“…BACKGROUND: Early diastolic left ventricular (LV) filling can be accurately described using the same methods used in classical mechanics to describe the motion of a loaded spring as it recoils, a validated method also referred to as the Parameterized Diastolic Filling (PDF) formalism. …”
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“…MATERIALS AND METHODS: The method consists of molecular dynamics simulation of adsorption process by implementing classical mechanics theory to calculate the final response of the sensor as tip deflection. …”
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“…The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and hence with the principle of stationary action. …”
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“…Cortical bone cross-section diameters and published bone biomechanical properties were substituted into classical mechanics equations to predict the intact test segment theoretical stiffness for comparison and thus loading-measurement system verification. …”
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“…SLEND is a time-dependent, variational, non-adiabatic and direct method that adopts a nuclear classical-mechanics description and an electronic single-determinantal wavefunction in the Thouless representation. …”
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“…Some have argued that rather than resulting from electron donation, carbonyl interactions are a particular example of dipolar interactions that are well-approximated by classical mechanics. However, experimental evidence has demonstrated otherwise. …”
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“…The probability is examined of the action of attraction forces due to electromagnetic interaction of rotating charged baryonic particles, instead of the classical Newton theory of gravitation, i.e., the law describing gravitational interaction in classical mechanics. A discussion is provided of the nature and role of black holes in the Universe, which are seen as an integral and obligatory part of all physical structures of the Cosmos. …”
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“…To address such an “accuracy vs reality” dualistic requirement, mixed quantum mechanics/classical mechanics approaches within Atomistic (i.e., preserving the discrete particle configuration) Polarizable Embeddings (QM/APEs) methods have been proposed over the years. …”
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“…Writings by the founders of classical mechanics, G. Galilei and I. Newton, are reproduced, encouraging students to consult them. …”
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“…NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS Inadequacy of Classical Description for Small Systems Basis of Quantum Mechanics Representation of States Dual Vectors: Bra and Ket Vectors Linear Operators Adjoint of a Linear Operator Eigenvalues and Eigenvectors of a Linear Operator Physical Interpretation Observables and Completeness Criterion Commutativity and Compatibility of Observables Position and Momentum Commutation Relations Commutation Relation and the Uncertainty ProductAppendix: Basic Concepts in Classical MechanicsREPRESENTATION THEORY Meaning of Representation How to Set up a Representation Representatives of a Linear Operator Change of Representation Coordinate Representation Replacement of Momentum Observable p by -ih d/dqIntegral Representation of Dirac Bracket A2|F|A1> The Momentum Representation Dirac Delta FunctionRelation between the Coordinate and Momentum RepresentationsEQUATIONS OF MOTIONSchrödinger Equation of Motion Schrödinger Equation in the Coordinate Representation Equation of Continuity Stationary States Time-Independent Schrödinger Equation in the Coordinate Representation Time-Independent Schrödinger Equation in the Momentum Representation Time-Independent Schrödinger Equation in Matrix Form The Heisenberg Picture The Interaction Picture Appendix: MatricesPROBLEMS OF ONE-DIMENSIONAL POTENTIAL BARRIERS Motion of a Particle across a Potential Step Passage of a Particle through a Potential Barrier of Finite Extent Tunneling of a Particle through a Potential Barrier Bound States in a One-Dimensional Square Potential Well Motion of a Particle in a Periodic PotentialBOUND STATES OF SIMPLE SYSTEMS Introduction Motion of a Particle in a Box Simple Harmonic Oscillator Operator Formulation of the Simple Harmonic Oscillator Problem Bound State of a Two-Particle System with Central Interaction Bound States of Hydrogen (or Hydrogen-Like) Atoms The Deuteron Problem Energy Levels in a Three-Dimensional Square Well: General Case Energy Levels in an Isotropic Harmonic Potential Well Appendix 1: Special FunctionsAppendix 2: Orthogonal Curvilinear Coordinate SystemsSYMMETRIES AND CONSERVATION LAWS Symmetries and Their Group Properties Symmetries in a Quantum Mechanical System Basic Symmetry Groups of the Hamiltonian and Conservation Laws Lie Groups and Their Generators Examples of Lie Group Appendix 1: Groups and RepresentationsANGULAR MOMENTUM IN QUANTUM MECHANICS Introduction Raising and Lowering Operators Matrix Representation of Angular Momentum Operators Matrix Representation of Eigenstates of Angular Momentum Coordinate Representation of Orbital Angular Momentum Operators and States General Rotation Group and Rotation Matrices Coupling of Two Angular Momenta Properties of Clebsch-Gordan Coefficients Coupling of Three Angular Momenta Coupling of Four Angular Momenta (L - S and j - j Coupling)APPROXIMATION METHODS Introduction Nondegenerate Time-Independent Perturbation Theory Time-Independent Degenerate Perturbation Theory The Zeeman Effect WKBJ Approximation Particle in a Potential Well Application of WKBJ Approximation to a-decay The Variational Method The Problem of the Hydrogen Molecule System of n Identical Particles: Symmetric and Antisymmetric States Excited States of the Helium Atom Statistical (Thomas-Fermi) Model of the Atom Hartree's Self-consistent Field Method for Multi-Electron Atoms Hartree-Fock Equations Occupation Number RepresentationQUANTUM THEORY OF SCATTERING Introduction Laboratory and Center-of-Mass (CM) Reference Frames Scattering Equation and the Scattering AmplitudePartial Waves and Phase Shifts Calculation of Phase Shift Phase Shifts for Some Simple Potential Forms Scattering due to Coulomb Potential The Integral Form of Scattering Equation Lippmann-Schwinger Equation and the Transition Operator Born Expansion Appendix: The Calculus of ResiduesTIME-DEPENDENT PERTURBATION METHODS Introduction Perturbation Constant over an Interval of Time Harmonic Perturbation: Semiclassical Theory of Radiation Einstein Coeffcients Multipole Transitions Electric Dipole Transitions in Atoms and Selection Rules Photo-Electric Effect Sudden and Adiabatic Approximations Second-Order EffectsTHE THREE-BODY PROBLEM Introduction Eyges Approach Mitra's Approach Faddeev's Approach Faddeev Equations in Momentum Representation Faddeev Equations for a Three-Body Bound System Alt, Grassberger, and Sandhas (AGS) EquationsRELATIVISTIC QUANTUM MECHANICS Introduction Dirac Equation Spin of the Electron Free Particle (Plane Wave) Solutions of Dirac Equation Dirac Equation for a Zero Mass Particle Zitterbewegung and Negative Energy Solutions Dirac Equation for an Electron in an Electromagnetic FieldInvariance of Dirac Equation Dirac Bilinear Covariants Dirac Electron in a Spherically Symmetric Potential Charge Conjugation, Parity, and Time-Reversal Invariance Appendix: Theory of Special RelativityQUANTIZATION OF RADIATION FIELD Introduction Radiation Field as a Swarm of Oscillators Quantization of Radiation Field Interaction of Matter with Quantized Radiation Field Applications Bethe's Treatment of Atomic Level Shift Due to the Self Energy of the Electron: (Lamb-Retherford Shift)Compton Scattering Appendix: Electromagnetic Field in Coulomb GaugeSECOND QUANTIZATION Introduction Classical Concept of Field Analogy of Field and Particle Mechanics Field Equations from Lagrangian DensityQuantization of a Real Scalar (KG) Field Quantization of Complex Scalar (KG) Field Dirac Field and Its Quantization Positron Operators and SpinorsInteracting Fields and the Covariant Perturbation Theory Second-Order Processes in Electrodynamics Amplitude for Compton Scattering Feynman Graphs Calculation of the Cross-Section of Compton Scattering Cross-Sections for Other Electromagnetic Processes Appendix 1: Calculus of Variation and Euler-Lagrange Equations Appendix 2: Functionals and Functional Derivatives Appendix 3: Interaction of the Electron and Radiation Fields Appendix 4: On the Convergence of Iterative Expansion of the S OperatorEPILOGUE Introduction Einstein-Podolsky-Rosen Gedanken Experiment Einstein-Podolsky-Rosen-Bohm Gedanken Experiment Theory of Hidden Variables and Bell's Inequality Clauser-Horne Form of Bell's Inequality and Its Violation in Two-Photon Correlation Experiments GENERAL REFERENCESINDEX.…”
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“…This action can be mediated by either intracellular or transmembrane receptors. While the classical mechanisms of SSHs action are relatively well examined, the physiological importance of non-classical mechanism of SSHs action through membrane-associated and transmembrane receptors in the brain remains unclear. …”
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“…All the RNG’s we recommend here are based on the Kolmogorov–Anosov theory of mixing in classical mechanical systems, which guarantees under certain conditions and in certain asymptotic limits, that points on the trajectories of these systems can be used to produce random number sequences of exceptional quality. …”
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“…In this perspective, we provide an overview of mechanical metamaterials within and beyond their classical mechanical functionalities. We discuss various aspects of data-driven approaches for inverse design and optimization of multifunctional mechanical metamaterials. …”
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“…Archaebacterial and eukaryotic elongation factor 2 (EF-2) and bacterial elongation factor G (EF-G) are five domain GTPases that catalyze the ribosomal translocation of tRNA and mRNA. In the classical mechanism of activation, GTPases are switched on through GDP/GTP exchange, which is accompanied by the ordering of two flexible segments called switch I and II. …”
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“…In response to a comment by Chris Rourk on our article Computing the Integrated Information of a Quantum Mechanism, we briefly (1) consider the role of potential hybrid/classical mechanisms from the perspective of integrated information theory (IIT), (2) discuss whether the (Q)IIT formalism needs to be extended to capture the hypothesized hybrid mechanism, and (3) clarify our motivation for developing a QIIT formalism and its scope of applicability.…”
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“…We present three cases with non-classical mechanisms of injury, leading to a delayed diagnosis in all three cases. …”
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“…This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. …”
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“…We present the case of a giant distal aortic pseudoaneurysm 35 years after a classic mechanical Bentall operation. Computed tomography and coronary angiography showed that this originated from the distal suture line. …”
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“…This is not surprising as many galectins preferentially exist in cytosolic and nuclear compartments, which is consistent with the fact that they are exported outside the cells via a yet undefined non-classical mechanism. This review summarizes our most recent knowledge of their intracellular functions in cancer cells and provides some directions for future strategies to inhibit their role in cancer progression.…”
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“…A dislocation-theory based analysis suggests that the shape, spacing and orientation (with respect to the glide plane) of β(1) precipitates may favor glide of pinned dislocations along interfaces as opposed to the classical mechanism of bowing and looping around the precipitate.…”
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