Matrix Factorizations and Homological Mirror Symmetry on the Torus

We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model.Comment: 41 pages, 9 figures, v2: reference added, minor corrections and clarifications, version published in JHE

Synthesis of an automated control system for the flow of active power along a power line in overload condition

Currently, there are practically no automated systems for controlling power flow within the specified limits when the power line is overloaded by active power. Regulation is assigned to the dispatchers of the power system or is carried out by means of emergency automation, which disconnects consumers. Therefore, an urgent task is to expand the arsenal of tools for automatic control of active power flow in overload mode. Relevance. A significant increase in electricity consumers leads to a complication of the electric power system. The workload for dispatching personnel is increasing. Maintaining the smooth operation of the elements of the power system is a very important and responsible task. In modern electric power industry, timely warning and elimination of overloads of network elements are relevant. The study aims are development and research of an intelligent automatic control system for the flow of active power along a power line based on the mathematical apparatus of fuzzy logic. The system is based on the use of the regulating effect of the load. Research methodology. Methods of calculating static load model during their actualization were used. The method of fuzzy sets was used in the construction of an intelligence control system for active power flows in overload condition. The effectiveness was estimated by expert methods. Results. The use of artificial intelligence methods for automatic regulation of transformer voltage under load allows up to 5-7 % reducing the flow of active power in overload mode. Keywords: overload, automation, power systems, voltage regulation under load

Opening Mirror Symmetry on the Quintic

Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We reproduce the first few instanton numbers by a localization computation directly in the A-model, and check Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.Comment: 26 pages. v2: minor corrections and improvement

Magnetic Gaps related to Spin Glass Order in Fermionic Systems

We provide evidence for spin glass related magnetic gaps in the fermionic density of states below the freezing temperature. Model calculations are presented and proposed to be relevant for explaining resistivity measurements which observe a crossover from variable-range- to activated behavior. The magnetic field dependence of a hardgap and the low temperature decay of the density of states are given. In models with fermion transport a new metal-insulator transition is predicted to occur due to the spin-glass gap, anteceding the spin glass to quantum paramagnet transition at smaller spin density. Important fluctuation effects due to finite range frustrated interactions are estimated and discussed.Comment: 4 pages, 1 Postscript figure, revised version accepted for publication in Physical Review Letter

Mirror duality and noncommutative tori

In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence on generalized complex tori and generalize the mirror duality on complex tori to the case of noncommutative complex tori.Comment: 22pages, no figure

Effective superpotentials for B-branes in Landau-Ginzburg models

We compute the partition function for the topological Landau-Ginzburg B-model on the disk. This is done by treating the worldsheet superpotential perturbatively. We argue that this partition function as a function of bulk and boundary perturbations may be identified with the effective D-brane superpotential in the target spacetime. We point out the relationship of this approach to matrix factorizations. Using these methods, we prove a conjecture for the effective superpotential of Herbst, Lazaroiu and Lerche for the A-type minimal models. We also consider the Landau-Ginzburg theory of the cubic torus where we show that the effective superpotential, given by the partition function, is consistent with the one obtained by summing up disk instantons in the mirror A-model. This is done by explicitly constructing the open-string mirror map.Comment: 57p, 7 figs, harvma

A Point's Point of View of Stringy Geometry

The notion of a "point" is essential to describe the topology of spacetime. Despite this, a point probably does not play a particularly distinguished role in any intrinsic formulation of string theory. We discuss one way to try to determine the notion of a point from a worldsheet point of view. The derived category description of D-branes is the key tool. The case of a flop is analyzed and Pi-stability in this context is tied in to some ideas of Bridgeland. Monodromy associated to the flop is also computed via Pi-stability and shown to be consistent with previous conjectures.Comment: 15 pages, 3 figures, ref adde

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

Low temperature breakdown of coherent tunneling in amorphous solids induced by the nuclear quadrupole interaction

We consider the effect of the internal nuclear quadrupole interaction on quantum tunneling in complex multi-atomic two-level systems. Two distinct regimes of strong and weak interactions are found. The regimes depend on the relationship between a characteristic energy of the nuclear quadrupole interaction $\lambda_{\ast}$ and a bare tunneling coupling strength $\Delta_{0}$. When $\Delta_{0}>\lambda_{\ast}$, the internal interaction is negligible and tunneling remains coherent determined by $\Delta_{0}$. When $\Delta_{0}<\lambda_{\ast}$, coherent tunneling breaks down and an effective tunneling amplitude decreases by an exponentially small overlap factor $\eta^{\ast}\ll1$ between internal ground states of left and right wells of a tunneling system. This affects thermal and kinetic properties of tunneling systems at low temperatures $T<\lambda_{*}$. The theory is applied for interpreting the anomalous behavior of the resonant dielectric susceptibility in amorphous solids at low temperatures $T\leq 5$mK where the nuclear quadrupole interaction breaks down coherent tunneling. We suggest the experiments with external magnetic fields to test our predictions and to clarify the internal structure of tunneling systems in amorphous solids.Comment: To appear in the Physical Review

ДОСЛІДЖЕННЯ ПРОЯВУ ПОСУХИ ТА ЇЇ ВПЛИВУ НА ТЕПЛОВИЙ РЕЖИМ ВЕГЕТАЦІЙНОЇ ПОВЕРХНІ СІЛЬСЬКОГОСПОДАРСЬКИХ КУЛЬТУР ПРИ ЗРОШЕННІ

&nbsp;Relevance of the topic. In recent years, irrigation management practices have faced new challenges related to climate change and the increase in the frequency and intensity of droughts in the southern regions. In addition, the latest technical and technological capabilities have emerged in irrigated agriculture to more effectively manage technological processes. All these processes occurring in real production and in the market of scientific and technical products, have determined the possibility and necessity of studying the influence of natural and agricultural conditions on the processes of energymass transfer in the "soil-plant-atmosphere" environment to improve management methods in modern irrigation conditions.&nbsp;Purpose of research is to investigate the features of formation of crop thermal regime in the conditions of air and soil drought manifestation under irrigation during 2018-2019.&nbsp;Research object. The research was carried out at the production fields of the farm&nbsp; “Freedom Farm International” in the Kakhovsky district of Kherson region during 2018-2019. Two experimental sites were equipped to carry out experimental studies on the crop rotation of "Gornostayevske -2".&nbsp;Methodology and Research methods. The methodology for the conduct of thermal water balance and phenological observations on the growth and development of crops at the experimental sites was applied. Standard field research techniques were used. Analytical, field, simulation modeling, mathematical statistics, geoinformation technologies (GIS), remote sensing of the Earth (RS) methods were used.&nbsp;Research results. As a result of the research in 2018-2019 a database of farm fields (crops, sowing dates, soil conditions, initial moisture reserves, irrigation machines and their characteristics) was created; phenological observations of plant growth and development were performed, heat and water balance calculations were made. It was established that to ensure optimal conditions for the use of thermal energy in different drought conditions, it is necessary to improve models and algorithms for operational planning of crop irrigation. Thus, to mitigate the influence of atmospheric drought, it is recommended to conduct refreshing irrigation, the timing of which can be determined on the basis of monitoring the temperature of the vegetation surface, using the data from the space images or ground-based observations. In addition, under drought conditions, in the case of applying water-balance methods used in irrigation management, it is necessary to adjust the biological coefficients of water consumption by crops, based on modeling the production process using the WOFOST model and identifying its parameters with the help of space images. The obtained new knowledge is aimed at improving irrigation management methods in modern conditions.Представлено результати експериментальних досліджень, проведених протягом 2018-2019 років на дослідних полях господарства Каховського району Херсонської області з визначення особливостей формування теплового режиму посівів в умовах прояву атмосферної та ґрунтової посух при зрошенні. Обґрунтовано параметри моделей волого-теплопереносу в приземному шарі повітря та в ґрунті, визначено параметри моделі продукційного процесу з метою уточнення розрахунків водоспоживання сільськогосподарських культур та відповідно удосконалення управління поливами для забезпечення більшої продуктивності сільськогосподарських культур. Розрахунки та аналіз енергетичного балансу дослідних полів показав суттєвий вплив посухи на продуктивність використання сонячної енергії. Результатами проведених досліджень у 2018-2019 рр. підтверджено найсильніше цей вплив проявляється при сумісній дії атмосферної та ґрунтової посух. Встановлено, що за таких умов основними факторами, що впливають на процеси &nbsp;в середовищі «ґрунт-рослина–атмосфера» та уповільнюють продукційний процес рослин є: дефіцит активних вологозапасів у ґрунті при відхиленні термінів поливів більше ніж на три дні від рекомендованих; тривалі періоди з високими денними температурами повітря (більше 30 °С), що збільшують температуру підстилаючої поверхні та відповідно збільшують відношення між непродуктивною частиною теплової енергії, що йде на турбулентний обмін повітря у посівах, та продуктивною її складовою, що йде на випаровування та продукційний процес (число Боуена). Кількісна &nbsp;характеристика даних впливів залежить від інтенсивності та тривалості атмосферної посухи та якості оперативного управління поливами. Тому для планування поливів в умовах атмосферної посухи важливо зменшити тривалість періодів перевищення максимально допустимих температур підстилаючої поверхні ґрунту, при яких число Боуена коливається в межах 1,2–1,5, за рахунок проведення освіжаючих поливів. Якщо внаслідок різних причин при управлінні поливами все ж таки не вдається повністю уникнути прояву посухи, необхідним є коригування біокліматичних коефіцієнтів сумарного випаровування для врахування редукції випаровування в цих умовах