26,474 research outputs found
Quantum Mechanics Lecture Notes. Selected Chapters
These are extended lecture notes of the quantum mechanics course which I am
teaching in the Weizmann Institute of Science graduate physics program. They
cover the topics listed below. The first four chapter are posted here. Their
content is detailed on the next page. The other chapters are planned to be
added in the coming months.
1. Motion in External Electromagnetic Field. Gauge Fields in Quantum
Mechanics.
2. Quantum Mechanics of Electromagnetic Field
3. Photon-Matter Interactions
4. Quantization of the Schr\"odinger Field (The Second Quantization)
5. Open Systems. Density Matrix
6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation
7. Mean Field Approaches for Many Body Systems -- Fermions and Boson
Soliton Gas: Theory, Numerics and Experiments
The concept of soliton gas was introduced in 1971 by V. Zakharov as an
infinite collection of weakly interacting solitons in the framework of
Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted
soliton gas, solitons with random parameters are almost non-overlapping. More
recently, the concept has been extended to dense gases in which solitons
strongly and continuously interact. The notion of soliton gas is inherently
associated with integrable wave systems described by nonlinear partial
differential equations like the KdV equation or the one-dimensional nonlinear
Schr\"odinger equation that can be solved using the inverse scattering
transform. Over the last few years, the field of soliton gases has received a
rapidly growing interest from both the theoretical and experimental points of
view. In particular, it has been realized that the soliton gas dynamics
underlies some fundamental nonlinear wave phenomena such as spontaneous
modulation instability and the formation of rogue waves. The recently
discovered deep connections of soliton gas theory with generalized
hydrodynamics have broadened the field and opened new fundamental questions
related to the soliton gas statistics and thermodynamics. We review the main
recent theoretical and experimental results in the field of soliton gas. The
key conceptual tools of the field, such as the inverse scattering transform,
the thermodynamic limit of finite-gap potentials and the Generalized Gibbs
Ensembles are introduced and various open questions and future challenges are
discussed.Comment: 35 pages, 8 figure
Evolutionary Multi-Objective Aerodynamic Design Optimization Using CFD Simulation Incorporating Deep Neural Network
An evolutionary multi-objective aerodynamic design optimization method using
the computational fluid dynamics (CFD) simulations incorporating deep neural
network (DNN) to reduce the required computational time is proposed. In this
approach, the DNN infers the flow field from the grid data of a design and the
CFD simulation starts from the inferred flow field to obtain the steady-state
flow field with a smaller number of time integration steps. To show the
effectiveness of the proposed method, a multi-objective aerodynamic airfoil
design optimization is demonstrated. The results indicate that the
computational time for design optimization is suppressed to 57.9% under 96
cores processor conditions
Numerical solution of system of second-order integro-differential equations using nonclassical sinc collocation method
Abstract In this paper, a nonclassical sinc collocation method is constructed for the numerical solution of systems of second-order integro-differential equations of the Volterra and Fredholm types. The novelty of the approach is based on using the new nonclassical weight function for sinc method instead of the classic ones. The sinc collocation method based on nonclassical weight functions is used to reduce the system of integro-differential equations to a system of algebraic equations. Furthermore, the convergence of the method is proposed theoretically, showing that the method converges exponentially. By solving some examples, including problems with a non-smooth solution, the results are compared with other existing results to demonstrate the efficiency of the new method
Regularised Learning with Selected Physics for Power System Dynamics
Due to the increasing system stability issues caused by the technological
revolutions of power system equipment, the assessment of the dynamic security
of the systems for changing operating conditions (OCs) is nowadays crucial. To
address the computational time problem of conventional dynamic security
assessment tools, many machine learning (ML) approaches have been proposed and
well-studied in this context. However, these learned models only rely on data,
and thus miss resourceful information offered by the physical system. To this
end, this paper focuses on combining the power system dynamical model together
with the conventional ML. Going beyond the classic Physics Informed Neural
Networks (PINNs), this paper proposes Selected Physics Informed Neural Networks
(SPINNs) to predict the system dynamics for varying OCs. A two-level structure
of feed-forward NNs is proposed, where the first NN predicts the generator bus
rotor angles (system states) and the second NN learns to adapt to varying OCs.
We show a case study on an IEEE-9 bus system that considering selected physics
in model training reduces the amount of needed training data. Moreover, the
trained model effectively predicted long-term dynamics that were beyond the
time scale of the collected training dataset (extrapolation)
Partially Adaptive Multichannel Joint Reduction of Ego-noise and Environmental Noise
Human-robot interaction relies on a noise-robust audio processing module
capable of estimating target speech from audio recordings impacted by
environmental noise, as well as self-induced noise, so-called ego-noise. While
external ambient noise sources vary from environment to environment, ego-noise
is mainly caused by the internal motors and joints of a robot. Ego-noise and
environmental noise reduction are often decoupled, i.e., ego-noise reduction is
performed without considering environmental noise. Recently, a variational
autoencoder (VAE)-based speech model has been combined with a fully adaptive
non-negative matrix factorization (NMF) noise model to recover clean speech
under different environmental noise disturbances. However, its enhancement
performance is limited in adverse acoustic scenarios involving, e.g. ego-noise.
In this paper, we propose a multichannel partially adaptive scheme to jointly
model ego-noise and environmental noise utilizing the VAE-NMF framework, where
we take advantage of spatially and spectrally structured characteristics of
ego-noise by pre-training the ego-noise model, while retaining the ability to
adapt to unknown environmental noise. Experimental results show that our
proposed approach outperforms the methods based on a completely fixed scheme
and a fully adaptive scheme when ego-noise and environmental noise are present
simultaneously.Comment: Accepted to the 2023 IEEE International Conference on Acoustics,
Speech, and Signal Processing (ICASSP 2023
Evaluating environmental effects in construction and demolition waste recycling plant with the Iranian Leopold Matrix method
BACKGROUND AND OBJECTIVES: Recycling and reusing construction and demolition debris is a productive step toward solving this problem. Still, the recycling process also leaves industrial effluents, which is evident in producing recycled sand. The present research has investigated the environmental effects of recycling construction debris at sand recycling plants. Considering the negative impacts of sand washing mud produced at the plant in the Aab'Ali Landfill of Tehran in Iran, the material's physicochemical characteristics and environmental impact have also been investigated to regulate practices.                       METHODS: The Environmental Impact Assessment has been carried out in physicochemical, biological, socio-cultural, and economic-technical areas. Due to the large dispersion of the studied soil and the composition diversity in each sampling, 30 samples of the sand washing mud and the material mixed with the surrounding soil have been collected. The exploitation phase during the factory construction plan's implementation stage was considered the current research's main phase. Hence, 13 micro activities and 23 environmental parameters were identified, and the results were analyzed in the Environmental Impact Assessment Plus Software using the Iranian Leopold Matrix method and discussed based on the results of the experiments.FINDINGS: According to the results of the matrix calculation, the three micro-activities included washing the sand through a sand-washing machine, fine sand washing through the EvoWash machine with a score of -3.6, converting concrete pieces and large boulders into smaller pieces by jackhammers, transferring to the jaw crusher machine with a score of -2.8, and transferring the remaining sand washing mud produced by the EvoWash machine to the storage pond with a score of -2.7 had the most negative effects. The three micro-activities of waste processing for green space irrigation (+2.2), selling products (+0.9), and hiring employees with a score of +0.5 have the most positive effects on the environment. As ranking smaller than -31 forming 50% of the total average of rows and columns, the activity of the plant and the sand extraction process in this landfill is approved by providing modification alternatives.CONCLUSION: Considering the positive impact on the economy, increasing green spaces in the region, job creation, and also reducing the amount of increasing debris accumulated in the landfill is evaluated positively and can be done considering the reforms; including the prevention of releasing remnant sand washing mud freely and recycling it instead. Reusing the sand washing mud requires improving the water purification systems used in the EvoWash machine
Eigen-Factors an Alternating Optimization for Back-end Plane SLAM of 3D Point Clouds
Modern depth sensors can generate a huge number of 3D points in few seconds
to be latter processed by Localization and Mapping algorithms. Ideally, these
algorithms should handle efficiently large sizes of Point Clouds under the
assumption that using more points implies more information available. The Eigen
Factors (EF) is a new algorithm that solves SLAM by using planes as the main
geometric primitive. To do so, EF exhaustively calculates the error of all
points at complexity , thanks to the {\em Summation matrix} of
homogeneous points.
The solution of EF is highly efficient: i) the state variables are only the
sensor poses -- trajectory, while the plane parameters are estimated previously
in closed from and ii) EF alternating optimization uses a Newton-Raphson method
by a direct analytical calculation of the gradient and the Hessian, which turns
out to be a block diagonal matrix. Since we require to differentiate over
eigenvalues and matrix elements, we have developed an intuitive methodology to
calculate partial derivatives in the manifold of rigid body transformations
, which could be applied to unrelated problems that require analytical
derivatives of certain complexity.
We evaluate EF and other state-of-the-art plane SLAM back-end algorithms in a
synthetic environment. The evaluation is extended to ICL dataset (RGBD) and
LiDAR KITTI dataset. Code is publicly available at
https://github.com/prime-slam/EF-plane-SLAM
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