# Konstantin "Kostya" Turitsyn

I work in industry since late 2018. With any inquries regarding prior research and possible collaborations, contact my former group members.

I work in industry since late 2018. With any inquries regarding prior research and possible collaborations, contact my former group members.

Being inherently fragile, power systems may not return back to equilibrium after contingency. Fast second-scale dynamics implies that automatic emergency response is required to prevent this from happening. Power electronic components in the form of HVDC lines, FACTS devices and renewable inverters can save the facilitate the arrest of instability and prevent the system from collapsing.

We have developed novel algorithms for synthesis of emergency control systems exploiting the flexibility of power electronic components. Specificically, opportunity for fast reallocation of virtual storage on renewable generators, reconfiguration of network topology, remedial rerouting of power flows via FACTS enabled structural control.

T. L. Vu, H. D. Nguyen, A. Megretski, J. Slotine, K. Turitsyn, Inverse Stability Problem and Applications to Renewables Integration, IEEE Control Systems Letters 2, 133--138
(2018) [PDF]

T. L. Vu, S. Chatzivasileiadis, H. Chiang, K. Turitsyn, Structural Emergency Control Paradigm, IEEE Journal on Emerging and Selected Topics in Circuits and Systems 7, 371--382
(2017) [PDF]

S. Chatzivasileiadis, T. L. Vu, K. Turitsyn, Remedial actions to enhance stability of low-inertia systems, 2016 IEEE Power and Energy Society General Meeting (PESGM)
(2016) [PDF]

T. L. Vu, S. Chatzivasileiadis, K. Turitsyn, Towards electronics-based emergency control in power grids with high renewable penetration, 2016 American Control Conference (ACC)
(2016) [PDF]

Power system components are often described by nonlinear differential algebraic equation (DAE) models. These models are hard to analyze using conventional Lyapunov function techniques. There are no universal scalable approaches for constructing attraction basin estimates and designing nonlinear control systems.

We have been new techniques for certification of stability of DAE systems based on establishing contraction metrics. These techniques allowed to develop new approaches for certifying transient stability and estimating robustness of trajectories to parameter uncertainty and stochastic noise.

D. Lee, K. Turitsyn, Dynamic Polytopic Template Approach to Robust Transient Stability Assessment, arXiv:1705.01189v1
(2017) [PDF]

D. Lee, K. Turitsyn, Robust Transient Stability Assessment via Reachability Analysis, 2017 X Bulk Power Systems Dynamics and Control Symposium IREP
(2017) [PDF]

H. D. Nguyen, T. L. Vu, J. Slotine, K. Turitsyn, Contraction Analysis of Nonlinear DAE Systems, IEEE Transactions on Automatic Control, 2nd revision, also at arXiv:1702.07421
(2017) [PDF]

Direct energy methods are the only alternative to simulations for transient stability analysis and are currently used by a number of system operators around the world. Despite many decades of research these methods still rely on NP-hard algorithms and cannot be applied directly to standard models.

We proposed an alternative approach based on more general Lyapunov functions.This technique is based solely on convex optimization algorithms, extends to wider range of models, and is less conservative in comparison to classical energy methods.

T. L. Vu, K. Turitsyn, A Framework for Robust Assessment of Power Grid Stability and Resiliency, IEEE Transactions on Automatic Control 62, 1165--1177
(2017) [PDF]

T. L. Vu, S. M. Al Araifi, M. S. El Moursi, K. Turitsyn, Toward Simulation-Free Estimation of Critical Clearing Time, IEEE Transactions on Power Systems 31, 4722--4731
(2016) [PDF]

T. L. Vu, K. Turitsyn, Lyapunov Functions Family Approach to Transient Stability Assessment, IEEE Transactions on Power Systems 31, 1269--1277
(2016) [PDF]

T. L. Vu, K. Turitsyn, Synchronization stability of lossy and uncertain power grids, 2015 American Control Conference (ACC)
(2015) [PDF]

T. L. Vu, K. Turitsyn, Geometry-based estimation of stability region for a class of structure preserving power grids, 2018 IEEE Power & Energy Society General Meeting
(2015) [PDF]

Regions of safe and stable operating conditions are generally non-convex. Their non-trivial shape is responsible for NP-hardness of many critical decision-making processes in power systems: optimal resource allocation, risk assessment, emergency control.

We use modern analysis and optimization techniques to construct inner approximations of the feasibility sets of simple convex shape suitable for real-time computations. Resulting approximations are then used for security assessment in the presence of renewable generation, design of optimal remedial actions and other time-critical applications.

K. Dvijotham, H. Nguyen, K. Turitsyn, Solvability Regions of Affinely Parameterized Quadratic Equations, IEEE Control Systems Letters 2, 25--30
(2018) [PDF]

K. Dvijotham, K. Turitsyn, Construction of power flow feasibility sets, arXiv:1506.07191v3
(2015) [PDF]

S. Yu, H. D. Nguyen, K. S. Turitsyn, Simple certificate of solvability of power flow equations for distribution systems, 2018 IEEE Power & Energy Society General Meeting
(2015) [PDF]

Heavily loaded grids may experience a voltage instability resulting in blackout in most dramatic scenarios. Stability margin of safe operating points depends on the dynamic response of the loads that are difficult to model due to inherent uncertainty and lack of observability.

To address this problem, we developed novel robust stability certificates based on structured Lyapunov functions. These certificates provide mathematical guarantees that an operating point is stable for any load response. Safe regions identified with the approach can be naturally used for security assessment and emergency control.

H. D. Nguyen, K. Turitsyn, Robust Stability Assessment in the Presence of Load Dynamics Uncertainty, IEEE Transactions on Power Systems 31, 1579--1594
(2016) [PDF]

Modern power systems are protected against failures of any individual component (N-1 security), so blackouts are usually triggered by simultaneous failures of at least 2 components (N-2 contingency). Identification of dangerous N-2 contingencies is very challenging due to large number of possible pairs of lines and generators.

We invented a unique filtering technique for selection of dangerous contigencies that allows fast screening of safe scenarios with zero missing rate guarantees. On medium sized models the algorithm leads to thousand fold acceleration of the selection process and allows real-time blackout risk assessment.

P. Kaplunovich, K. Turitsyn, Fast and Reliable Screening of N-2 Contingencies, IEEE Transactions on Power Systems 31, 4243--4252
(2016) [PDF]

P. A. Kaplunovich, K. S. Turitsyn, Statistical Properties and Classification of N-2 Contingencies in Large Scale Power Grids, 2014 47th Hawaii International Conference on System Sciences (HICSS)
(2014) [PDF]

P. A. Kaplunovich, K. S. Turitsyn, Fast selection of N-2 contingencies for online security assessment, 2013 IEEE Power & Energy Society General Meeting
(2013) [PDF]

K. S. Turitsyn, P. A. Kaplunovich, Fast Algorithm for N-2 Contingency Problem, 2013 46th Hawaii International Conference on System Sciences (HICSS)
(2013) [PDF]

Interconnection of independent single-source microgrids allows for sharing of resources and can dramatically reduce the costs of operation. However, such a system is prone to instabilities arising due to competition of multiple master (voltage source) inverters interacting through a strong networks with electromagnetic delays.

We have elucidated the origins of instability, used singular perturbation theory to derive more accurate dynamic equations, and developed simple simple interconnection rules that guarantee stability even in the presence of uncertainty.

P. Vorobev, P. Huang, M. A. Hosani, J. L. Kirtley, K. Turitsyn, A framework for development of universal rules for microgrids stability and control, 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
(2017) [PDF]

P. Vorobev, P. Huang, M. Al Hosani, J. L. Kirtley, K. Turitsyn, High-Fidelity Model Order Reduction for Microgrids Stability Assessment, IEEE Transactions on Power Systems 33, 874--887
(2018) [PDF]

More than 1 billion people in the world are still lacking power access and won't likely get access to main power grids in the next decades. Low voltage dc microgrids provide a unique opportunity for improving the lifes of those communities. However, the approaches to system design and operation have to be revisited to make them truly affordable.

We have proposed the concept of ad hoc microgrids composed of modular source and load components that can be interconnected in arbitrary manner without pre-planning. Simple design rules guarantee existence of equilibrium and transient stability of the system after switching events. Distributed secondary controls allow for optimal power sharing.

K. Cavanagh, J. A. Belk, K. Turitsyn, Transient Stability Guarantees for Ad Hoc DC Microgrids, IEEE Control Systems Letters 2, 139--144
(2018) [PDF]

J. A. Belk, W. Inam, D. J. Perreault, K. Turitsyn, Stability and control of ad hoc dc microgrids, 2016 IEEE 55th Conference on Decision and Control (CDC)
(2016) [PDF]

W. Inam, J. A. Belk, K. Turitsyn, D. J. Perreault, Stability, control, and power flow in ad hoc DC microgrids, 2016 IEEE 17th Workshop on Control and Modeling for Power Electronics (COMPEL)
(2016) [PDF]

High penetration levels of distributed generation may result in reversal of power flow in modern distribution grids. We have shown that reversed power flow may result in appearance of new previously unobserved operating equilibria.

The resulting solutions are generally low-voltage and undesirable for normal operation. However, the system may get trapped in the new equilibria during the post-fault recovery. We have proposed new algorithms for identification of all the solutions, as well as special emergency control actions that can help maintain stability and enable adoption of high levels of clean renewable energy.

D. Mehta, D. K. Molzahn, K. Turitsyn, Recent advances in computational methods for the power flow equations, 2016 American Control Conference (ACC)
(2016) [PDF]

H. D. Nguyen, D. Mehta, K. Turitsyn, Numerical polynomial homotopy continuation method to locate all the power flow solutions, IET Generation, Transmission & Distribution 10, 2972--2980
(2016) [PDF]

H. D. Nguyen, K. Turitsyn, Voltage Multistability and Pulse Emergency Control for Distribution System With Power Flow Reversal, IEEE Transactions on Smart Grid 6, 2985--2996
(2015) [PDF]

H. D. Nguyen, K. S. Turitsyn, Appearance of multiple stable load flow solutions under power flow reversal conditions, 2014 IEEE Power & Energy Society General Meeting
(2014) [PDF]

D. Wang, K. Turitsyn, M. Chertkov, DistFlow ODE: Modeling, analyzing and controlling long distribution feeder, 2012 IEEE 51st Annual Conference on Decision and Control (CDC)
(2012) [PDF]

Introduction of high penetrations of distributed photovoltaic resources like roof-top panel causes a lots of headaches to the utilities and forces them to rethink how to operate distribution grids that were not designed with distributed generation in mind. Flexibility of power electronics circuits on individual inverters can be naturally leveraged to support the reactive power in the system.

We have explored several strategies for controlling the photovoltaic inverters and demonstrated that their reactive power capabilities can be naturally used to both supporting the voltage levels and reducing the losses. The centralized control strategies can be formulated as simple convex optimization problems, while the decentralized control achieves strong improvement effect even without prior coordination.

K. Turitsyn, P. Sulc, S. Backhaus, M. Chertkov, Options for Control of Reactive Power by Distributed Photovoltaic Generators, Proceedings of the IEEE 99, 1063--1073
(2011) [PDF]

K. Turitsyn, P. Sulc, S. Backhaus, M. Chertkov, Local Control of Reactive Power by Distributed Photovoltaic Generators, 2010 1st IEEE International Conference on Smart Grid Communications (SmartGridComm)
(2010) [PDF]

K. Turitsyn, P. Šulc, S. Backhaus, M. Chertkov, Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration, Energy Society General Meeting
(2010) [PDF]

Sustained oscillations on low frequencies is a regularly observed phenomenon in large scale power systems that can compromise their stability and contribute to wear and tear of equipment. Several mechanisms can cause these oscillations, and PMU technologies provide an opportunity to quickly identify and fix the underlying problem.

We are developing algorithms that process the PMU data and point to the mechanism and source of oscillations. Diagnostics of the mechanism of the sustained oscillations is performed based on Kurtosis - higher order statistical indicator sensitive to nonlinear effects. The source of forced oscillations can be identified by comparing the natural to the observed response of individual generators.

X. Wang, K. Turitsyn, Data-Driven Diagnostics of Mechanism and Source of Sustained Oscillations, IEEE Transactions on Power Systems 31, 4036--4046
(2016) [PDF]

Estimation of generator/power plant parameters is a complicated but important task essential for ensurance of stable power system operations. Traditional approaches are focused on mean values of parameters and provide little insight in the confidence intervals and accuracy of the predictions.

We have proposed a Bayesian approach to estimation of generator parameters that can provide a full posterior distribution of uncertain quantities. The algorithm is based on particle filter techniques and paves the path for more systematic uncertainty quantification in power systems.

T. Bogodorova, L. Vanfretti, V. S. Peri{\'c}, K. Turitsyn, Identifying Uncertainty Distributions and Confidence Regions of Power Plant Parameters, IEEE Access 5, 19213--19224
(2017) [PDF]

T. Bogodorova, L. Vanfretti, K. Turitsyn, Bayesian Parameter Estimation of Power System Primary Frequency Controls under Modeling Uncertainties, IFAC-PapersOnLine
(2015) [PDF]

Power systems are never truly stationary and are always fluctuating in stochastic manner. These fluctuations are typically viewed as nuisance. However, their statistics captures a lot of useful information about the current state of the system and the changes the system experiences.

We have proposed a number of approaches for detecting the statistical precursors of instability: approach of Hopf or saddle-node bifurcations. Later, we have broadly extended the approach to allow for full power flow Jacobian reconstruction purely from correlation function estimates.

X. Wang, J. W. Bialek, K. Turitsyn, PMU-Based Estimation of Dynamic State Jacobian Matrix and Dynamic System State Matrix in Ambient Conditions, IEEE Transactions on Power Systems 33, 681--690
(2018) [PDF]

D. Podolsky, K. Turitsyn, Critical slowing-down as indicator of approach to the loss of stability, 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm)
(2014) [PDF]

D. Podolsky, K. Turitsyn, Random load fluctuations and collapse probability of a power system operating near codimension 1 saddle-node bifurcation, 2013 IEEE Power & Energy Society General Meeting
(2013) [PDF]

Intriguing morphologies and surface patterns in nature at different scales from wrinkles on skins of mammalians, plants, and fruits to crumpled membranes of blood cells have inspired a big body of research in soft matter instabilities. In this project, we extend the application of soft matter instabilities to kinetic energy harvesting.

Conventional vibratory energy harvesters usually suffer from narrow bandwidth and are very inefficient at small scale for low frequency harvesting. Here, to improve the harvesting effectiveness, we propose to exploit surface instability or in general instability in layered composites, e.g. wrinkling, where intriguing morphological patterns with large strain are formed under compressive loads. The induced large strains which are independent of the excitation frequency, could be exploited to give rise to large strains in an attached piezoelectric layer to generate charge and, hence energy.

A. Haji Hosseinloo, K. Turitsyn, Effective kinetic energy harvesting via structural instabilities, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring
(2017) [PDF]

A. Haji Hosseinloo, K. Turitsyn, Energy harvesting via wrinkling instabilities, Applied Physics Letters 110, 013901
(2017) [PDF]

Uncertainty in parameters is inevitable with any physical device mainly due to manufacturing tolerances, defects, and environmental effects; hence, optimization under uncertainty is consequential for effective harvesting. All optimization studies in energy harvesting have focused on expectation optimization that is not appropriate for many practical applications.

Here we have proposed and formulated a new optimization strategy; optimization for the worst-case scenario (minimum power). This is particularly useful when there is a minimum power requirement for the self-powered device. We have shown harvesters thus optimized are much more robust to uncertainties.

A. Haji Hosseinloo, K. Turitsyn, Optimization of vibratory energy harvesters with stochastic parametric uncertainty: a new perspective, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring
(2016) [PDF]

A. H. Hosseinloo, K. Turitsyn, Design of vibratory energy harvesters under stochastic parametric uncertainty: a new optimization philosophy, Smart Materials and Structures 25, 055023
(2016) [PDF]

Purposeful inclusion of nonlinearity, in particular the bistable potential, into energy harvesting devices has been the focus of tremendous research efforts in the recent years. However, recent research has proven that the bistable harvester is effective only when the vibration intensity is just enough to trigger interwell oscillations.

We have proposed a novel adaptive bistable system with variable potential height. We have shown that a bistable system whose potential barrier changes following a buy-low-sell-high strategy outperforms its linear and conventional bistable counterparts, and is much more robust to changes in excitation statistics. More recently we have also introduced novel strategies for driving the nonlinear systems to the most energy effective attractors.

A. Haji Hosseinloo, J. Slotine, K. Turitsyn, Robust and adaptive control of coexisting attractors in nonlinear vibratory energy harvesters, Journal of Vibration and Control 9799, 107754631668899
(2017) [PDF]

A. H. Hosseinloo, K. Turitsyn, Non-resonant energy harvesting via an adaptive bistable potential, Smart Materials and Structures 25, 015010
(2015) [PDF]

Every little bit counts toward energy efficiency, including catching what would be lost to stray mechanical vibrations. Current research into harvesting of vibrational energy aims to exploit nonlinearity for effective energy harvesting, but one of the key challenges in designing such harvesters is the immense range of possible nonlinearities.

Rather than focusing on specific nonlinearities, we have studied the fundamental limits, and have shown that for a simple vibratory system, this limit forms into a simple non-resonant harvesting strategy called buy-low-sell-high, for any generic excitation statistics. A harvester following this strategy outperforms the linear and conventional nonlinear harvesters.

A. H. Hosseinloo, T. L. Vu, K. Turitsyn, Optimal control strategies for efficient energy harvesting from ambient vibration, 2015 54th IEEE Conference on Decision and Control (CDC)
(2015) [PDF]

A. Haji Hosseinloo, K. Turitsyn, Fundamental Limits to Nonlinear Energy Harvesting, Physical Review Applied 4, 1
(2015) [PDF]

Classical Shannon capacity limits the spectral efficiency, and more broadly channel capacity of linear systems with additive noise. However, as the signal to noise ratio is increased the nonlinear effects start to come into play. Their effect on fundamental limits to channel capacity is still poorly understood.

In a series of papers we have demonstrated that the traditional Kerr nonlinearity observed in fiber optical channels does not result in significant reduction in channel capacity in comparison to linear channels. Moreover, carefully designed nonlinearity with regenerative effect can increase the capacity well beyond Shannon limit.

K. S. Turitsyn, S. K. Turitsyn, Nonlinear communication channels with capacity above the linear Shannon limit, Optics Letters 37, 3600
(2012) [PDF]

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn, Information Capacity of Optical Fiber Channels with Zero Average Dispersion, Physical Review Letters 91, 379
(2003) [PDF]

The polarization properties of light are now actively exploited in modern coherent fiber-optic communication systems for transmission of infor- mation. The possibility to control, regenerate and manipulate pulse polarization by purely optical means would have major impact in the field, enabling development of new generation of high speed optical communication systems.

In a series of works we have analyzed the phenomenon of polarization rotation in optical fibers with co- and counter-propagating beams. We have developed a theoretical description of the polarization attraction phenomenon, derived stability regions and proposed a possible technological realization of all-optical polarizers.

K. Turitsyn, S. Wabnitz, Stability analysis of polarization attraction in optical fibers, Optics Communications 307, 62--66
(2013) [PDF]

S. Wabnitz, K. S. Turitsyn, Mitigation of Nonlinear and PMD Impairments by Bit-Synchronous Polarization Scrambling, Journal of Lightwave Technology 30, 2494--2501
(2012) [PDF]

V. V. Kozlov, K. Turitsyn, S. Wabnitz, Nonlinear repolarization in optical fibers: polarization attraction with copropagating beams, Optics Letters 36, 4050
(2011) [PDF]

Traditional models of communication channels assume independent propagation of individual signals. However, in nonlinear channels, the signals interact with each other and the form of interaction may depend on the alphabet symbol pattern.

We have studied a simple but realistic model of signal interactions within fiber optical channel. For this system specific three symbol patterns have the highest error rate and their frequency should be suppressed in encoding. Specific algorithms for optimal encoding were proposed and analyzed.

A. Shafarenko, K. S. Turitsyn, S. K. Turitsyn, Information-Theory Analysis of Skewed Coding for Suppression of Pattern-Dependent Errors in Digital Communications, IEEE Transactions on Communications 55, 237--241
(2007) [PDF]

A. Shafarenko, Skewed coding for suppression of pattern-dependent errors, 31st European Conference on Optical Communications (ECOC 2005)
(2005) [PDF]

Carbon dioxide capture and storage in deep saline aquifiers is a viable technology that allows for reduction in emissions even without immediate replace of fossil-fueled power plants. At the same time, there is still a very limited understanding of the hihgly nonlinear carbon sequestration phenomenon, in particular the rates of mixing and the role of convective instabilities.

In collaboration with experimental groups, I have studied the characteristics of the convective density driven Rayleigh instability occuring in Hele Shaw setup. Unlike classical instabilities that have been studied for almost a century, the unique features of this system is miscible nature of the liquids that leads to dissolution of initial fingers.

S. Backhaus, K. Turitsyn, R. E. Ecke, Convective Instability and Mass Transport of Diffusion Layers in a Hele-Shaw Geometry, Physical Review Letters 106, 104501
(2011) [PDF]

Formation of air bubbles following air entrapment is a complicated though very common process occuring on every nonequilibrium water-air surfaces. The final stage of this process - bubble neck pinch-off is charactherzed by singular growth of pressure and extremely fast development on shape instabilities.

Although the initial growth of instability is a relatively well-understood process, the final stages of the dynamics have been poorly understood until our paper. We have developed a unique approach based on conformal mapping capable of predicting the evolution of the neck cross-section shape and demonstrated that the neck actually separates into two before final collapse. The results were in a good agreement with high-speed camera experiments.

K. S. Turitsyn, L. Lai, W. W. Zhang, Asymmetric Disconnection of an Underwater Air Bubble: Persistent Neck Vibrations Evolve into a Smooth Contact, Physical Review Letters 103, 124501
(2009) [PDF]

Lipid bilayer vesicles are composed of liquid membrane surrounding a liquid drop. They are a natural transport vehicle in many cellular processes and also actively used for artificial drug delivery. When subjected to external flow they experience a very rich dynamics.

We have developed an analytic reduced model for dynamics of nearly-spherical vesicles and shown that it accurately reproduces the phase diagram of experimentally observed motion types. Moreover, it can be used to predict the statistical properties of the wrinkling dynamics observed during buckling instability.

K. S. Turitsyn, S. S. Vergeles, Wrinkling of Vesicles during Transient Dynamics in Elongational Flow, Physical Review Letters 100, 693
(2008) [PDF]

V. V. Lebedev, K. S. Turitsyn, S. S. Vergeles, Dynamics of Nearly Spherical Vesicles in an External Flow, Physical Review Letters 99, 340
(2007) [PDF]

V. V. Lebedev, K. S. Turitsyn, S. S. Vergeles, Nearly spherical vesicles in an external flow, New Journal of Physics 10, 043044
(2008) [PDF]

Addition of small concenctrations of flexible polymer molecules can dramatically reduce the viscosity of the liquids. This effect is actively used to reduce the fluid drag in pipes, however its microscopic origins are still poorly understood.

We have developed a theoretical description of nonequilibrium and nonlinear dynamics of individual polymer molecules exposed to external shear flows. Our theory predicts multiple statistical properties of motions, such as tumbling time distribution, probability of different orientation etc. Most of the predictions have been successfully confirmed by experimental groups.

K. S. Turitsyn, Polymer dynamics in chaotic flows with a strong shear component, Journal of Experimental and Theoretical Physics 105, 655--664
(2007) [PDF]

M. Chertkov, I. Kolokolov, V. Lebedev, K. Turitsyn, Polymer statistics in a random flow with mean shear, Journal of Fluid Mechanics 531, 251--260
(2005) [PDF]

A. Celani, A. Puliafito, K. Turitsyn, Polymers in linear shear flow: A numerical study, Europhysics Letters (EPL) 70, 464--470
(2005) [PDF]

A. Puliafito, K. Turitsyn, Numerical study of polymer tumbling in linear shear flows, Physica D: Nonlinear Phenomena 211, 9--22
(2005) [PDF]

Turbulent mixing of inertial particles like droplets is a process that occurs frequently in nature (for example during rain formation) and in engineering (for example in internal combustion engines). Unlike passive tracers, inertial particles do not follow Lagrangian trajectories, and tend to cluster due to random centrifugal process. This is an inherently stochastic process that is hard to characterize using conventional deterministic approaches.

We have developed a theoretical description for two aspects of this process. First, we have derived the fractal dimension of the resulting clusters for Markovian stochastic flows. Second, we have characterized the dynamics during the caustic formation events when the local concentration experiences explosive growth.

J. Bec, M. Cencini, R. Hillerbrand, K. Turitsyn, Stochastic suspensions of heavy particles, Physica D: Nonlinear Phenomena 237, 2037--2050
(2008) [PDF]

S. A. Derevyanko, G. Falkovich, K. Turitsyn, S. Turitsyn, Lagrangian and Eulerian descriptions of inertial particles in random flows, Journal of Turbulence 8, N16
(2007) [PDF]

Random motion of particles, in viscoelastic media, for example motion of individual proteins on the membranes is very sensitive to the environment. It's statistical properties can be naturally used to probe the medium and test hypotheses about its composition. However, traditional approaches have been focused on simple second-order characteristics like (anomalous) diffusion coefficient.

We have proposed a non-conventional measure based on displacement kurtosis that is sensitive to nonlinear interactions that the particle experience. It can distinguish between different mechanisms characterized by the same diffusion coefficient and naturally detect lipid rafts and other membrance constituents.

P. M. Lushnikov, P. Sulc, K. S. Turitsyn, Non-Gaussianity in single-particle tracking: Use of kurtosis to learn the characteristics of a cage-type potential, Physical Review E 85, 051905
(2012) [PDF]

Markov Chain Monte Carlo algorithms are the most popular strategies for sampling from complicated probability distributions. Most popular versions of these algorithms rely on the detailed balance principle, also referred to as "reversibility" of the Markov Chain. Although reversibility is a sufficient condition that leads to relatively simple step acceptance rules, it restricts the class of algorithms and limits their performance.

We have explored the idea of breaking reversibility/detailed balance and proposed simple strategies for breaking detailed balance of a given reversible chain. The procedure of breaking detailed balance can be interpreted as either lifting the chain in a higher dimensional space or introducing memory in otherwise Markovian dynamics.

K. S. Turitsyn, M. Chertkov, M. Vucelja, Irreversible Monte Carlo algorithms for efficient sampling, Physica D: Nonlinear Phenomena 240, 410--414
(2011) [PDF]

Non-equilibrium irreversible processes increase the entropy of the universe, but do so in a temporally non-steady manner. While the second law of thermodynamics guarantees that the average increase is positive, the exact amounts of entropy produced in a given period are stochastic and have a finite probability of being negative. Understanding these flucutations of entropy is essential for describing processes occuring on micro and nano-scales.

We have proposed a systematic approach for calculation of entropy production for systems in non-equilibrium steady state experiencing weakly nonlinear or linear fluctuations. Our results were illustrated on an example polymer molecule in shear flow system.

K. Turitsyn, M. Chertkov, V. Y. Chernyak, A. Puliafito, Statistics of Entropy Production in Linearized Stochastic Systems, Physical Review Letters 98, 695
(2007) [PDF]

P. Vorobev, D. Greenwood, J. Bell, J. Bialek, P. Taylor, K. Turitsyn, Deadbands, Droop and Inertia Impact on Power System Frequency Distribution, IEEE Transactions on Power Systems, 1st revision
(2018) [PDF]

P. Huang, P. Vorobev, M. Al Hosani, J. L. Kirtley, K. Turitsyn, Plug-and-Play Compliant Control for Inverter-Based Microgrids, IEEE Transactions on Power Systems, 2nd revision
(2018) [PDF]

D. Lee, L. Aolaritei, T. L. Vu, K. Turitsyn, Robustness against Disturbances in Power Systems under Frequency Constraints, IEEE Transactions on Control of Networked Systems, 1st revision, also at arXiv:1803.00817
(2018) [PDF]

H. D. Nguyen, T. L. Vu, J. Slotine, K. Turitsyn, Contraction Analysis of Nonlinear DAE Systems, IEEE Transactions on Automatic Control, 2nd revision, also at arXiv:1702.07421
(2017) [PDF]

D. Lee, H. D. Nguyen, K. Dvijotham, K. Turitsyn, Convex Restriction of Power Flow Feasibility Set, IEEE Transactions on Control of Networked Systems, 1st revision, also at arXiv:1803.00818
(2018) [PDF]

H. D. Nguyen, K. Dvijotham, S. Yu, K. Turitsyn, A Framework for Robust Long-Term Voltage Stability of Distribution Systems, IEEE Transactions on Smart Grid , 1--1
(2018) [PDF]

X. Wang, J. W. Bialek, K. Turitsyn, PMU-Based Estimation of Dynamic State Jacobian Matrix and Dynamic System State Matrix in Ambient Conditions, IEEE Transactions on Power Systems 33, 681--690
(2018) [PDF]

T. L. Vu, H. D. Nguyen, A. Megretski, J. Slotine, K. Turitsyn, Inverse Stability Problem and Applications to Renewables Integration, IEEE Control Systems Letters 2, 133--138
(2018) [PDF]

D. O. Amoateng, M. Al Hosani, M. S. Elmoursi, K. Turitsyn, J. L. Kirtley, Adaptive Voltage and Frequency Control of Islanded Multi-Microgrids, IEEE Transactions on Power Systems 33, 4454--4465
(2018) [PDF]

S. C. Chevalier, P. Vorobev, K. Turitsyn, Using Effective Generator Impedance for Forced Oscillation Source Location, IEEE Transactions on Power Systems 33, 6264--6277
(2018) [PDF]

M. Ali, A. Dymarsky, K. Turitsyn, Transversality enforced Newton-Raphson algorithm for fast calculation of maximum loadability, IET Generation, Transmission & Distribution 12, 1729--1737
(2018) [PDF]

Q. Li, S. Yu, A. S. Al-Sumaiti, K. Turitsyn, Micro Water-Energy Nexus: Optimal Demand-Side Management and Quasi-Convex Hull Relaxation, IEEE Transactions on Control of Networked Systems in press, also at arXiv:1805.07626
(2018) [PDF]

P. Vorobev, P. Huang, M. Al Hosani, J. L. Kirtley, K. Turitsyn, High-Fidelity Model Order Reduction for Microgrids Stability Assessment, IEEE Transactions on Power Systems 33, 874--887
(2018) [PDF]

K. Dvijotham, H. Nguyen, K. Turitsyn, Solvability Regions of Affinely Parameterized Quadratic Equations, IEEE Control Systems Letters 2, 25--30
(2018) [PDF]

H. D. Nguyen, T. L. Vu, K. Turitsyn, J. Slotine, Contraction and Robustness of Continuous Time Primal-Dual Dynamics, IEEE Control Systems Letters 2, 755--760
(2018) [PDF]

S. Chevalier, P. Vorobev, K. Turitsyn, A Bayesian Approach to Forced Oscillation Source Location Given Uncertain Generator Parameters, IEEE Transactions on Power Systems , 1--1
(2018) [PDF]

L. Aolaritei, D. Lee, T. L. Vu, K. Turitsyn, A Robustness Measure of Transient Stability Under Operational Constraints in Power Systems, IEEE Control Systems Letters 2, 803--808
(2018) [PDF]

H. D. Nguyen, K. Dvijotham, K. Turitsyn, Constructing Convex Inner Approximations of Steady-State Security Regions, IEEE Transactions on Power Systems , 1--1
(2018) [PDF]

K. Cavanagh, J. A. Belk, K. Turitsyn, Transient Stability Guarantees for Ad Hoc DC Microgrids, IEEE Control Systems Letters 2, 139--144
(2018) [PDF]

K. Cavanagh, P. Vorobev, K. Turitsyn, Stability of DC Networks with Generic Load Models, arXiv:1803.01918
(2018) [PDF]

Q. Li, S. Yu, A. Al-Sumaiti, K. Turitsyn, Modeling A Micro-Nexus of Water and Energy for Smart Villages/Cities/Buildings, 2018 IEEE Power & Energy Society General Meeting
(2018) [PDF]

T. L. Vu, S. Chatzivasileiadis, H. Chiang, K. Turitsyn, Structural Emergency Control Paradigm, IEEE Journal on Emerging and Selected Topics in Circuits and Systems 7, 371--382
(2017) [PDF]

T. L. Vu, K. Turitsyn, A Framework for Robust Assessment of Power Grid Stability and Resiliency, IEEE Transactions on Automatic Control 62, 1165--1177
(2017) [PDF]

A. Haji Hosseinloo, K. Turitsyn, Energy harvesting via wrinkling instabilities, Applied Physics Letters 110, 013901
(2017) [PDF]

A. Haji Hosseinloo, J. Slotine, K. Turitsyn, Robust and adaptive control of coexisting attractors in nonlinear vibratory energy harvesters, Journal of Vibration and Control 9799, 107754631668899
(2017) [PDF]

T. Bogodorova, L. Vanfretti, V. S. Peri{\'c}, K. Turitsyn, Identifying Uncertainty Distributions and Confidence Regions of Power Plant Parameters, IEEE Access 5, 19213--19224
(2017) [PDF]

Q. Li, Q. Wang, K. Turitsyn, A Stability-constrained Optimization Framework for Lur'e Systems and Application in Power Grids, arXiv:1709.05048v1
(2017) [PDF]

D. Lee, K. Turitsyn, Dynamic Polytopic Template Approach to Robust Transient Stability Assessment, arXiv:1705.01189v1
(2017) [PDF]

D. Lee, K. Turitsyn, Robust Transient Stability Assessment via Reachability Analysis, 2017 X Bulk Power Systems Dynamics and Control Symposium IREP
(2017) [PDF]

P. Huang, P. Vorobev, M. A. Hosani, J. L. Kirtley, K. Turitsyn, Systematic design of virtual component method for inverter-based microgrids, 2017 IEEE Power & Energy Society General Meeting (PESGM)
(2017) [PDF]

X. Wang, K. Turitsyn, PMU-based estimation of dynamic state Jacobian matrix, 2017 IEEE International Symposium on Circuits and Systems (ISCAS
(2017) [PDF]

P. Vorobev, P. Huang, M. A. Hosani, J. L. Kirtley, K. Turitsyn, A framework for development of universal rules for microgrids stability and control, 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
(2017) [PDF]

A. Haji Hosseinloo, K. Turitsyn, Effective kinetic energy harvesting via structural instabilities, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring
(2017) [PDF]

T. L. Vu, S. Chatzivasileiadis, H. Chiang, K. Turitsyn, Structural emergency control for power grids, 2017 American Control Conference (ACC
(2017) [PDF]

T. L. Vu, S. M. Al Araifi, M. S. El Moursi, K. Turitsyn, Toward Simulation-Free Estimation of Critical Clearing Time, IEEE Transactions on Power Systems 31, 4722--4731
(2016) [PDF]

X. Wang, K. Turitsyn, Data-Driven Diagnostics of Mechanism and Source of Sustained Oscillations, IEEE Transactions on Power Systems 31, 4036--4046
(2016) [PDF]

T. L. Vu, K. Turitsyn, Lyapunov Functions Family Approach to Transient Stability Assessment, IEEE Transactions on Power Systems 31, 1269--1277
(2016) [PDF]

P. Kaplunovich, K. Turitsyn, Fast and Reliable Screening of N-2 Contingencies, IEEE Transactions on Power Systems 31, 4243--4252
(2016) [PDF]

H. D. Nguyen, K. Turitsyn, Robust Stability Assessment in the Presence of Load Dynamics Uncertainty, IEEE Transactions on Power Systems 31, 1579--1594
(2016) [PDF]

H. D. Nguyen, D. Mehta, K. Turitsyn, Numerical polynomial homotopy continuation method to locate all the power flow solutions, IET Generation, Transmission & Distribution 10, 2972--2980
(2016) [PDF]

A. H. Hosseinloo, K. Turitsyn, Design of vibratory energy harvesters under stochastic parametric uncertainty: a new optimization philosophy, Smart Materials and Structures 25, 055023
(2016) [PDF]

A. Zlotnik, M. Chertkov, K. Turitsyn, Assessing Risk of Gas Shortage in Coupled Gas-Electricity Infrastructures, 2016 49th Hawaii International Conference on System Sciences (HICSS)
(2016) [PDF]

J. A. Belk, W. Inam, D. J. Perreault, K. Turitsyn, Stability and control of ad hoc dc microgrids, 2016 IEEE 55th Conference on Decision and Control (CDC)
(2016) [PDF]

D. Mehta, D. K. Molzahn, K. Turitsyn, Recent advances in computational methods for the power flow equations, 2016 American Control Conference (ACC)
(2016) [PDF]

W. Inam, J. A. Belk, K. Turitsyn, D. J. Perreault, Stability, control, and power flow in ad hoc DC microgrids, 2016 IEEE 17th Workshop on Control and Modeling for Power Electronics (COMPEL)
(2016) [PDF]

T. Bogodorova, L. Vanfretti, K. Turitsyn, Voltage control-based ancillary service using thermostatically controlled loads, 2016 IEEE Power and Energy Society General Meeting (PESGM)
(2016) [PDF]

M. Parandehgheibi, K. Turitsyn, E. Modiano, Distributed frequency control in power grids under limited communication, 2016 IEEE 55th Conference on Decision and Control (CDC)
(2016) [PDF]

T. L. Vu, K. Turitsyn, Robust transient stability assessment of renewable power grids, 2016 IEEE International Conference on Sustainable Energy Technologies (ICSET)
(2016) [PDF]

A. Haji Hosseinloo, K. Turitsyn, Optimization of vibratory energy harvesters with stochastic parametric uncertainty: a new perspective, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring
(2016) [PDF]

H. D. Nguyen, K. Turitsyn, Voltage multi-stability in distribution grids with power flow reversal, 2016 IEEE International Conference on Sustainable Energy Technologies (ICSET)
(2016) [PDF]

T. L. Vu, S. Chatzivasileiadis, K. Turitsyn, Towards electronics-based emergency control in power grids with high renewable penetration, 2016 American Control Conference (ACC)
(2016) [PDF]

S. Chatzivasileiadis, T. L. Vu, K. Turitsyn, Remedial actions to enhance stability of low-inertia systems, 2016 IEEE Power and Energy Society General Meeting (PESGM)
(2016) [PDF]

T. L. Vu, K. Turitsyn, Options for emergency control of power grids with high penetration of renewables, 2016 IEEE International Conference on Sustainable Energy Technologies (ICSET)
(2016) [PDF]

A. H. Hosseinloo, K. Turitsyn, Non-resonant energy harvesting via an adaptive bistable potential, Smart Materials and Structures 25, 015010
(2015) [PDF]

M. Vucelja, K. S. Turitsyn, M. Chertkov, Extreme-value statistics of work done in stretching a polymer in a gradient flow, Physical Review E 91, 135
(2015) [PDF]

H. D. Nguyen, K. Turitsyn, Voltage Multistability and Pulse Emergency Control for Distribution System With Power Flow Reversal, IEEE Transactions on Smart Grid 6, 2985--2996
(2015) [PDF]

A. Haji Hosseinloo, K. Turitsyn, Fundamental Limits to Nonlinear Energy Harvesting, Physical Review Applied 4, 1
(2015) [PDF]

K. Dvijotham, K. Turitsyn, Construction of power flow feasibility sets, arXiv:1506.07191v3
(2015) [PDF]

Z. Zhang, H. D. Nguyen, K. Turitsyn, L. Daniel, Probabilistic Power Flow Computation via Low-Rank and Sparse Tensor Recovery, arXiv:1508.02489v1
(2015) [PDF]

M. Parandehgheibi, K. Turitsyn, E. Modiano, Modeling the impact of communication loss on the power grid under emergency control, 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm)
(2015) [PDF]

C. Jaworsky, C. Spataru, K. Turitsyn, Vulnerability Assessment for Interdependent Gas and Electricity Networks, 2015 48th Hawaii International Conference on System Sciences (HICSS)
(2015) [PDF]

S. Yu, H. D. Nguyen, K. S. Turitsyn, Simple certificate of solvability of power flow equations for distribution systems, 2018 IEEE Power & Energy Society General Meeting
(2015) [PDF]

T. L. Vu, K. Turitsyn, Synchronization stability of lossy and uncertain power grids, 2015 American Control Conference (ACC)
(2015) [PDF]

T. L. Vu, K. Turitsyn, Geometry-based estimation of stability region for a class of structure preserving power grids, 2018 IEEE Power & Energy Society General Meeting
(2015) [PDF]

A. H. Hosseinloo, T. L. Vu, K. Turitsyn, Optimal control strategies for efficient energy harvesting from ambient vibration, 2015 54th IEEE Conference on Decision and Control (CDC)
(2015) [PDF]

T. Bogodorova, L. Vanfretti, K. Turitsyn, Bayesian Parameter Estimation of Power System Primary Frequency Controls under Modeling Uncertainties, IFAC-PapersOnLine
(2015) [PDF]

C. Jaworsky, K. Turitsyn, S. Backhaus, The Effect of Forecasting Accuracy on the Sizing of Energy Storage, ASME 2014 Dynamic Systems and Control Conference
(2014) [PDF]

D. Podolsky, K. Turitsyn, Critical slowing-down as indicator of approach to the loss of stability, 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm)
(2014) [PDF]

P. A. Kaplunovich, K. S. Turitsyn, Statistical Properties and Classification of N-2 Contingencies in Large Scale Power Grids, 2014 47th Hawaii International Conference on System Sciences (HICSS)
(2014) [PDF]

H. D. Nguyen, K. S. Turitsyn, Appearance of multiple stable load flow solutions under power flow reversal conditions, 2014 IEEE Power & Energy Society General Meeting
(2014) [PDF]

K. Turitsyn, S. Wabnitz, Stability analysis of polarization attraction in optical fibers, Optics Communications 307, 62--66
(2013) [PDF]

P. A. Kaplunovich, K. S. Turitsyn, Fast selection of N-2 contingencies for online security assessment, 2013 IEEE Power & Energy Society General Meeting
(2013) [PDF]

D. Podolsky, K. Turitsyn, Random load fluctuations and collapse probability of a power system operating near codimension 1 saddle-node bifurcation, 2013 IEEE Power & Energy Society General Meeting
(2013) [PDF]

K. S. Turitsyn, P. A. Kaplunovich, Fast Algorithm for N-2 Contingency Problem, 2013 46th Hawaii International Conference on System Sciences (HICSS)
(2013) [PDF]

C. Jaworsky, K. Turitsyn, Effect of storage characteristics on wind intermittency mitigation effectiveness, 2013 American Control Conference (ACC)
(2013) [PDF]

P. M. Lushnikov, P. Sulc, K. S. Turitsyn, Non-Gaussianity in single-particle tracking: Use of kurtosis to learn the characteristics of a cage-type potential, Physical Review E 85, 051905
(2012) [PDF]

K. S. Turitsyn, S. K. Turitsyn, Nonlinear communication channels with capacity above the linear Shannon limit, Optics Letters 37, 3600
(2012) [PDF]

S. Wabnitz, K. S. Turitsyn, Mitigation of Nonlinear and PMD Impairments by Bit-Synchronous Polarization Scrambling, Journal of Lightwave Technology 30, 2494--2501
(2012) [PDF]

M. Vucelja, G. Falkovich, K. S. Turitsyn, Fractal Iso-Contours of Passive Scalar in Two-Dimensional Smooth Random Flows, Journal of Statistical Physics 147, 424--435
(2012) [PDF]

D. Wang, K. Turitsyn, M. Chertkov, DistFlow ODE: Modeling, analyzing and controlling long distribution feeder, 2012 IEEE 51st Annual Conference on Decision and Control (CDC)
(2012) [PDF]

K. Turitsyn, P. Sulc, S. Backhaus, M. Chertkov, Options for Control of Reactive Power by Distributed Photovoltaic Generators, Proceedings of the IEEE 99, 1063--1073
(2011) [PDF]

S. Backhaus, K. Turitsyn, R. E. Ecke, Convective Instability and Mass Transport of Diffusion Layers in a Hele-Shaw Geometry, Physical Review Letters 106, 104501
(2011) [PDF]

K. S. Turitsyn, M. Chertkov, M. Vucelja, Irreversible Monte Carlo algorithms for efficient sampling, Physica D: Nonlinear Phenomena 240, 410--414
(2011) [PDF]

V. V. Kozlov, K. Turitsyn, S. Wabnitz, Nonlinear repolarization in optical fibers: polarization attraction with copropagating beams, Optics Letters 36, 4050
(2011) [PDF]

R. Pfitzner, K. Turitsyn, M. Chertkov, Controlled Tripping of Overheated Lines Mitigates Power Outages, arXiv:1104.4558v2
(2011) [PDF]

R. Pfitzner, K. Turitsyn, M. Chertkov, Statistical classification of cascading failures in power grids, Energy Society General Meeting
(2011) [PDF]

K. Turitsyn, S. Backhaus, M. Ananyev, M. Chertkov, Smart finite state devices: A modeling framework for demand response technologies, 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011)
(2011) [PDF]

V. Y. Chernyak, M. Chertkov, D. A. Goldberg, K. Turitsyn, Non-Equilibrium Statistical Physics of Currents in~Queuing Networks, Journal of Statistical Physics 140, 819--845
(2010) [PDF]

K. S. Turitsyn, Statistics of voltage drop in radial distribution circuits: a dynamic programming approach, arXiv:1006.0158v1
(2010) [PDF]

Q. Zhang, K. S. Turitsyn, T. A. Witten, Plugs in rough capillary tubes: enhanced dependence of motion on plug length, arXiv:1003.2732v1
(2010) [PDF]

K. Turitsyn, N. Sinitsyn, S. Backhaus, M. Chertkov, Robust Broadcast-Communication Control of Electric Vehicle Charging, 2010 1st IEEE International Conference on Smart Grid Communications (SmartGridComm)
(2010) [PDF]

K. Turitsyn, P. Sulc, S. Backhaus, M. Chertkov, Local Control of Reactive Power by Distributed Photovoltaic Generators, 2010 1st IEEE International Conference on Smart Grid Communications (SmartGridComm)
(2010) [PDF]

K. Turitsyn, P. Šulc, S. Backhaus, M. Chertkov, Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration, Energy Society General Meeting
(2010) [PDF]

K. S. Turitsyn, L. Lai, W. W. Zhang, Asymmetric Disconnection of an Underwater Air Bubble: Persistent Neck Vibrations Evolve into a Smooth Contact, Physical Review Letters 103, 124501
(2009) [PDF]

J. Bec, M. Cencini, R. Hillerbrand, K. Turitsyn, Stochastic suspensions of heavy particles, Physica D: Nonlinear Phenomena 237, 2037--2050
(2008) [PDF]

K. S. Turitsyn, S. S. Vergeles, Wrinkling of Vesicles during Transient Dynamics in Elongational Flow, Physical Review Letters 100, 693
(2008) [PDF]

V. V. Lebedev, K. S. Turitsyn, S. S. Vergeles, Nearly spherical vesicles in an external flow, New Journal of Physics 10, 043044
(2008) [PDF]

S. A. Derevyanko, G. Falkovich, K. Turitsyn, S. Turitsyn, Lagrangian and Eulerian descriptions of inertial particles in random flows, Journal of Turbulence 8, N16
(2007) [PDF]

V. V. Lebedev, K. S. Turitsyn, S. S. Vergeles, Dynamics of Nearly Spherical Vesicles in an External Flow, Physical Review Letters 99, 340
(2007) [PDF]

K. S. Turitsyn, Polymer dynamics in chaotic flows with a strong shear component, Journal of Experimental and Theoretical Physics 105, 655--664
(2007) [PDF]

K. Turitsyn, M. Chertkov, V. Y. Chernyak, A. Puliafito, Statistics of Entropy Production in Linearized Stochastic Systems, Physical Review Letters 98, 695
(2007) [PDF]

A. Shafarenko, K. S. Turitsyn, S. K. Turitsyn, Information-Theory Analysis of Skewed Coding for Suppression of Pattern-Dependent Errors in Digital Communications, IEEE Transactions on Communications 55, 237--241
(2007) [PDF]

A. Celani, A. Puliafito, K. Turitsyn, Polymers in linear shear flow: A numerical study, Europhysics Letters (EPL) 70, 464--470
(2005) [PDF]

A. Puliafito, K. Turitsyn, Numerical study of polymer tumbling in linear shear flows, Physica D: Nonlinear Phenomena 211, 9--22
(2005) [PDF]

M. Chertkov, I. Kolokolov, V. Lebedev, K. Turitsyn, Polymer statistics in a random flow with mean shear, Journal of Fluid Mechanics 531, 251--260
(2005) [PDF]

A. Shafarenko, Skewed coding for suppression of pattern-dependent errors, 31st European Conference on Optical Communications (ECOC 2005)
(2005) [PDF]

I. V. Kolokolov, K. S. Turitsyn, Effective equation of nonlinear pulse evolution in a randomly anisotropic medium, Journal of Experimental and Theoretical Physics 98, 348--351
(2004) [PDF]

V. V. Lebedev, K. S. Turitsyn, Passive scalar evolution in peripheral regions, Physical Review E 69, 639
(2004) [PDF]

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn, Information Capacity of Optical Fiber Channels with Zero Average Dispersion, Physical Review Letters 91, 379
(2003) [PDF]

K. S. Turitsyn, Air parcel random walk and droplet spectra broadening in clouds, Physical Review E 67, 3620
(2003) [PDF]

I. V. Kolokolov, K. S. Turitsyn, Dynamic correlations in a thermalized system described by the Burgers equation, Journal of Experimental and Theoretical Physics 94, 1193--1200
(2002) [PDF]