Spectrum of π\pi-electrons in Graphene As a Macromolecule

We report the exact solution of spectral problem for a graphene sheet framed by two armchair- and two zigzag-shaped boundaries. The solution is found for the $\pi$ electron Hamiltonian and gives, in particular, a closed analytic expression of edge-state energies in graphene. It is shown that the lower symmetry of graphene, in comparison with $C_{6h}$ of 2D graphite, has a profound effect on the graphene band structure. This and other obtained results have far going implications for the understanding of graphene electronics. Some of them are briefly discussed.Comment: Revised in connection with publication in PRL, editin

Spectrum of π\pi Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance

An exact description of $\pi$ electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped edges. This suggests an instructive alternative to the most commonly used approach, where the reference is made to the honeycomb lattice periodic in its A and B sublattices. Several advantages of the macromolecule model are demonstrated. The newly derived analytical relations detail our understanding of $\pi$ electron nature in achiral graphene ribbons and carbon tubes and classify these structures as quantum wires.Comment: 13 pages 8 figures, revised in line with referee's comment

The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.Comment: 13 pages, 11 figure

Landau-Zener transitions in a linear chain

We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for the case of infinite number of states in discrete spectrum. In addition to transition amplitudes we calculate an effective diffusion constant.Comment: 3 figure

Modeling transport through single-molecule junctions

Non-equilibrium Green's functions (NEGF) formalism combined with extended Huckel (EHT) and charging model are used to study electrical conduction through single-molecule junctions. Analyzed molecular complex is composed of asymmetric 1,4-Bis((2'-para-mercaptophenyl)-ethinyl)-2-acetyl-amino-5-nitro-benzene molecule symmetrically coupled to two gold electrodes [Reichert et al., Phys. Rev. Lett. Vol.88 (2002), pp. 176804]. Owing to this model, the accurate values of the current flowing through such junction can be obtained by utilizing basic fundamentals and coherently deriving model parameters. Furthermore, the influence of the charging effect on the transport characteristics is emphasized. In particular, charging-induced reduction of conductance gap, charging-induced rectification effect and charging-generated negative value of the second derivative of the current with respect to voltage are observed and examined for molecular complex.Comment: 8 pages, 3 figure

Lattice Green's function approach to the solution of the spectrum of an array of quantum dots and its linear conductance

In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an attached adatom are derived. The expressions for the linear conductance for the perfect array as well as for the array with a defect are presented. The calculations are illustrated for a dot made of three atoms. The results derived here are also the starting point to include the effect of electron-electron and electron-phonon interactions on the transport properties of quantum dot arrays. Different derivations of the exact lattice Green's functions are discussed

Coherent electron-phonon coupling and polaron-like transport in molecular wires

We present a technique to calculate the transport properties through one-dimensional models of molecular wires. The calculations include inelastic electron scattering due to electron-lattice interaction. The coupling between the electron and the lattice is crucial to determine the transport properties in one-dimensional systems subject to Peierls transition since it drives the transition itself. The electron-phonon coupling is treated as a quantum coherent process, in the sense that no random dephasing due to electron-phonon interactions is introduced in the scattering wave functions. We show that charge carrier injection, even in the tunneling regime, induces lattice distortions localized around the tunneling electron. The transport in the molecular wire is due to polaron-like propagation. We show typical examples of the lattice distortions induced by charge injection into the wire. In the tunneling regime, the electron transmission is strongly enhanced in comparison with the case of elastic scattering through the undistorted molecular wire. We also show that although lattice fluctuations modify the electron transmission through the wire, the modifications are qualitatively different from those obtained by the quantum electron-phonon inelastic scattering technique. Our results should hold in principle for other one-dimensional atomic-scale wires subject to Peierls transitions.Comment: 21 pages, 8 figures, accepted for publication in Phys. Rev. B (to appear march 2001

Біомаркери в діагностиці хвороб пародонта

The chronic course of periodontitis and gingivitis affects up to 80 % of the adult population, making them one of the most common diseases of mankind. The disease is initiated by the accumulation of bacteria along the gingival margin and in the space between the gingival tissue and the teeth. The absence of an acute pain clinic for periodontal diseases is one of the main reasons for the low level of patients seeking dental care. Diagnosis of periodontal disease, as a rule, is carried out by a dentist, it includes a visual examination of the gum tissue and a number of other protocol procedures, including additional diagnostic methods – a clinical assessment of the roentgenogram. At the same time, conventional clinical and radiographic methods for periodontal diagnostics are capable of only a retrospective diagnosis, they cannot detect or predict the activity of periodontitis. For these reasons, in recent years, potential biomarkers for the diagnosis of periodontal tissue diseases have been actively investigated. The source of biomarkers, in the first place, are considered gingival fluid and saliva, such as those that are in direct contact with the affected tissues. Given the foregoing, it seems appropriate to review the literature on biomarkers of gingival fluid and saliva used to diagnose periodontal diseases and the possibility of developing easy-to-use test methods for their early diagnosis. The aim of the study – to evaluate the prospects of using biomarkers in dental practice, in particular in the diagnosis of parathon tissue pathology, including peri-implant pathology, based on the analysis of literature data. Materials and Methods. The study used biblical and analytical methods. Results and Discussion. The sources of scientific and medical information on the application of biomarkers in the diagnosis of periodontal diseases are analyzed and processed. Conclusions. Despite the fact that the diagnostic value of oral fluids is recognized and there is a significant number of potential biomarkers, the studies conducted to date have proved inadequate to provide clinically reliable and useful information for practitioners in terms of more accurate diagnosis and treatment planning.Хроническое течение пародонтита и гингивита поражает до 80 % взрослого населения, ставши одной из самых распространенных болезней человечества. Заболевания инициируется накоплением бактерий вдоль десневого края и в пространстве между десневыми тканями и зубами. Отсутствие клиники острой боли при заболеваниях пародонта является одной из основных причин низкого уровня обращений пациентов за стоматологической помощью. Диагностику заболеваний пародонта, как правило, проводит врач-стоматолог. Она включает визуальный осмотр тканей десен и ряд других протокольных процедур, в том числе дополнительных методов диагностики – клиническую оценку рентенограммы. В то же время, обычные клинические и рентгенографические методы диагностики пародонта способны лишь к ретроспективному диагнозу, они не могут обнаружить или предсказать активность пародонтита. Поэтому в последние годы активно исследуются потенциальные биомаркеры для диагностики болезней тканей пародонта. Источником биомаркеров в первую очередь является десневая жидкость и слюна, как такие, которые непосредственно контактируют с пораженными тканями. Учитывая сказанное, целесообразно проанализировать литературные данные по биомаркерам десневой жидкости и слюны, которые используют для диагностики болезней пародонта и возможности разработать простые в применении тест-методы для ранней диагностики. Цель исследования – проанализировать литературные данные по оценке перспективы применения биомаркеров в стоматологической практике, в частности в диагностике патологии тканей пародонта вместе с периимплантной патологией. Материалы и методы. В исследовании применены библиосематический и аналитический методы. Результаты исследований и их обсуждение. В статье проанализированы и обработаны источники научно-медицинской информации, касающиеся применения биомаркеров в диагностике болезней пародонта. Выводы. Несмотря на то, что в диагностике ротовой жидкости имеется значительное количество потенциальных биомаркеров, проведенные на сегодняшний день исследования оказались недостаточными для предоставления клинически достоверной и полезной информации для практиков с точки зрения более точной диагностики и планирования лечения.Хронічний перебіг пародонтиту та гінгівіту вражає до 80 % дорослого населення, стаючи одним із найпоширеніших серед хвороб людства. Захворювання ініціюється накопиченням бактерій вздовж ясенного краю і в просторі між ясенними тканинами та зубами. Відсутність клініки гострого болю при захворюваннях пародонта є однією з основних причин низького рівня звернень пацієнтів за стоматологічною допомогою. Діагностику захворювань пародонта, як правило, проводить лікар-стоматолог. Вона включає візуальний огляд тканин ясен та ряд інших протокольних процедур, у тому числі додоткових методів діагностики – клінічну оцінку рентенограми. Водночас, звичайні клінічні та рентгенографічні методи діагностики пародонта здатні лише до ретроспективного діагнозу, вони не можуть виявити або передбачити активність пародонтиту. Тому в останні роки активно досліджують потенційні біомаркери для діагностування хвороб тканин пародонта. Джерелом біомаркерів перш за все є ясенна рідина та слина, як такі, що безпосередньо контактують з ураженими тканинами. Враховуючи сказане, доцільно проаналізувати літературні дані щодо біомаркерів ясенної рідини та слини, які використовують для діагностики хвороб пародонта та можливості розробити прості у застосуванні тест-методи для ранньої діагностики. Мета дослідження – проаналізувати літературні дані щодо оцінки перспективи застосування біомаркерів у стоматологічній практиці, зокрема в діагностиці патології тканин парадонта разом із періімплантною патологією. Матеріали і методи. У дослідженні застосовано бібліосематичний та аналітичний методи. Результати досліджень та їх обговорення. У статті проаналізовано та опрацьовано джерела науково-медичної інформації, що стосуються застосування біомаркерів у діагностиці хвороб пародонта. Висновки. Незважаючи на те, що в діагностиці рогової рідини наявна значна кількість потенційних біомаркерів, проведені на сьогодні дослідження виявилися недостатніми щодо надання клінічно достовірної та корисної інформації для практиків з точки зору більш точної діагностики та планування лікування

The Innovation Clusters in the Developments by the Scandinavian School of Cluster Theory

The article generalizes and analyzes the developments by the Scandinavian School of cluster theory (scientists from Sweden, Norway and Denmark) on innovative clusters. It has been found that the Scandinavian scientists considered innovative clusters as an integral component of both the regional and the national innovation systems. It has been clarified that the efficiency of an innovative cluster depends largely on the «knowledge base». It was emphasized that innovative clusters, by facilitating interactive training and generating new ideas, stimulate the development of the «economy of training». It has been determined that the coordinating structures of innovative clusters are the institutions of cooperation that facilitate interaction between enterprises, scientific centres, and authorities. It has been specified that innovative clusters contribute to the emerging of benefits for participants, including the growing opportunities for innovation, improved conditions for establishing a business, and increased productivity. It has been concluded that the development of the inner environment of an innovative cluster depends largely on its relationships to the external environment