Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma. Part two: Solar flares dynamics

In this study which is the continuation of the first part (Pavlos et al. 2012) [1], the nonlinear analysis of the solar flares index is embedded in the non-extensive statistical theory of Tsallis (1988) [3]. The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the singular value decomposition (SVD) components of the solar flares timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using theq$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000) [25]. Our analysis showed clearly the following: (a) a phase transition process in the solar flare dynamics from a high dimensional non-Gaussian self-organized critical (SOC) state to a low dimensional also non-Gaussian chaotic state, (b) strong intermittent solar corona turbulence and an anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes a phase transition to low dimensional chaos, (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of the functions: (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) f(a)$f\left(a\right)$ and D(q)$D\left(q\right)$, and (iii) J(p)$J\left(p\right)$ for the solar flares timeseries and its underlying non-equilibrium solar dynamics, and (d) the solar flare dynamical profile is revealed similar to the dynamical profile of the solar corona zone as far as the phase transition process from self-organized criticality (SOC) to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone.     

Adaptive distributed partitioning filters: non-gaussian initial conditions

The problem of the state estimation of partially unknown, linear systems with non-Gaussian initial conditions in a multisensor environment is addressed in this paper. Two distributed algorithms are presented which can locally process the data collected by different local sensor subsystems. The local estimates are forwarded to a central processing center where the overall optimal estimate is obtained. The proposed algorithms are computationally attractive as well as theoretically interesting     

Gauging the flexibility of fluorescent markers for the interpretation of fluorescence resonance energy transfer

Intramolecular distances in proteins and other biomolecules can be studied in living cells by means of fluorescence resonance energy transfer (FRET) in steady-state or pulsed-excitation experiments. The major uncertainty originates from the unknown orientation between the optical dipole moments of the fluorescent markers, especially when the molecule undergoes thermal fluctuations in physiological conditions. We introduce a statistical method based on the von Mises-Fisher distribution for the interpretation of fluorescence decay dynamics in donor-acceptor FRET pairs that allows us to retrieve both the orientation and the extent of directional fluctuations of the involved dipole moments. We verify the method by applying it to donor-acceptor pairs controllably attached to DNA helices and find that common assumptions such as complete rotational freedom or fully hindered rotation of the dipoles fail a physical interpretation of the fluorescence decay dynamics. This methodology is applicable in single-molecule and ensemble measurements of FRET to derive more accurate distance estimates from optical experiments, without the need for more complex and expensive NMR studies.     

Tsallis statistics and magnetospheric self-organization

In this study we use Tsallis non-extensive statistics for a new understanding the magnetospheric dynamics and the magnetospheric self-organization during quiet and intensive superstorm periods. The _qsens$q_{sens}$, _qstat$q_{stat}$, and _qrel$q_{rel}$ indices set known as the Tsallis q$q$-triplet was estimated during both quiet and strongly active periods, as well as the correlation dimensions and Lyapunov exponents spectrum for magnetospheric bulk plasma flows data. The results obtained by our analysis clearly indicate the magnetospheric phase transition process from a high-dimensional quiet SOC state to a low-dimensional global chaotic state when superstorm events are developed. During such a phase transition process the non-extensive statistical character of the magnetospheric plasma is strengthened as the values of the q$q$-triplet indices changes obtaining higher values than their values during the quiet periods.     

Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma,Part one: Sunspot dynamics

In this study, the non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988, 2004, 2009) ,  and . The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using the q$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2001, 2000)  and . Our analysis showed clearly the following: (a) a phase transition process in the solar dynamics from high dimensional non-Gaussian SOC state to a low dimensional non-Gaussian chaotic state, (b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov’s studies (Zelenyi and Milovanov (1991) [21]); Milovanov and Zelenyi (1993) [22]; Ruzmakin et al. (1996) [26]) (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) multifractal scaling exponent spectrum f(a)$f\left(a\right)$ and generalized Renyi dimension spectrum _Dq$D_q$, (iii) exponent spectrum J(p)$J\left(p\right)$ of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.     

Photochemistry of 1-(N,N-diethylamino)diazen-1-ium-1,2-diolate: an experimental and computational investigation

The aqueous photochemistry of the sodium salt of 1-(N,N-diethylamino)-diazen-1-ium-1,2-diolate (3) has been investigated by both experimental and computational methods. Photolysis results in the formation of the N-nitrosodiethylamine radical anion (5) and nitric oxide (NO) via a triplet excited state. The nitrosamine radical anion either undergoes electron transfer with NO before cage escape to form triplet NO(-) and nitrosamine (minor process) or rapidly dissociates to form an additional molecule of NO and ultimately amine (major process). The production of nitrosamine radical anion 5 upon photolysis of diazeniumdiolate 3 is confirmed by low-temperature EPR spectroscopy. The calculated energetics for the ground and excited states of the parent diazeniumdiolate ion at the CIS and B3LYP levels of theory as well as B3LYP calculations on the fragmentation processes were very effective in rationalizing the observed photodissociation processes.     

10-Alkyl-10-demethylcolchicines

It is shown that colchicine ( 4 ) can regiospecifically be transetherified at C(10) by heating in ROH in the presence of (RO)₄M (M = Ti, Zr; cf. Scheme 2). (PrO)₄Zr in PrOH gives better yields than (PrO)₄Ti in PrOH, and also in the catalytic variant of the conversion is (PrO)₄Zr more effective than (PrO)₄Ti.     

From Colchicine and Some of Its Derivatives to 1,2,3,9,10-Pentamethoxybenzo[a]heptalenes

A two-step synthesis of 4-methylcolchicine ( 13 ), starting from colchicine ( 2 ), has been developed (Scheme 5). In three steps, 4-ethylcolchicine ( 28 ) is also accessible from 2 (Scheme 8). Colchicine ( 2 ) and its derivatives 13 and 28 have been transformed into the benzo[a]heptalene derivatives 9 , 18 , and 34 , respectively, by Hofmann degradation of the corresponding deacetylcolchiceine 3, 19 , and 29 , respectively, followed by methylation of the two O-functions first with diazomethane and then with trimethoxonium tetrafluoroborate (Scheme 2 and 6). The thus formed tropylium salts gave, on deprotonation with Me₃N in CHCl₃, the expected pentamethoxybenzo[a]heptalenes 9, 18 , and 34 , respectively. X-Ray crystal-structure analysis of 9 (Fig.3) and 18 (Fig. 7), determination of the vicinal coupling constants of the H-atoms at the heptalene skeleton as well as the measurement of the racemization rate of the new benzo[a]heptalenes revealed a marked influence of the substituent at C(4) on the degree of twisting of the heptalene skeleton. The absolute configuration of the resolved heptalenes was deduced from their long-wavelength CD maxima around 350 nm. The heptalenes with a negative maximum in this range possess (7aP)-configuration.     

Wilson's functional equation for vector and matrix functions

We determine the general solution of the functional equation

where is a 2-divisible abelian group, is a vector-valued function and is a matrix-valued function. Using this result we solve the scalar equation

which contains as special cases, among others, the d'Alembert and Wilson equations and the parallelogram law.

     

Time-scale for critical growth of partial and supercavitation development over impulsively translating projectiles

A physical mechanism is proposed to explain an experimentally observed critical time scale that governs the partial cavity development over blunt free flying cylindrical projectiles. The projectiles were ejected using a modified gas-gun mechanism consisting of a barrel and explosive charge. Upon ignition, high-pressure gases forced a projectile down the launch barrel and into quiescent water. Results indicate that initial small cavities created at the projectile forebody are convected downstream where they subsequently grow towards the forebody, partially enveloping the projectile in a vapor cavity. The time at which the initially stable bubbles rapidly expand signifies that the partial cavity development process has begun. When this time is quantified and is non-dimensionalized appropriately, a time-scale for the critical growth (CGTS) for the cavitation is revealed. A plausible explanation of the partial cavity development process observed in these experiments is that the process is due to the interaction between small cavitation bubbles shed from the projectile forebody and the vortex ring generated by the impulsively started projectile. This interaction mediates the destabilization and spontaneous growth of small unstable bubbles resulting in the formation of partial cavitation over the projectile. An additional supercavitation formation mechanism was observed and is attributed to the launch mechanism. This process is not due to pure hydrodynamic cavitation, but rather an effect we term “gas-leakage” whereby the driving gases contaminated the aft flow field near the projectile and thus facilitated supercavitation to occur on a reduced time scale. This mechanism is equivalent to off-body ventilated supercavitation.