MAX PRINCIPLE AND UNIVERSAL SPECTRUM OF PERIODS: COMPLEMENTARY FRACTAL DISTRIBUTIONS AS CONSEQUENCE OF RATIONAL AND IRRATIONAL RELATIONS BETWEEN PARTS OF THE WHOLE SYSTEM

The paper discusses the assumption that Mach principle should result in existence of a universal spectrum of periods. It is shown that fragments of such a spectrum were found in time series of fluctuations of various processes. A general approach is considered that demonstrates the emergence of discrete states in the spectra of periods, which is based on two basic concepts: resonance and roughness of a physical system. This approach leads to the existence of two complementary fractal distributions associated with sets of rational and irrational relations between the elements of the whole system. A brief review of works that also consider universal spectra of periods is given.

Phonons transmission through atomic interface connecting two semi-infinite 2D lattices with different meshes

A calculation of the phonon contribution to the coherent transport between two-dimensional (2D) lattices is presented in this paper. The model structure is obtained by the juxtaposition of semi-infinites square ([Formula: see text] and triangular ([Formula: see text] leads, which thus define the nanojunction [Formula: see text]/[Formula: see text] and its inverse [Formula: see text]/[Formula: see text]. We determine, numerically and by simulation, the 2D interface observables for different values of masses and elastic coupling in the nanojunction zone. The local dynamics and atomic nanojunction response to the microscopic changes, in the interfacial domain, are subjects to our investigation. The theoretical formalism based on the matching technique is applied to describe the lattice dynamics and the evanescent phonon modes, in the two studied 2D interfaces. We mainly analyze the vibration spectra, the coherent phonon transmission/reflection and the phononic transmittance through the interface, as elements of a Landauer–Büttiker type scattering matrix. The obtained results show that the nanojunction domain is an effective phonon splitter and suggest that its characteristics may be controlled by varying its nanometric parameters. The observed fluctuations are due to the coherent coupling between continuum modes and the phonons’ discrete states induced by the connected atomic sites.

Quasi-band structure of quantum-confined nanocrystals

We discuss the electronic properties of quantum-confined nanocrystals. In particular, we show how, starting from the discrete molecular states of small nanocrystals, an approximate band structure (quasi-band structure) emerges with increasing particle size. Finite temperature is found to broaden the discrete states in energy space forming even for nanocrystals in the quantum-confinement regime quasi-continuous bands in k-space. This bands can be, to a certain extend, interpreted along the lines of standard band structure theory, while taking also finite size and surface effects into account. We discuss this on various prototypical nanocrystal systems.

Episodic timing: how spontaneous alpha clocks, retrospectively

We seldom time life events intently yet recalling the duration of events is lifelike. Is episodic time the outcome of a rational after-thought or of physiological clocks keeping track of time without our conscious awareness of it? To answer this, we recorded human brain activity with magnetoencephalography (MEG) during quiet wakefulness. Unbeknownst to participants, we asked them after the MEG recording to guess its duration. In the absence of overt attention to time, the relative amount of time participants’ alpha brain rhythms (α ~10 Hz) were in bursting mode predicted participants’ retrospective duration estimate. This relation was absent when participants prospectively measured elapsed time during the MEG recording. We conclude that α bursts embody discrete states of awareness for episodic timing.One-Sentence SummaryIn the human brain, the relative number of alpha oscillatory bursts at ~10 Hz can tell time when the observer does not attend to it.

Assessment of Border Patrol Group Ammunition Amount Required for Border Fighting

he purpose of the article was to assess the amount of ammunition required by the border guard during the battle with the sabotage and reconnaissance group until the arrival of reinforcements. To achieve the goal, a method of mathematical modeling of combat processes in the class of Markov processes with continuous time and discrete states was chosen. As a result, the method made it possible to construct the required models, check their adequacy, due to the found internal law of battle, and evaluate the performance on a specific practical example.

Tracking interfacial single-molecule pH and binding dynamics via vibrational spectroscopy

Understanding single-molecule chemical dynamics of surface ligands is of critical importance to reveal their individual pathways and, hence, roles in catalysis, which ensemble measurements cannot see. Here, we use a cascaded nano-optics approach that provides sufficient enhancement to enable direct tracking of chemical trajectories of single surface-bound molecules via vibrational spectroscopy. Atomic protrusions are laser-induced within plasmonic nanojunctions to concentrate light to atomic length scales, optically isolating individual molecules. By stabilizing these atomic sites, we unveil single-molecule deprotonation and binding dynamics under ambient conditions. High-speed field-enhanced spectroscopy allows us to monitor chemical switching of a single carboxylic group between three discrete states. Combining this with theoretical calculation identifies reversible proton transfer dynamics (yielding effective single-molecule pH) and switching between molecule-metal coordination states, where the exact chemical pathway depends on the intitial protonation state. These findings open new domains to explore interfacial single-molecule mechanisms and optical manipulation of their reaction pathways.