Filter by program: (reset)
Jump to a particular term:
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies.
Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies.
First and second principles of thermodynamics analysis are presented and applied to the analyzed systems as well as commercial state of the art process engineering software: Heat exchangers and Boilers, Steam and Organic Rankine Cycles, Gas Turbines, Natural Gas Combined Cycles and Heat Recovery Steam Generator, Internal Combustion Engines, Compression Heat Pumps and Chillers as well as Absorption Chillers, co- and tri-generative solutions. The environmental aspects, like pollutants formation and their abatement, are also taken into consideration.
Matematical methods of modern theory of Hamiltonian systems are based on the concepts, arosen in different fields of mathematics: differential equations and dynamical systems, Lie groups and algebras, differential geometry on manifolds. Many modern directions in mathematics (e.g. symplectic geometry) got their origin from the problems of classical mechanics.This course is recommended to all students, interested in mathematical physics, and it does not imply any special preliminary education in physics.
The preliminary program of the course includes: 1. Lagrangian formalism: minimal action principle, Euler-Lagrange equations, symmetries and integrals of motion, Noether theorem. 2. Simplest examples: dynamics for a single degree of freedom, Kepler’s problem etc. 3. Basis of the Hamiltonian formalism: phase space, Legebdre transform, Hamilton equations, the Poisson and symplectic structures, Darboux theorem. 4. The Hamilton-Jacobi equation, canonical transform, Liouville theorem. 5. Integrable systems: separation of variables, Liouville integrability. Systems with Lax representation. 6. Examples of integrable systems: Toda and Calogero problems, integrable systems on Lie groups, geometry of spectral curves etc.
Here is the list of topics which will be discussed in the course.
- Coordinate Bethe ansatz on the example of the Heisenberg model and one-dimensional Boe gas with point-like interaction between particles.
- Bethe ansatz in exactly solvable models of statistical mechanics on the lattice.
- Calculation of physical quantities in integrable models in thermodynamic limit, thermodynamic Bethe ansatz.
- Bethe equations and the Yang-Yang function, caclulation of norms of Bethe vectors.
- Quantum inverse scattering method and algebraic Bethe ansatz, quantum R-matrices, transfer matrices, Yang-Baxter equation.
- Functional Bethe ansatz and the method of Baxter’s Q-operators, functional relations for transfer matrices, transfer matrices as classical tau-functions.
The knowledge of quantum mechanics and statistical physics for understanding of the course is highly desirable but not absolutely necessary. Out of the physical context ansatz Bethe in its finite-dimensional version is simply a method for diagonalization of big matrices of a special form. In this sense it does not require anything except the basic notions of linear algebra.
As to the vicinity of the metal-insulator transition, I give a qualitative discussion of the mechanism behind the transition, as well as the most powerful tools for probing the properties of the system near the transition: analysis of inverse participation ratios and the concept of multifractality of the wave-functions.
In the metallic phase I discuss the weak localization corrections, including magnetoresistance, inelastic phase-breaking mechanisms and interaction-induced anomalies in the density of states near the Fermi surface.
At the end of the course I give a brief introduction to mesoscopics, including the Landauer formalism and quantization of the ballistic conductance.
Tentative plan: linear Lie groups and their Lie algebras; universal enveloping algebras; Haar measure on a linear Lie group; general facts about representations of compact groups and their characters; radial part of Haar measure; Weyl’s formula for characters of the unitary groups; Weyl’s unitary trick; classification and realization of representations; symmetric functions.
Course goal is to give students basic knowledge about the main areas of mathematics used in the data science, who will continue to study their chosen more specialized areas of the modern data science.
One of the emphases is on the development of a common set of tools that have proved to be useful in a wide range of applications in different areas. Topics will include the concentration of measure, Stein’s methods, suprema of random processes and etc. Another main emphasis is on the application of these tools for the study of spectral statistics of random matrices, which are remarkable examples of random structures in high dimension and may be used as models for data, physical phenomena or within randomized computer algorithms.
The topics of this course form an essential basis for work in the area of high dimensional data. Students will study how to apply the main modern probabilistic methods in practice and learn important topics from the random matrix theory.
In the course, we will discuss aspects of the conformal theory, basic, but not included in the usual introductory courses. A small preliminary acquaintance with string theory and conformal field theory is assumed. We will mainly focus on the mathematical aspects of the theory, the relations with the representation theory, geometry, combinatorics, special functions.
The design includes: concept development, conceptual design, systems engineering, 3D physical simulation (CFD and FEM), parametric and topology optimization, final solid design.
Educational process is focused on teamwork in this course. Siemens Teamcenter PLM platform is used as to provide interaction within students workgroup.
The course provides students with a theoretical and practical basis for implementing projects devoted to the design of complex technical systems, such as unmanned aerial vehicles.
The course assumes basic preliminary knowledge of quantum mechanics and statistical physics. Second-quantization formalism is introduced and used throughout the course.
Foundation of continuum mechanics consists of: 1) material continuum model in the form of a deformable (with mechanical stresses and other macroparameters) continuous medium, described via several piecewise continuous differentiable functions. Building such a model is carried out by averaging the parameters of real materials that have a discrete atomic and molecular structure; 2) differential, integral, tensor calculus and the theory of dimensions with the fundamental idea of invariance under transformation of coordinate systems and systems dimension; 3) The laws of conservation of mass, momentum, angular momentum and energy, the laws of thermodynamics, expressed in terms of macroscopic parameters of the material continuum; 4) mechanical (rheological), thermal and electrical experiments that allow us to find connections between macroparameters of different substances at different mechanical, thermal, electromagnetic and physical-chemical processes. These representations constitute, in particular, the mathematical theory of thermo-electro-magneto-mechanical field.
This course uses tensor representations in the Cartesian coordinate system of the observer. But it will one shown in detail how to to write the continuum mechanics equations in the arbitrary curvilinear coordinate system. This way the common link is not lost and the exposition becomes easier and clearer.
The Exam has two parts:
Part 1 – Pre-exam activities (Assignments 1, 2a, 2b) Part 2 – Activities on Examination day (Assignment 3): a ten-minute presentation based on the student’s research, followed by a discussion.
At the same time, through creativity lab students will be introduced to a variety of creative problem solving techniques and learn how to apply these techniques in the context of the development, evaluation and application of ideas and concepts with commercial potential; consider the evaluation of business ideas that translate existing business models into new national contexts.
The course is designed to help students develop the ability to find, evaluate, and develop technological ideas into commercially viable product and process concepts, and build those concepts into viable business propositions. The material covered is research and theory-based but the course is practice-oriented with much of the term spent on shaping technology-based opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels.
The course is focused on the human immune system. The main medical aspects related to the functioning of the immune system will be considered, such as: autoimmune diseases, allergies, tumor-immune system interactions, immunotherapy, vaccinations and transplantation. Particular attention will be paid to the adaptive part of the immune system and immunogenomics: application of the new sequencing technologies and associated computational data analysis approaches to the studying of the antibody and T-cell receptor repertoires in health and disease.
The course is designed for students of different biomedical background. The necessary foundation will be given in the form of lectures. Independent work of students, mainly in the form of presentations aimed to dissect the particular immunological questions at the seminars, will be differentiated in compliance with individual background.
A workshop in applied bioinformatics is included within the course. In a few hours of guided and independent work it will cover the data analysis of immune receptor high-throughput sequencing.
-) Introduction to cryptography, type of ciphers. Private and Public crypto systems -) Hash functions.Digital signatures and certificates. Public key infrastructure -) Secret sharing, esoteric protocols, mental poker -) Introduction to data base systems. Distributed data base systems -) Main concept of blockchain. Consensus and Impossibility of Distributed consensus with One Faulty Process -) Network and computational assumptions. Consensus properties -) Atomic broadcast. Tendermint. Exonum -) Cryptocurrency, Certification, Anchoring. Industrial examples
Upon completion of this course the students will be able to master:
1.Classes of Materials
crystalline solids ionic, covalent, metallic, polymers 3-D structures, polymorphism, importance of defects, effect of nanoscale phase diagrams, transformations, glasses, composites
2. Property of Materials
Electrical Optical Magnetic
3. Materials Chemistry Analysis Methods
Surface Sensitivity and Specificity X-ray Photoelectron Spectroscopy Ultraviolet Photoelectron Spectroscopy
It includes considering strategies to choose the relevant variables, parameters and observables, model nature (e.g. discrete vs continuous), modeling technique (e.g. agent-based simulations vs. dynamical system approach), and visualization and interpretation of the results. The following classes of systems will be used as examples:
1. Population models 2. Evolution and speciation 3. Systems biology 4. Reaction-diffusion systems and pattern formation 5. Networks 6. Game-theoretical models
In this course I will show, how numerical linear algebra methods and algorithms are used to solve practical problems. Matrix decompositions play the key role in numerical linear algebra. We will study different matrix decompositions in details: what are they, how to compute them efficiently and robustly, and most importantly, how they are applied to the solution of linear systems, eigenvalue problems and data analysis applications. For large-scale problems iterative methods will be described. I will try to highlight recent developments when it is relevant to the current lecture.
This course should serve as a basis for other IT Skoltech courses. It will also serve as a first-time place where programming environment and infrastructure is introduced in a consistent manner.
The course covers the entire spectrum of lifecycle management of a system, encompassing conception, design, implementation, assembly-Integration and Test, operations, and disposal of systems.
Being a foundational course for the Space and Engineering Systems students of Skoltech, the course discusses many applications of systems engineering including some parts of space systems engineering . The course also discusses systems architecture principles.
The Systems Engineering course follows the systems engineering V-model as an educational guideline throughout the term. Tradeoff analysis and systems architecture will be introduced as part of the course, but more detailed coverage of these topics will be provided by the ad-hoc Systems Architecture course already in place at Skoltech. The course includes a journal club to review academic articles and standards pertinent to systems engineering, which form a complement to weekly homework assignments and a design project that is conducted throughout the term.
The course lays the foundation to undertake a robust analysis and design of opportunities for technological innovation. It helps PhD students to develop the ability to recognize, evaluate, and develop technological ideas into commercially viable product and service concepts, and build those concepts into viable business propositions.
We introduce tools and frameworks to help isolate and control the factors shaping the identification, evaluation and development of commercial opportunities. During the course, students first gain practical experience in shaping technology-based opportunities (originating from problems found in engineering and scientific education) and in identifying market-based opportunities (from social, economic and environmental contexts). Students are then challenged to employ that same commercialization framework to reflect on and examine ideas and scientific results from their own doctoral research, link these with appropriate market-based opportunities, and identify one or more pathways to create practical impact from their ideas.
The material covered is research and theory-based but the course is practice-oriented with much of the term spent on shaping technology-based opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels.
Students activities include:
- attending the lectures – participating in discussions/seminars -homework
The main goal of this course is to represent the latest developments in the field of additive manufacturing to the students. In this course a wide range of questions will be addressed, beginning from the process of designing the structures up to various printing technologies, as well as analysis of the final structures. Various kinds of applications of these materials from engineering to bio regenerative medicine will be considered. During laboratory class we will get acquainted with the additive technologies on various printing machines. Students will be able to create their own models, print them in metals, ceramics and polymers, and also analyze the properties of the final samples. During this course a complete cycle of production of samples using various 3D printing techniques will be explored both theoretically and practically.
During the course, students should develop the technology for small unmanned aerial vehicle (UAV) prototype production. Educational process includes manufacturing technology development, prototype production, prototype testing, model validation. During the course, students learn how to use special software Simcenter 3D, LMS Test.Lab, LabView, 3D printers’ software, test machines
The course provides students with a theoretical and practical basis for advanced manufacturing of complex systems, such as UAV and forms the final understanding of the product lifecycle management.
Course structure: lectures, seminars, exam.
We start with several practical examples which demonstate the need for geomechanics in each of considered technological application with special application to hydraulic fracturing technology.
We then stop on continuum mechanics formulations for one phase models, suitable for one-point-view description of reservoir and well flow deformation processes. We also describe two-phase models, although intentionally do not go too deep in the topic. We also do not goal to make our formulations rigorous enough in mathematical sense. We do not thing that Master students need that at this stage. Instead, we put significant effort (and number of contact hours) to let Master students fell free in practical solutions of the governing equations they were just taught. To make the procedure more effective, the governing equations are divided into several (20) basic groups with their own specific modelling recipes which are taught to students at classes until they ensure that the procedures are simple. For doing that we developed 20 matlab codes. During their further project exercises, students will utilize these 20 “bricks” to construct solutions for real field and/or technological problems, presented in the first section of the course.
It has to be noticed, that the course is suitable for PhD students as well, although the project topics for them would be more complicated that that for the master students
Intellectual property affects not only technology commercialization strategy but also the direction of scientific research itself. University research groups increasingly compete with each other for scientific reputation and access to resources on the basis of their ability to obtain patent protection for the practical applications of their research; but also on the basis of their ability to plot research pathways to maneuver around the “proprietary territory” of other research groups. Skill in using IP data bases, and associated analytical tools, can empower university scientific teams to craft more powerful research strategies.
This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IP-related rights, such as patents, copyright, trade secrets, trademarks, design rights, database rights, domain names, and demarcations of origin. The classroom sessions will include lively discussions of case studies of the management of IP and the resolution of IP-related problems in the process of technology commercialization. Each student will conduct an analysis of intellectual property issues related to his or her own Ph.D. research topic. Use will be made of special IP data and IP analytics tools.
Tensor and matrix factorizations play the crucial role in the construction of efficient methods for compression. These are non-linear representations. We will cover basic tensor formats, and describe algorithms for working with such formats.
The course is intended to provide the understanding and working knowledge of numerical methods required for modeling and simulation of complex phenomena. The course focuses on understanding fundamentals of numerical methods such as accuracy, stability, convergence, and consistency rather than learning how to use canned computer codes. The course involves a fair amount of first-hand experience with programing and solving real problems on computers. Although the solid knowledge of calculus, linear algebra, complex variables is essential, only basic understanding of the theory of ordinary and partial differential equations as governing equations for physical and engineering systems as well as basic programming skills are required. The following topics are discussed: interpolation, numerical differentiation, numerical integration, numerical solutions of ordinary differential equations, and numerical solution of partial differential equations. Students will have to complete four computer projects, mid-term and final exams.
The course also rests on the approach that learning is promoted by feedback. The assessment design that participants in the course design will therefore be required to reflect significant and effective use of continuous formative assessment. Such formative assessment requires strategic learning activities and assignments, and the course therefore comes with an emphasis on communication-to-learn activities including peer learning.
Skoltech is an English medium instruction environment, and the course contains discussion topics to highlight ways of addressing the potential effects of language and culture barriers for high quality student learning.
All topics in the course are applied by participants on their own teaching and learning experiences and are meant to be used as they prepare and plan for their teaching assistantships or their supervisory activities to come. All participants will have a task to produce a reflection on their future actions to evolve as facilitators and meet the requirements of the scholarship of teaching and learning.
It turns out that all these problems have a general mathematical structure, which can be encoded in the term “integrability”. This structure is behind a lot of beautiful exact mathematical results. Moreover, these results have remarkable universality property, which play the same role as the law of large numbers and the central limit theorem in the probability theory. Looking at our random systems from afar, we find that they posess completely nonrandom limiting forms. Random fluctuations around these forms are described by a small number of universal probability distributions that are completely independent of the details of original system. The course attendees are going to get acquainted with the range of issues described and to learn about the latest achievements in the field.
This course will cover the fundamentals of signal and image processing. We will provide a mathematical framework to describe and analyze images as two- or three-dimensional signals in the spatial and frequency domains. The students will become familiar with the theory behind fundamental processing tasks including image enhancement, recovery and reconstruction. They will also learn how to perform these key processing tasks in practice using current state-of-the-art techniques and computational tools. A wide variety of such tools will be introduced including large-scale optimization algorithms and statistical methods. Emphasis will also be given on sparsity, which plays a central role in modern image processing systems
This class will focus on concept preparation in the V-diagram logic. Further results can be explored either in the Space Sector course, where commercial aspects of the mission can be considered, as well as in the PLM course, where technical details can be worked out in a systematic fashion.
The goal of this course is to give a broad review of modern photonic and spectroscopic studies of quantum materials. The course requires basic knowledge of quantum mechanics, optics and solid state physics. In the introductory part of the course, the basic theory of electromagnetic response of quantum systems, centered around linear response functions and their spectral properties, is outlined. The rest of the course describes such quantum materials as graphene and graphene-based structures, topological insulators, topological Dirac and Weyl semimetals, high-temperature superconductors, exotic magnetics, transition metal dichalcogenides, oxide interfaces, and novel electromagnetically-engineered quantum materials. The students will be introduced to basic models and to both conventional and ultrafast pump-probe spectroscopy studies of these materials.
Independent student work on discipline includes preparation for lectures, seminars, labs and other learning activities, as well as the implementation of individual tasks / independent works / projects and others. Educational and methodical support of Independent student work presented by topics of all kinds of tasks and guidelines for their implementation.
Totally 32 hours of lectures, 12 hours of exercises and 4 hours of discussion work. During the courses each student is supposed to give a short presentation (15 min) on a selected topic, to write an essay on other selected topic and to prepare an exercise report.
• Introduction: What is a composite? Classification. Metals vs composites, advantages and disadvantages. Applications in industry. • Matrices. Micromechanics. • Mesomechanics: Stresses and strains. Ply. Laminate theories. Hygrothermal strains and stresses. Edge effect. • Manufacturing: Unidirectional vs. textile. Thermoplastic vs. thermoset. Prepreg vs. infusion. • Experimental characterisation: Tension, bending, compression, shear, impact, fatigue. • Damage and failure. Fracture toughness. • Finite element analysis. Abaqus.
Participants will learn fundamentals of these areas through active participation in teamwork. The course will provide practical knowledge on applications of composite materials in aerospace and mechanical engineering. The course includes practical experience of composite manufacturing and mechanical tests. During the last part of the course the participants will be presented a ‘challenge’ project in design and structural analysis, which they may attack experimentally, analytically or by means of finite-element package Abaqus. Participants are expected to demonstrate their collective knowledge while at the same time solving individually a real problem.
Topics also include clearing agents and techniques, optical imaging of brain activity in vivo using genetically encoded probes, immediate early gene mapping, intravital imaging, applications for functional analyses of neuronal circuits.
The course aims to teach students to understand basic principles of the current imaging techniques, microscope design, and image formation. The course will also offer a practice in image analysis with open source software. Students will learn how to choose the most appropriate imaging method for their own research project.