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... 

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... 

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 focuses on physics-informed neural networks, which are trained to solve supervised machine learning tasks while adhering to physical laws described by general nonlinear partial differential equations. Previous studies utilized Gaussian process regression to develop functional representations designed for a given linear operator. However, despite the flexibility of Gaussian processes, solving nonlinear problems presents two major limitations: first, authors had to linearize each nonlinear term over time, and second, the Bayesian nature of Gaussian process regression requires specific assumptions that may limit the model’s representational capacity. For these reasons, data-driven... 

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... 

The Quantum Central Limit Theorem states that when you convolve a centered quantum state, the resulting sequence of states converges to a Gaussian quantum state with the same first and second moments as the original quantum state. Similar to the classical setting, there are various metrics to measure convergence in the Quantum Central Limit Theorem. In this thesis, we aim to examine this theorem under different metrics such as Quantum Relative Entropy and Trace distance, and to prove tight convergence rates for the Quantum Central Limit Theorem  

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... 

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... 

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... 

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... 

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... 

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... 

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... 

Deep learning algorithms combined with supervision rely heavily on labeled data, posing challenges in the data labeling process. Addressing this issue, researchers in the field of machine learning have focused on developing approaches to reduce the dependency on labeled data and improve the efficiency of data collection for labeling purposes. This thesis investigates the training of a classification model using data collected through a human-in-the-loop system. Notably, this research pioneers the application of active learning techniques to differentiate between political and non-political Persian tweets. The dataset introduced in this study is the sole available collection for this specific... 

One of the most significant factors for the on-time and successful implementation of construction projects is contract management. Proper management of construction contracts and assessment of potential risks in the bidding process and before its signing have a significant impact on preventing or reducing the occurrence of claims and disputes between the contract parties at various stages of the project. In this research, using the latest deep learning (DL) and natural language processing (NLP) state-of-the-art methods, and various deep neural networks (DNN) architectures a model has been developed for extracting Persian contract risk-prone clauses. In addition, this study provides a...