Integral methods in complex analysis and algebraic geometry
Krasnoyarsk Scientific School carrying out the multidimensional complex analyses was formed in 1965 under the direction of L. A. Aizenberg and A. P. Yuzhakov; the first one directed the integral representations for holomorphic functions and the second was at the head of the theory of multidimensional residues mentioned in the works of E. Martinelli and J.-P. Leray.
During the years of the school formation the basic principles of the theory of integral representations and deductions have been established, integrated methods were linked with algebraic and differential equations. These studies are reflected in monographs by L. A. Aizenberg and A. P. Yuzhakov; A. K. Tsikh; A. M. Kytmanov; N. N. Tarkhanov; L. S. Maergoiz.
Fundamental results were drawn in complex convexity, which were subsequently used and expanded to the developed theory in the monographs of Scandinavian mathematicians L. Hörmander; M. Andersson, M. Passare and R. Sigursson. The stability problem of two-dimensional digital recursive filters was also solved.
Scientific fields and research issues
It is widely known that one of the most popular of integral transformations — Fourier transform — plays an important role in the issue of showing the dualistic relations between the wave and the corpuscular theory of light. All the related integral transforms (by Laplace, Mellin, Cauchy and also much later Radon transform describing the principle of modern tomograph operating) have similar properties as, essentially, they are functionals in spaces of other functional objects defined on manifolds.
The effectiveness of integral transformations use is particularly evident within the complex analysis, where, due to the Cauchy-Poincare theorem, i. e. theory of residues, the possibility of exact or asymptotic computation of integrals is greatly enhanced. The theory of residues, which stands at the crossroads of complex analysis and algebraic geometry plays an important role in these maths fields and in their applications too: in the theory of commutative algebra duality, in the study of vector fields, differential and difference equations.
Traditionally, two approaches are mainly considered in the theory of multidimensional residues: homological (the theory of integration of closed differential forms over cycles) and stream-based (based on the integration of finite test forms).
Both approaches are based on two things: the first is the construction of residual nuclei issue, and the second is the issue of natural dual cycles to specified nuclei selection.
Dendroclimate and dendroecological monitoring of Northern Eurasia forests
Goals and research focus:
- expanding the existing network of dendroclimate monitoring stations in Northern Eurasia region and improving the methods of estimating the influence of climatic and non-climatic nature factors on the trees growth;
- using the indicative possibilities of tree rings for getting knowledge about the carbon exchange between vegetation and atmosphere.
- Data collection and construction of long tree-ring chronologies in Western Siberia territory, Yakutia and Chita region, the north of Finland. Updating of existing chronologies and obtaining new ones of a thousand years long and more.
- Improving the statistical and imitation models of tree growth reaction to the local and regional climate changes.
- Spatial analysis of changes in the tree growth in different time intervals in the 20th and 21st centuries due to regional climate change at high latitudes.
- Improving the methods of statistical long tree-ring chronologies forecasting (MTM spectral decomposition, wavelet analysis, etc.) to isolate and estimate the cyclicities of different intensity in the growth of woody plants.
- Analysis of connections between long tree-ring chronologies of northern Eurasia and the indices of atmospheric circulation.
- Joint analysis of long growth changes, the compactness of tree rings, and the content of 13C and 18O isotopes as a tension indicators of physiological processes for carbon storage, and indirect indicators of climate change.
- Analysis of the seasonal dynamics of the ratio of carbon isotopes and the anatomical structure of annual rings of conifers in the north of Central Siberia and in the north of Sweden due to weather factors for the development of improved eco-physiological model of carbon dioxide accumulation in trees.
- Analysis of the climatic factors impact on the annual production of various components (trees, shrubs, mosses) for the quantitative assessment of current trends in northern ecosystems productivity changes.
Among the first academic scientific schools that were created in Krasnoyarsk and received the world recognition, the School of Environmental Biophysics was founded by the research of Professor Terskova and Professor Gitelzon, Acting member of the Russian Academy of Sciences. Subsequently it was developed by I. I. Gitelzon into modern school of Biophysics and Biotechnology of supraorganism systems.
Achievements and results
Methodology for the synthesis of closed ecological systems based on the developed biotechnology of biosynthesis parametric control in populations of microorganisms and plants was developed. It allowed developing «Bios», the first functioning closed ecosystem for human life support remaining unique. Nowadays the research is going on in collaboration with the European Space Agency.
The experimental model of a new generation Bioregenerative life support systems (BLSS) for deep space missions, based on a new approach to the repeating of matter cycle — the biological and physico-chemical «burning» of dead-end vegetable products, which provided BLSS increased resistance and cycle degree of isolation more than 95 % has been calculated and created.
The developed methodology is transferred to the study of nature ecosystems.
Based on the received fundamental knowledge of the mechanisms controlling the synthesis of polymeric macromolecules by bacteria hemoautotrophic a family of bioresorbable linear biopolymers with different chemical structures was synthesized, their basic physical and chemical properties were studied. A family of polymeric medical devices was received from polyalcanoates. A complex biomedical research was carried out, specifications were developed and registered by the Russian State Standard for three types of polymers: for heart vessels prosthetics, for growing cells scaffolds, and for a long deposit of medicines within a body.
The genes and protein structure of emitting ferments — luciferases of several species of animals have been decoded. Based on these research of luminescent ferments and their genes by genetic engineering and chemical synthesis highly sensitive bioluminescent labels for molecular diagnostics (immune-ferment analysis, thyroid and gonadotropic hormones, alpha-fetoprotein, hepatitis B and reagents for the quantitative analysis of PCR products) have been created.
Radio navigation and radar systems and devices
Radio Engineering Scientific School was established in 1941.
It was originated by outstanding designers of radiotechnical systems: Member of the Russian Academy of Sciences A.A. Raspletin; Dr. of Technical Sciences, Professor G.F. Ignatiev; Dr. of Technical Sciences, Professor V. G. Taranenko; M. K. Chmykh — one of the greatest specialists in the field of digital measurement equipment, the organizer of the Research Institute of Radio Engineering of the Krasnoyarsk State Technical University, Head. Chair of «Radio-technical systems»; Dr. of Technical Sciences, Professor G. Y. Shaidurov.
Achievements and results
Under the leadership of candidate. tech. Sciences, Professor V.I. Kokorin basic theory and hardware and software were developed to create a domestic multi-function receiver-satellite-navigation systems (RNS) GLONASS, compatible with American GPS system.
The bases of the theory of goniometric radio navigation measurements of satellite RNS GLONASS — GPS, for the first time in Russia implemented in receivers of IRA-type were created.
Algorithmic and hardware and software for high-precision marine radar station in the UHF wave band and system in the medium-wave range were developed.
A wide variety of Research Laboratories and Centers give opportunities to do research for our faculty, students, postdoctoral fellows and visiting scientists.
Ecosystem Biogeochemistry laboratory
Goals and research focus
Carrying out the multidisciplinary research in next fields: biology (basic), ecology, space research and technologies, including instrument engineering and economics. Three interacting research groups are included: the data gained during many-year observations from the international tall tower facilities as a part of projects studying the dynamics of greenhouse gases in the atmosphere, the data from the satellite data receiving station of Sukachev Institute of Forest (Siberian Branch of the Russian Academy of Sciences) and SibFU geoinformation system.
- Experimental and theoretical studies of carbon stocks, including greenhouse and dispersed gases affecting Eurasia ecosystems.
- Development and implementation of multisensored concept for remote sensing data application in spatial analysis and carbon and greenhouse stock modeling as well as the efficiency of Eurasia ecosystems under the observed climate changes and the replacement of nature management type.
- Ecological and economical estimate of Eurasia ecosystems’ capacity and the bases for carbon quotas on the territory of Russian Federation in terms of international policies and standards.
- Response of carbon exchange flows in above-ground ecosystems with atmosphere and hydrosphere in river Yenisei basin to climate changes.
Dr. Ernst Detlef Schulze, Max-Planck-Institute, Jena, Germany
Bioluminescent biotechnologies laboratory
The laboratory «Bioluminescent biotechnologies» was created under the direction of Nobel Prize winner professor Osamu Shimomura with the support of the Russian Federation Government.
Goals and research focus
- The study molecular and cellular organization of different organisms’ bioluminescent systems.
- Development and implementation of highly effective methods for analytical use of bioluminescent phenomenon in biology, medical diagnostics and environment health monitoring.
- Development of academic programs based on bioluminescent phenomenon.
- General patterns and differences within the molecular mechanisms of coelenterazine-dependent bioluminescent proteins functioning.
- New data on the molecular-cellular organization and the behavior of luminescent higher fungi and annelids bioluminescent systems.
- Experimental physico-chemical models for studying ferment coupling chain functioning and mechanisms of ferments stabilization inside the cell and composite at the sample of the luminescent system of lumi-bacteria.
- Highly-effective bioluminiscent molecular diagnosticums, suitable for implementation in medical practice.
- Portative lab for samples toxicity determination.
- Lectures and practical courses on the molecular principles of bioluminescence and biolumi-based analytical systems and workshops on microbiology, biophysics and biochemistry using bioluminescence.
Complex Analysis and Differential Equations laboratory
The Laboratory was created in June, 2014 with the supported of the Russian Federation Government.
Goals and research focus
The main laboratory mission is based on the development of integral methods for multidimensional complex analysis, and the spectral theory of differential equations methods and their implementation to solve fundamental problems of modern mathematics. Particularly, special attention is paid to the problems of digital signal processing, theoretical physics, complexity theory.
Research supervisor: professor Ari Laptev
Laboratory of new biomaterials biotechnology
Goals and research focus: organization of research, design and pilot production of the biodegradable material based on polymers of microbial origin.
The foundation of «Biotechnology of new materials» laboratory at SibFU to create a scientific basis and the experimental point of convenient use of biodegradable PHAs polymers to develop new high-tech biomedical technologies.
Research supervisor: professor Anthony J. Sinskey.
Forest Genomics Laboratory
Was created in April, 2014 in terms of the project «Genomic studies of the main boreal forest forming conifer species and their most dangerous pathogens in Russian Federation», supported by the Russian Federation Government.
Goals and research focus
The main objective of the project is the creation of new, competitive, modern, dynamic and well-equipped laboratory of Forest Genomics, integrated both in scientific and educational SibFU infrastructure, able to carry out modern scientific research including those stated in the framework of the full genome sequencing, comparative analysis and annotation of genomes in main forest-forming species of the Russian Federation — Siberian larch (Larix sibirica Ledeb.), Scotch pine (Pinus sylvestris L.) and Siberian stone pine (Pinus sibirica, Du Tour.) and their most dangerous pathogens, primarily fungi belonging to the complexes Armillaria mellea s.l. and Heterobasidion annosum s.l., which cause catastrophic shrinking of Russian boreal forests, aggravating by established decrease in precipitation and a simultaneous increase in surface air temperature in the physiologically important periods for woody plants , frequent in the last two decades and likely related to global climate change.
In addition, this project will help to get important information and develop highly informative molecular genetic markers, which can be effectively used to determine the origin of wood, study and monitoring of genetic variability of coniferous forests, their adaptation to climate change and to create a breeding and nature conservation programs. These very problems have been claimed as the highest priority for the forestry in Integrated Biotechnology Development Program in the Russian Federation for the period until 2020, approved by the Government of the Russian Federation, April 24, 2012.
Dr. Konstantin Krutovsky, a leading researcher at the N. Vavilov Institute of General Genetics, Russian Academy of Sciences, professor of the Agricultural and Mechanical University of Texas (USA) and University of Göttingen (Germany).
Laboratory for nonlinear optics and spectroscopy
Goals and Research Focus
- Energy transfer and improving light harvesting for efficient biosolar energy production. Photosynthesis is might be the most important biological process on Earth. Directly or indirectly, photosynthesis provides many of mankind requirements such as food, building materials and the energy. The energy stored in natural resources like as petroleum, natural gas, coal and wood all came from the sun using photosynthesis. This is the reason why scientific research of photosynthesis is actually important. If we can understand and control the intricacies of the photosynthetic process, we can learn how to increase crop yields of food, fiber, wood, fuel, and so and fourth. The light-harvesting secrets of plants being adapted to artificial systems could provide even more efficient (compare with the natural) ways to collect and use solar energy. Recent researches show the crucial importance of collective molecular excitons in light-harvesting. In our research we study the first step of photosynthesis process, namely, so-called light-harvesting and energy transfer, making accent to nonlinear optics and spectroscopy and molecular excitons theory. Special attention currently paid to the role of vibronic effects in two-dimension optical Fourier Spectroscopy.
Nanoplasmonics. At the laboratory, we are doing the nonlinear refraction measurements using Z-scan setup. The Z-scan technique is often used for measuring the strength of the Kerr nonlinearity (i.e. the value of the nonlinear index n2, third order nonlinear susceptibility χ(3)) and nonlinear absorption of an optical material. The list of the samples under investigation using Z-scan technique includes: transparent crystal materials, glasses, liquid solutions, thin films, complex biological solutions and tissues, metamaterials, nanoparticles and quantum dots solutions etc. Nonlinear properties of new materials can be predicted using quantum chemistry analysis and verified by Z-scan measurements. This is important in searching for new media for lasing, all-optical switching, sensor protection and development of supercontinuum radiation sources. Also this technique allows determining the concentration of biological substances in blood.More about research in nanoplasmonics
The sample of the material under investigation is moved through the focus of a laser beam, and the on-axis intensity is measured at some point behind the focus as a function of the sample position. At specific distance after the sample an aperture is placed to prevent some of the light from reaching the detector. The measured intensity is affected by the self-focusing (defocusing) effect. If the nonlinear index is positive, and the sample is placed behind the focus, self-focusing reduces the beam divergence and thus increases the detector signal. If the sample is moved to the left-hand side of the focus, the focus is moved to the left, and the stronger divergence after the focus decreases the detector signal. From the measured dependence of the detector signal on the sample position, it is possible to calculate the magnitude of the nonlinear index.
Femtosecond oscillator (Tsunami, Spectra-Physics) is used as the laser radiation source. The main characteristics are: averaged power 0.8 W, central wavelength 720-960 nm, FWHM 10 nm, pulse duration 100 fs, repetition rate 80 MHz. The measurement is performed automatically using translation stage controlled by National Instruments PXI acquisition system. At every translation step the averaged intensity is measured by high-sensitivity silicon photodiode and stored. Then, nonlinear refractive index and absorption coefficient are extracted from experimental data.
- Optics of photonic-crystals. We study spectral and polarization properties of photonic crystals — metamaterials with dielectric permittivity varying periodically in space at a period permitting the Bragg diffraction of light. An important feature of photonic crystal is the localization of electromagnetic waves on the structural defect at the boundary or in the bulk. The defect consists of either metal-dielectric nanocomposite with giant optical response, or liquid crystal material with robust control by voltage. The defect layer may arrange a localized defect mode in the band gap of photonic crystal. Defect mode frequency and transmittance, as well as the shape and the size of the band gap can be effectively controlled by varying the geometric and structural parameters of the photonic crystal. New photonic crystal waveguides, nanoresonators with high Q and low threshold lasers may be created on the basis of controllable and resonant defect modes.
The Laboratory for Nonlinear Optics and Spectroscopy of Siberian Federal University warmly welcomes any talented students to join our Lab. You will get an extensive research experience and become involved in the international projects we are doing together with our colleagues worldwide. You will be able to attend various PhD courses related to the lab’s research. We are a young and developing research group of talented students and postdocs and you will have much fun if you join the team. Our students tend to attend international conferences and visit international research centers. The visits are supported through internal funding and external grants.
- M. Schroter, S. D. Ivanov, J. Schulze, S. P. Polyutov, Y. Yan, T. Pullerits, O.Kuhn, Exciton-Vibrational Coupling in the Dynamics and Spectroscopy of Frenkel Excitons in Molecular Aggregates, Physics Reports, 567:1-78 · (April 2015). (Highly cited paper).
- Ershov, A. E., Gavrilyuk, A. P., Karpov, S. V., Semina, P. N., Effect of local environment in resonant domains of polydisperse plasmonic nanoparticle aggregates on optodynamic processes in pulsed laser fields, Chinese physics B, V. 24, No 4, p047804, (2015).
- Ershov, A.E., Gavrilyuk, A.P., Karpov, S.V., Plasmonic Nanoparticle Aggregates in High-Intensity Laser Fields: Effect of Pulse Duration, Plasmonics, DOI: 10.1007/s11468-015-0054-8 (2015).
- Timofeev I. V., Gunyakov V. A., Sutormin V. S., Myslivets S. A., Arkhipkin V. G., Vetrov S. Y., Lee W., and Zyryanov V. Y., Geometric phase and o-mode blueshift in a chiral anisotropic medium inside a Fabry-Pérot cavity, Phys. Rev. E. 2015. Т. 92. № 5. С. 052504.
- Vetrov S.Y., Pankin P.S., Timofeev I. V. Spectral Properties of One-Dimensional Photonic Crystal with Anisotropic Defect Layer of Nanocomposite, Phys. Wave Phenom, Т. 23, № 1, С. 35–38 (2015).
- Vetrov S.Y., Pyatnov M. V, Timofeev I. V., Spectral and polarization properties of a ‘cholesteric liquid crystal—phase plate—metal’ structure, J. Opt., Т. 18. № 1. С. 015103 (2016).
- Komogortsev, S. V., Iskhakov, R. S., Zimin, A. A., Filatov, E. Y., Korenev, S. V., Shubin, Y. V., Eremin, E. V., The exchange interaction effects on magnetic properties of the nanostructured CoPt particles. Journal of Magnetism and Magnetic Materials, 401, 236–241, (2016).
- Arkhipkin, V. G.; Myslivets, S. A., Transmission and reflection spectra of a Raman induced grating in atomic media, Optics And Spectroscopy, Vol. 119 Issue 5, P. 770-775 (2015).
- Vyunishev A. M., Arkhipkin V. G., Chirkin A. S., Theory of second harmonic generation in a chirped 2D nonlinear optical superlattice under nonlinear Raman-Nath diffraction, J. Opt. Soc. Am. B, V.32, P.2411-2416, (2015).
- Vyunishev A. M., Arkhipkin V. G., Slabko V.V., Baturin I. S., Akhmatkhanov A. R., Shur V.Ya., Chirkin A. S., Nonlinear Raman–Nath diffraction of femtosecond laser pulses in a 2D nonlinear photonic crystal, Opt. Lett. V.40, P. 4002-4005 (2015).
- Arkhipkin V. G., Myslivets S. A, Coherent manipulation of the Raman induced gratings in atomic media, Phys. Rev. A (2016) (accepted).
- R. Z. Pen, A. A. Polyutov, Pulping chemical processing in the "background noise": experience of robust control, Fibre Chemistry (2016) (accepted).
- I. L. Rasskazov, S. V. Karpov, G. Y. Panasyuk, V. A. Markel, Overcoming the adverse effects of substrate on the waveguiding properties of plasmonic nanoparticle chains, Journal of Applied Physics (2016) (accepted).
- I. L. Rasskazov, S. V. Karpov, V. A. Markel, Surface plasmon polaritons in curved chains of metal nanoparticles, Physical Review B, 2014, V. 90, № 7, P. 075405(9).
- I. L. Rasskazov, S. V. Karpov, V. A. Markel, Waveguiding properties of short linear chains of nonspherical metal nanoparticles, Journal of the Optical Society of America B, 2014, V. 31, № 12, P. 2981-2989.
- A. E. Ershov, A. P. Gavrilyuk, S. V. Karpov, P. N. Semina, Optodynamic phenomena in aggregates of polydisperse plasmonic nanoparticles, Applied Physics B. 2014. V.115. P. 547-560.
- A. O. Lykhin, G. V.Novikova, A. A. Kuzubov, N. A. Staloverova, N. I. Sarmatova, S. A. Varganov, P. O. Krasnov, A complex of ceftriaxone with Pb(II): synthesis, characterization, and antibacterial activity study Journal of Coordination Chemistry. — August 2014. — Vol. 67, Issue 16 — P. 2783–2794. DOI:10.1080/00958972.2014.938065 2013.
- Artem V. Kuklin, Alexander A. Kuzubov, Pavel O. Krasnov, Aleksandr O. Lykhin, Lyudmila V. Tikhonova Ni-doping effect of Mg(0 0 0 1) surface to use it as a hydrogen storage material // Journal of Alloys and Compounds Volume 609, 5 October 2014, Pages 93–99.
- Vetrov, S. Y., Pyatnov, M. V. & Timofeev, I. V., Photonic defect modes in a cholesteric liquid crystal with a resonant nanocomposite layer and a twist defect, Phys. Rev. E 90, 032505 (2014).
- В. С. Герасимов, А. Е. Ершов, С. В. Карпов, С. П. Полютов, П. Н. Сёмина, Оптимизация фототермических методов лазерной гипертермии злокачественных клеток с применением биоконъюгатов Au наночастиц с ДНК–аптамерами, Colloid journal (2016). (accepted).
- Ветров С. Я., Панкин П. С., Тимофеев И. В. Особенности спектральных свойств фотонного кристалла с дефектом из нанокомпозита с учетом размерных эффектов, Оптика и спектроскопия, Т. 119. № 1. С. 69–72 (2015).
- Бикбаев Р. Г., Ветров С. Я., Тимофеев И. В.. Оптические таммовские состояния на границе фотонного кристалла и сильно анизотропного нанокомпозита // Ученые записки физического факультета МГУ. 2015. № 4. С. 154330–3.
- Ветров С. Я., Панкин П. С., Тимофеев И. В. Спектральные свойства фотонного кристалла, сопряженного с нанокомпозитом, содержащим частицы с оболочками // Ученые записки физического факультета МГУ, 2015b. № 4. С. 154315–4.
- Вьюнышев А. М., Тимофеев И. В., Поспелов Г. И., Наседкин Б. А., Шереметьева Ю. А., Чиркин А. С., Усиление эффекта нелинейной дифракции Рамана-Ната в двумерных нелинейных структурах, Ученые записки физического факультета МГУ, 2015, № 4. С. 154302–3.
- Ершов Александр Евгеньевич, Оптодинамические эффекты в системах связанных плазмонных наночастиц и их проявление в спектрах плазмонного поглощения, Молодой ученый, том. 11, стр. 39-45.
- В. B. Бывшев, М. А. Катанаева, А. А. Полютов, «Методика управления качеством образовательных услуг на основе статистических методов контроля, Наука и бизнес: Пути развития, 2014, №12 (42), Стр. 99-102.