Potts model on complex networks

We consider the general p-state Potts model on random networks with a given degree distribution (random Bethe lattices). We find the effect of the suppression of a first order phase transition in this model when the degree distribution of the network is fat-tailed, that is, in more precise terms, when the second moment of the distribution diverges. In this situation the transition is continuous and of infinite order, and size effect is anomalously strong. In particular, in the case of p = 1, we arrive at the exact solution, which coincides with the known solution of the percolation problem on these networks.Received: 3 December 2003, Published online: 17 February 2004PACS: 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 87.18.Sn Neural networks     

Cyclical games with prohibitions

We consider a certain combinatorial game on a digraph for two cases of the price function. For one case the game in question extends the cyclical game studied in Ehrenfeucht and Mycielski (1979) and Gurvitch, Karzanov and Khachiyan (1988) which, in its turn, is a generalization of the well-known problem of finding a minimum mean cycle in an edge-weighted digraph. We prove the existence of optimal uniform stationary strategies for both cases and give algorithms to find such strategies.This work was partially supported by Chaire municipale, Mairie de Grenoble.     

The Effect of Olive Fruit Fly Bactrocera oleae (Rossi) Infestation on Certain Chemical Parameters of Produced Olive Oils

Olives affected by active and damaging infestation (olive fruit fly Bactrocera oleae (Rossi)) were assayed for their chemical composition. Biophenols were determined by HPLC, sterols, triterpenic dialcohols, and fatty acids by gas chromatography analysis. The acquired data were statistically analyzed. Oils produced from “Istrska belica” fruit affected by active infestation compared to the oils made from fruit affected by damaging infestation showed higher amounts of total oleuropein biofenols (377.3 versus (vs.) 106.6 mg/kg), total biophenols (755 vs. 377 mg/kg), lignans (85.3 vs. 32.9 mg/kg), the dialdehydic form of decarboxymethyl oleuropein aglycone (DMO-Agl-dA) (148.3 vs. 49.0 mg/kg), its oxidized form (DMO-Agl-dA)ox (35.2 vs. 8.5 mg/kg), the dialdehydic form of oleuropein aglycone (O-Agl-dA) (61.1 vs. 8.0 mg/kg), the dialdehydic form of ligstroside aglycone (L-Agl-dA) (63.5 vs. 28.0 mg/kg), the aldehydic form of oleuropein aglycone (O-Agl-A) (40.6 vs. 8.4 mg/kg), and lower amounts of tyrosol (Tyr) (6.0 vs. 13. 9 mg/kg) and the aldehydic form of ligstroside aglycone (L-Agl-A) (13.8 vs. 40.3 mg/kg). Higher values of stigmasterol (2.99%) and lower values of campesterol (2.25%) were determined in oils affected by damaging infestation; an increase in triterpenic dialcohols was also observed (3.04% for damaging and 1.62% for active infestation). Oils affected by damaging infestation, compared to active infestation, showed lower amounts of oleic acid (73.89 vs. 75.15%) and higher amounts of myristic (0.013 vs. 0.011%), linoleic (7.27 vs. 6.48%), and linolenic (0.74 vs. 0.61%) acids.     

k-Core organization of complex networks

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures--k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birthpoints--the bootstrap percolation thresholds. We show that in networks with a finite mean number zeta2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if zeta2 diverges, the networks contain an infinite sequence of k-cores which are ultrarobust against random damage.     

Topological and morphological transformations of developing singular paraxial vector light fields

The paper is devoted to establishment of the real-time topological and morphological dynamics of generic developing paraxial elliptic speckle fields generated and driven by the system ‘laser beam + photorefractive crystal LiNbO₃:Fe’. Generic space-time development of full gamut of polarization ellipse parameters (ellipticity, azimuth, morphology of C points, optical diabolos and handedness) and their combination in fixed beam cross-section was measured in details by the elaborated quick-action real-time Stokes-polarimetry. Whole field irreversible evolution is fulfilled through totality of random space/time C point pair nucleation/annihilation. The ‘life-story’ of C point and optical diabolo pairs is realized through ‘local topological/morphological transition’ with fully reversible scenario. It starts from smooth fragment of speckle field by formation of pre-nucleation local structure and finishes by after-annihilation local structure which decays to another smooth structure. Scenarios of star-monstar pair nucleation/annihilation and monstar  ↔  lemon transformation were established. Measured statistics of C point and diabolo morphological forms was in excellent agreement with theory predictions. All allowed scenarios of diabolo pair ‘life-story’ started/finished as star-hyperbolic monstar-hyperbolic pair were measured. Evolution of polarization ellipses handedness is implemented through L contours movement and reconnection with a saddle as the catalyst. Reconnection of L contour peninsula leads to birth of closed L contour delimiting island of fixed handedness ellipses with/without C points. Elaborated approach and presented results start the dynamic singular optics of time-dependent vector light fields.     

The competitive salesman problem on a network: a worst-case approach

We provide a complexity analysis of the problem of optimal routing of a server on a transportation network in the presence of a competing server. The server that reaches a node first gets the profit from the node. The objective is to maximize the worst-case profit.     

Advances on photosystem II investigation by measurement of delayed chlorophyll fluorescence by a phosphoroscopic methods

A method for data acquisition based on recording of light signal from a conventional phophoroscope fluorometer with high-speed digitalization is proposed to extract more information from a delayed chlorophyll a fluorescence (DF) signal. During the signal processing from all points registered by the fluorometer, we obtain simultaneously a large number of induction curves of DF decaying at different time ranges. In addition, it is possible to register a series of dark relaxation kinetics of DF, recorded at different moments during the induction period or at different temperatures. This allows the evaluation of the contribution of DF kinetic components during the induction period or at different temperatures and the comparison between DF signals registered with different phophoroscopes. With the phosphoroscope system used in this study, we have shown that the contribution of the millisecond components (with lifetimes 0.6 and 2-4 ms) predominates during the first second of the induction period. After 1 s of illumination, the amplitudes of the 0.6 ms and 2-4 ms components and of the slower one (with lifetime more than 10 ms) become approximately equal. The change in lifetime of the different components during the induction and during gradual heating is also observed. It is shown that all registered DF kinetic components have different temperature dependences.     

Polymer-Modified Single-Walled Carbon Nanotubes Affect Photosystem II Photochemistry,Intersystem Electron Transport Carriers and Photosystem I End Acceptors in Pea Plants

Single-walled carbon nanotubes (SWCNT) have recently been attracting the attention of plant biologists as a prospective tool for modulation of photosynthesis in higher plants. However, the exact mode of action of SWCNT on the photosynthetic electron transport chain remains unknown. In this work, we examined the effect of foliar application of polymer-grafted SWCNT on the donor side of photosystem II, the intersystem electron transfer chain and the acceptor side of photosystem I. Analysis of the induction curves of chlorophyll fluorescence via JIP test and construction of differential curves revealed that SWCNT concentrations up to 100 mg/L did not affect the photosynthetic electron transport chain. SWCNT concentration of 300 mg/L had no effect on the photosystem II donor side but provoked inactivation of photosystem II reaction centres and slowed down the reduction of the plastoquinone pool and the photosystem I end acceptors. Changes in the modulated reflection at 820 nm, too, indicated slower re-reduction of photosystem I reaction centres in SWCNT-treated leaves. We conclude that SWCNT are likely to be able to divert electrons from the photosynthetic electron transport chain at the level of photosystem I end acceptors and plastoquinone pool in vivo. Further research is needed to unequivocally prove if the observed effects are due to specific interaction between SWCNT and the photosynthetic apparatus.     

Thermopower of a moderate heavy-fermion compound YbZnCu4

The thermopower coefficients S of samples of a moderate heavy-fermion compound YbZnCu₄ and metallic LuZnCu₄ are measured in the temperature range 5–300 K. Data on the temperature dependence of the thermopower coefficient S of YbZnCu₄ suggest that this material is a heavy-fermion compound with a Kondo temperature of ～50 K.     

Structure and interaction of antiferromagnetic domain walls in hexagonal YMnO3

The structure of antiferromagnetic (AFM) domain walls and their interaction with lattice strain are derived taking the multiple-order-parameter compound YMnO3 as a model example. Contrary to the conviction that AFM domain walls are energetically unfavorable, their interaction with lattice strain lowers the total energy of the system and leads to a piezomagnetic clamping of the electric and magnetic order parameters in good agreement with the available experimental data.