Sharif Digital Repository

The Onsager's conjecture is concerned with the dichotomy between rigidity and flexibility of weak solutions of incompressible Euler equations. Lars Onsager conjectured that weak solutions of Euler equations that are not smooth enough could be dissipative, even without the help of viscosity. On the other hand, it is well known that $C^1$ solutions conserve energy. Onsager conjectured that C^(1/3) regularity marks the threshold for this dichotomy. In other words, Hölder continuous solutions with Hölder exponent greater than 1/3 conserve the energy, while for every Hölder exponent less than 1/3, there are dissipative Hölder continuous solutions. The threshold 1/3 is intimately tied with... 

This thesis is devoted to the study of suitable functional frameworks for proving propagation of chaos and mean-field limit of nonlinear Vlasov-type equations for indistinguishable particles. The Kac model is a classic example and the motivation of this functional structure. On the one hand, Kac considered a spatially homogeneous gas, and on the other hand, he reduced the problem to one-dimensional collisions and dropped the conservation of momentum assumption. Therefore, he obtained a simplified version of the Boltzmann equation, which is named after him, the Kac equation. The main results which we study are quantitative estimates
on the decay of fluctuations around the deterministic... 

In 1952, Choquet-Bruhat proved the well-posedness of the Cauchy problem for Einstein’s equation, and demonstrated that a given initial data on a Cauchy hypersurface in spacetime propagates forward in time as a solution to the wave equation. It took nearly half a century for mathematicians to build the necessary tools and techniques for proving the stability of the most basic solution of Einstein’s vacuum equations (EVE), namely Minkowski spacetime. In 1993, Christodoulou and Klainerman showed the global nonlinear stability of this solution using the concept of a double null gauge. The Schwarzschild solution, introduced by Karl Schwarzschild in 1916 for spherically symmetric spacetimes as an... 

This research introduces temperature measurement by a non-intrusive pyrometric method of the ratio of two colors of soot. For pyrometry, the spectral sensitivity of the Nikon D7100 camera was obtained by developing a neural network based on the results of photographing colored papers and their spectrum, and this camera was used for temperature measurement. Based on the dependence of soot radiation on temperature and the spectral sensitivity of the camera, a calibration chart has been extracted on the ratio of the green channel to the red channel of the camera with the soot temperature, which is used to produce the temperature contour using the flame image. The temperature contour of... 

Many statistical systems such as earthquakes, road trafcs, forest fres, neurocortical avalanches etc. exhibit self-organized criticality (SOC). In such systems without tuning extrenal parameters, the system arrives at criticality. During recent decades, a number of models are introduced which show the same charactristics. These models have made a platform to investigate the physics of self-organized criticality. Among them, sandpile models are the best known models. They exhibit critical behaviour such as scaling laws. Also in some of them conformal invariance is checked nummerically.Most of sandpile models deal with slope parameters, that is, the main dynamical parameters are the local... 

The aim of these notes is to describe an exciting chapter in the recent development of quantum cohomology. Guided by ideas from physics, a remarkable structure on the solutions of certain rational enumerative geometry problems has been found: the solutions are coefficients in the multiplication table of a quantum cohomology ring. Associativity of the ring yields non-trivial relations among the enumerative solutions. In many cases, these relations suffice to solve the enumerative problem. For example, let $N_d$ be the number of degree $d$, rational plane curves passing through $3d$ − $1$ general points in $\mathbb{P}^2$. Since there is a unique line passing through 2 points, $N_1 = 1$. The... 

Centrifuge is a method in which great gravitational-like forces are used. Gravitational forces which cause molecules to move and are relevant to molecular weight; can cause isotope separation. The separation of light isotope from heavy one is done with a centrifugal field which produces a pressure gradient for the gas mixture. Pressure gradient is different for each of the isotopes due to the dependence of pressure gradient to the mass of the materials. But the separation in this way is very limited. The capacity of separation can be brought up by producing an additional axial flow in the rotor. This rotational flow can be produced with internal or external incitement. Rotational flow with... 

Petroleum based products are the major sources of energy for industry and daily life, With the development of social economy, the demands of the oil have increased dramatically. Petroleum hydrocarbons can cause environmental pollution during various stages of production, transportation, refining and use. Releases of petroleum products(e.g., gasoline, diesel, fuel oil) from aboveground and underground storage tanks or transport pipelines are the major causes of the environment pollution.The major constituents of petroleum hydrocarbons are biodegradable. Many soil microorganisms transform oil hydrocarbons into nontoxic compounds or mineralize them to inorganic compounds. In situ... 

The main goal of this thesis is to study the Teichmüller space and its geometric properties. The Teichmüller space of a surface can be studied from complex geometric or hyperbolic geometric points of view, and in this thesis we refer to both of these viewpoints where needed. Another goal of this thesis is to review a method of compactification of the Teichmüller space. Therefore, we introduce the compactification method proposed by Thurston. To this end, we first briefly review hyperbolic geometry. Then we extend some tools, and use some techniques in hyperbolic geometry, to describe Thurston’s construction and pave the way for it. In the second phase of this study, we introduce... 

Based on fog computing paradigm, new applications have become feasible through the use of hardware capabilities of smart phones. Many of these applications require a vast amount of computing and real-time execution should be guaranteed. Based on fog computing, in order to solve these problems in is necessary to offload heavy computing to servers with adequate hardware capabilities. On the other side, the offloading process causes time overhead and endangers the real-timeliness of the application. Also, because of the limited battery capacity of the handheld devices, energy consumption is very important and should be minimized.The usual proposed solution for this problem is to refactor the... 

Investors highly value the ability to predict the behavior of the capital market. Over time, various methods have been introduced to forecast the future of this market and anticipate its movements. A novel approach to achieving this is by developing data-driven decision support systems that can assist investors in making informed trading decisions. The opinions of experts play a crucial role in shaping people's perception of the market, which ultimately affects its final behavior. In this study, we have created a decision support system that can help investors by considering the complexities and meaningful relationships between different aspects of the problem. We have developed frameworks... 

In this dissertation, we will study partially hyperbolic diffeomorphisms. First, we are going to introduce partially hyperbolic diffeomorphisms and construct some examples. One of the important questions in the study of partially hyperbolic diffeomorphisms is their classification problem, which provides a deeper understanding of manifolds and also of partially hyperbolic diffeomorphisms themselves. We will go through this problem by examining Hammerlindl, Potrie’s [1]’s work. They have proved that a partially hyperbolic diffeomorphism on a 3-manifold with a virtually solvable fundamental group, that has no periodic torus tangent to contraction-center or expansion-center, is dynamically... 

There are a lot of ways to measure the soil compaction but all of them have some deficiencies like low precision, soil destructive, time consuming and etc. The usual ways to measure the compaction in Iran are so traditonal and have the above problems. To solve these problems, modern ways like intelligent compaction is recomonded to decrease the time and cost of compaction. The observor can also control the compaction of all the soil point to prevent any offenses by making the network between the rollers.In new methods the soil compaction is calculated by measuring the roller vibratory and usage of fourier transform from the drum response . To compact the soil more precisely and more quickly,... 

The competition for staying in the business world has intensified today with the rise of open-source and commercial software. As long as a software is tailor-made to suit the needs of users, it is so-called alive and can stay in the competition. So the maintenance phase is necessary to make changes to the software to meet the needs of users. To reduce costs associated with this phase, it is necessary to avoid software bugs. One way to avoid software bugs is to use peer code review. Peer code review has been recognized as one of the best software engineering principles of the last 35 years. This principle helps maintain the quality of the code due to changes made to parts of the code that... 

Many public projects in Iran are being developed with the participation of the private sector. Complaints, however, have arisen in both the public and the private sectors in many public-private-partnership (PPP) projects. It is claimed that the current PPP standard-form contract is unable to properly handle project risks. This investigation was set to improve risk responses in the PPP standard-form contract in the country. A comprehensive list of 66 universal PPP project risks was prepared by review of various related international research efforts. The list was refined to 36 risk items for the country in consultation with PPP project experts and assessing two PPP cases. These risks were... 

Today, the correct management of construction projects in IRAN's water industry has become a severe concern for its managers. Construction projects of the water industry constitute a considerable part of the country's construction industry. Several significant Issues such as operation management, water industry projects, correct management of resources, crisis management in the water industry, increased productivity and useful life of structures, increasing productivity, and preventing water loss are among the determinative challenges in construction projects in Iran. One of the new methods for the correct management of the life cycle of projects in this area is the use of Building... 

Representation learning methods on graphs have enabled using machine learning methods on graphs' discrete structure by transferring them to a continuous domain. As graphs' structures are not always static and may evolve through time, dynamic representation learning methods have recently gained scholars' attention. Several methods have been proposed to enable the model to update the embeddings graph changes, or new interactions happen between nodes. These online methods could significantly reduce the learning time by refreshing the model as the changes occur, so we don't need to retrain the model with the complete graph information. Moreover, by using the temporal information of interactions,... 

The municipality is an administrative, public and non-state institution that falls into the city district of the most countries’ administrative divisions. This institution has relatively autonomy and independent power. Municipalities are trying to apply the best approaches (Such as Building Information Modeling (BIM) as a procedure contributing the project management) to save time and money, as well as to satisfy the citizens in the implementation of civil projects. This study examines and evaluates the readiness of municipalities to modify the construction projects based on BIM. In addition, a pattern for identifying BIM applications, evaluating the organization readiness and the needs of... 

Stock price patterns are a technical analysis approach to forecast future trends with tremendous practical benefits. However, the current algorithms solely rely on machine learning techniques and deep neural networks which could be a problem in countries where data sets such as these are not available. We propose an algorithm based on geometry and mathematics for this problem, leading to an O(n^3logn + n^2k) complexity, where k is the number of triangular patterns  

Video games with respect to an ever Increasing player pool and Industry growth, have attracted a lot of attention in recent years. Dota 2, as one of the most successful games both in casual gamers’ community and E-sport community, is considered as a proper case study, however, most of the research done was limited to predicting games’ outcome. Despite The popularity, the rather unintelligent AI of the game has made quite a frustrating experience for new players. In this research, with a novel approach, hero features are used to predict their future positions. For this purpose, 35 professional games are collected and analyzed and 601 features are extracted. Then, suitable features are...