especially with anti-H. pylori activity.     

Effect of magnetic field and friction force on the velocity autocorrelation in two‐dimensional Yukawa liquids

The effect of an external magnetic field and gas‐induced friction on the velocity autocorrelation of the dust particles in strongly coupled two‐dimensional Yukawa liquids was investigated. The Langevin dynamics computer simulation method was used. The presence of the friction originating from the background gas leads to the disappearance of a collective oscillation mode, corresponding to the cyclotron frequency of the dust particles, and a decrease in the dominant mode.     

Determining distributed parameters in a neuronal cable model on a tree graph

For graph domains without cycles, we show how unknown coefficients and source terms for a parabolic equation can be recovered from the dynamical Neumann‐to‐Dirichlet map associated with the boundary vertices. Through use of a companion wave equation problem, the topology of the tree graph, degree of the vertices, and edge lengths can also be recovered. The motivation for this work comes from a neuronal cable equation defined on the neuron's dendritic tree, and the inverse problem concerns parameter identification of k unknown distributed conductance parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

Influence of dynamic screening on the conductivity of hydrogen plasma including electron–electron collisions

We investigate the dynamical conductivity of dense hydrogen plasmas on the basis of the effective interaction potential (taking into account static or dynamic screening and diffraction effects). We apply a generalized Drude–Lorentz formula related to the dynamical conductivity with collision frequency. The influence of electron–ion collisions as well as the influence of both electron–ion and electron–electron collisions were taken into account via a renormalization factor. All calculations were performed on the basis of the effective potential with static or dynamic screening.