Towards investigation of evolution of dynamical systems with independence of time accuracy: more classes of systems

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are much extended, now including systems that are; (1) non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent perturbation; (3) non-conservative (with dissipation). These systems cover various types of N-body gravitating systems of astrophysical and cosmological interest, such as the orbital evolution of planets, minor planets, artificial satellites due to tidal, non-tidal perturbations and thermal thrust, evolving close binary stellar systems, and the dynamics of accretion disks.Comment: Eur. Phys. Journ. C (in press), to match the published version, 4 page

A principal possibility for computer investigation of evolution of dynamical systems with independent on time accuracy

Extensive N-body simulations are among the key means for the study of numerous astrophysical and cosmological phenomena, so various schemes are developed for possibly higher accuracy computations. We demonstrate the principal possibility for revealing the evolution of a perturbed Hamiltonian system with an accuracy independent on time. The method is based on the Laplace transform and the derivation and analytical solution of an evolution equation in the phase space for the resolvent and using computer algebra.Comment: Eur Phys Journ C (in press), to match the version to appear, 7 pages, 3 fig

A weakly random Universe?

The cosmic microwave background (CMB) radiation is characterized by well-established scales, the 2.7 K temperature of the Planckian spectrum and the $10^{-5}$ amplitude of the temperature anisotropy. These features were instrumental in indicating the hot and equilibrium phases of the early history of the Universe and its large scale isotropy, respectively. We now reveal one more intrinsic scale in CMB properties. We introduce a method developed originally by Kolmogorov, that quantifies a degree of randomness (chaos) in a set of numbers, such as measurements of the CMB temperature in some region. Considering CMB as a composition of random and regular signals, we solve the inverse problem of recovering of their mutual fractions from the temperature sky maps. Deriving the empirical Kolmogorov's function in the Wilkinson Microwave Anisotropy Probe's maps, we obtain the fraction of the random signal to be about 20 per cent, i.e. the cosmological sky is a weakly random one. The paper is dedicated to the memory of Vladimir Arnold (1937-2010).Comment: 4 pages, 3 figs, A & A (Lett) in press; to match the published versio

Is nonrelativistic gravity possible?

We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.Comment: 4 pages, v2, typos corrected, published in Physical Review

МАСШТАБНЫЙ ЭФФЕКТ В СЕЙСМОТЕКТОНИКЕ

This publication consolidates and analyses experimental data in a wide range of scales in seismotectonics and geo­mechanics, from a micro-size seismic event (an earthquake focus of a few centimetres) to a mega earthquake. It reviews regularities in changes of geometric parameters of faults and fractures in various ranks, their mechanical properties, linear sizes of earthquake foci, time of preparation of dynamic events, and seismic energy.Averaging through the whole range of scales yields ratios close to the law of geometrical similarity. A more detailed consideration gives grounds to conclude that several hierarchic levels can be distinguished and, in different scale, changes of parameters of events follow laws that differ and often deviate from the laws of similarity.It is shown that linear sizes, L from ~500 to 1000 m comprise a transitional range that is a border between two ranges characterized by significantly different scale ratios. Seismicity with shallow foci which is associated with mining operations should be noted separately.According to energy calculation with reference to categories of seismic events, it is established that earthquakes of the Baikal rift system show an anomalous trend of strongly increasing specific energy with increasing scales. In the range of moment magnitudes from 5 to 6.3, an average specific value of seismic energy is higher than an average global value for the same range at least by a factor of 25. It should be clarified whether such an effect is an artefact related to errors in seismic energy calculations or an actual physical effect that is still unexplained. В настоящей работе собран и проанализирован обширный ряд экспериментальных данных во всем диапазоне масштабов, который относится к сейсмотектонике и геомеханике, – от микрособытий с линейным размером очага порядка нескольких сантиметров до мегаземлетрясений. Рассмотрены закономерности изменения геометрических характеристик разноранговых разломов и трещин и их механических свойств, линейных размеров очага землетрясения, времени подготовки динамического события и сейсмической энергии.Усреднение по всему диапазону масштабов дает соотношения, близкие к закону геометрического подобия. Более детальное рассмотрение позволяет обнаружить, что существует несколько иерархических уровней, в которых изменение параметров событий с масштабом происходит по разным законам, зачастую сильно отклоняющимся от законов подобия.Показано, что линейные размеры L~500–1000 м являются некоторой переходной областью, которая оказывается границей между двумя диапазонами, в которых масштабные соотношения существенно разные. Следует отличать и шахтную сейсмичность, глубина очагов которой невелика.Установлено, что для землетрясений Байкальской рифтовой системы отмечается аномальная тенденция сильного возрастания приведенной энергии, рассчитанной по величине класса события, с увеличением масштаба. В интервале моментных магнитуд от 5 до 6.3 усредненное приведенное значение сейсмической энергии превышает среднемировую величину для этого диапазона, по крайней мере, в 25 раз. Необходимо разобраться, является ли этот эффект артефактом, связанным с некорректным расчетом величины сейсмической энергии, или имеет место не объясненный пока физический эффект. 

PCR-Independent Detection of Bacterial Species-Specific 16S rRNA at 10 fM by a Pore-Blockage Sensor.

A PCR-free, optics-free device is used for the detection of Escherichia coli (E. coli) 16S rRNA at 10 fM, which corresponds to ~100-1000 colony forming units/mL (CFU/mL) depending on cellular rRNA levels. The development of a rapid, sensitive, and cost-effective nucleic acid detection platform is sought for the detection of pathogenic microbes in food, water and body fluids. Since 16S rRNA sequences are species specific and are present at high copy number in viable cells, these nucleic acids offer an attractive target for microbial pathogen detection schemes. Here, target 16S rRNA of E. coli at 10 fM concentration was detected against a total RNA background using a conceptually simple approach based on electromechanical signal transduction, whereby a step change reduction in ionic current through a pore indicates blockage by an electrophoretically mobilized bead-peptide nucleic acid probe conjugate hybridized to target nucleic acid. We investigated the concentration detection limit for bacterial species-specific 16S rRNA at 1 pM to 1 fM and found a limit of detection of 10 fM for our device, which is consistent with our previous finding with single-stranded DNA of similar length. In addition, no false positive responses were obtained with control RNA and no false negatives with target 16S rRNA present down to the limit of detection (LOD) of 10 fM. Thus, this detection scheme shows promise for integration into portable, low-cost systems for rapid detection of pathogenic microbes in food, water and body fluids