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Articoli di riviste sul tema "Matrix mechanics"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 25 luglio 2025

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1

Little, J. Paige, Clayton Adam, Graeme Pettet, and Mark J. Pearcy. "Initiation of Mechanical Derangement in the Anulus Fibrosus Ground Matrix(Soft Tissue Mechanics)." Proceedings of the Asian Pacific Conference on Biomechanics : emerging science and technology in biomechanics 2004.1 (2004): 183–84. http://dx.doi.org/10.1299/jsmeapbio.2004.1.183.

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2

Kawamura, Y. "Generalized Matrix Mechanics." Progress of Theoretical Physics 107, no. 6 (2002): 1105–15. http://dx.doi.org/10.1143/ptp.107.1105.

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3

Tran, J., L. Doughty, and J. K. Freericks. "The 1925 revolution of matrix mechanics and how to celebrate it in modern quantum mechanics classes." American Journal of Physics 93, no. 1 (2025): 14–20. https://doi.org/10.1119/5.0195658.

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In 1925, Heisenberg, Born, and Jordan developed matrix mechanics as a strategy to solve quantum-mechanical problems. While finite-sized matrix formulations are commonly taught in quantum instruction, following the logic and detailed steps of the original matrix mechanics has become a lost art. In preparation for the 100th anniversary of the discovery of quantum mechanics, we present a modernized discussion of how matrix mechanics is formulated, how it is used to solve quantum-mechanical problems, and how it can be employed as the starting point for a postulate-based formulation of quantum-mech

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4

Y., Seetharamarao, Bharathi C., and Sri ram Murthy P. "Journal of Fluid Mechanics and Mechanical Design." Journal of Fluid Mechanics and Mechanical Design 1, no. 1 (2019): 6–11. https://doi.org/10.5281/zenodo.3362104.

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The main objective of this work is to focus on modelling and analysis of connecting rod by varying material with same geometry. Many works are carried out by using alloys in the analysis of connecting rod such as aluminium, forged steel and titanium. The material for the connecting rod used here is Aluminium Reinforced with Boron Carbide Metal matrix composite. The solid model of connecting rod is created in CATIA V5. The static and dynamic analysis are performed by Finite Element Analysis (FEA) software to determine the parameters for connecting rod like von Mises stress, deformation and natu

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5

Anninos, Dionysios, Frederik Denef, and Ruben Monten. "Grassmann matrix quantum mechanics." Journal of High Energy Physics 2016, no. 4 (2016): 1–26. http://dx.doi.org/10.1007/jhep04(2016)138.

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6

Tschang, Y. "Matrix Mechanics and Hadron Statics." Physics Essays 10, no. 2 (1997): 315–26. http://dx.doi.org/10.4006/1.3028718.

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7

Betzios, P., U. Gürsoy, and O. Papadoulaki. "Matrix quantum mechanics onS1/Z2." Nuclear Physics B 928 (March 2018): 356–414. http://dx.doi.org/10.1016/j.nuclphysb.2018.01.019.

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8

Bebiano, N., J. da Providência, and R. Lemos. "Matrix inequalities in statistical mechanics." Linear Algebra and its Applications 376 (January 2004): 265–73. http://dx.doi.org/10.1016/j.laa.2003.07.004.

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9

Kawamura, Y. "Structure of Cubic Matrix Mechanics." Progress of Theoretical Physics 109, no. 1 (2003): 1–10. http://dx.doi.org/10.1143/ptp.109.1.

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10

Ren, Zhi. "Analysis of contribution of matrix mechanics on quantum mechanics." EPJ Web of Conferences 332 (2025): 01010. https://doi.org/10.1051/epjconf/202533201010.

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In this paper the analysis and discussion about the contribution made by matrix mechanics, i.e. the establishment of complex form of quantum mechanics and the proposal of mathematic formalism of uncertainty principle, to the development of quantum mechanics are conducted, thereby to disclose how the complex functions enter the quantum mechanics by accident and turn to be a must of it. The evolution of mathematic formula, which implies the uncertainty principle, is also outlined to reflect the contribution of three founders of matrix mechanics. Also disclosed is the physical meaning of coordina

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11

SHALYT-MARGOLIN, A. E., and J. G. SUAREZ. "QUANTUM MECHANICS AT PLANCK'S SCALE AND DENSITY MATRIX." International Journal of Modern Physics D 12, no. 07 (2003): 1265–78. http://dx.doi.org/10.1142/s0218271803003700.

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In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies in the fact that here the density matrix are subjected to deformation, whereas in the previous approaches only commutators are deformed. The density matrix obtained by deforming the quantum-mechanical one is named the density pro-matrix

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12

Perovic, Slobodan. "Why were Matrix Mechanics and Wave Mechanics considered equivalent?" Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39, no. 2 (2008): 444–61. http://dx.doi.org/10.1016/j.shpsb.2008.01.004.

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13

Han, Yu Long, Pierre Ronceray, Guoqiang Xu, et al. "Cell contraction induces long-ranged stress stiffening in the extracellular matrix." Proceedings of the National Academy of Sciences 115, no. 16 (2018): 4075–80. http://dx.doi.org/10.1073/pnas.1722619115.

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Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here, we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing nonlinear stress inference micr

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14

Wagenseil, Jessica E., and Robert P. Mecham. "Vascular Extracellular Matrix and Arterial Mechanics." Physiological Reviews 89, no. 3 (2009): 957–89. http://dx.doi.org/10.1152/physrev.00041.2008.

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An important factor in the transition from an open to a closed circulatory system was a change in vessel wall structure and composition that enabled the large arteries to store and release energy during the cardiac cycle. The component of the arterial wall in vertebrates that accounts for these properties is the elastic fiber network organized by medial smooth muscle. Beginning with the onset of pulsatile blood flow in the developing aorta, smooth muscle cells in the vessel wall produce a complex extracellular matrix (ECM) that will ultimately define the mechanical properties that are critical

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15

Marshall, D. B., B. N. Cox, and A. G. Evans. "The mechanics of matrix cracking in brittle-matrix fiber composites." Acta Metallurgica 33, no. 11 (1985): 2013–21. http://dx.doi.org/10.1016/0001-6160(85)90124-5.

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16

Muntz, Iain, Michele Fenu, Gerjo J. V. M. van Osch, and Gijsje H. Koenderink. "The role of cell–matrix interactions in connective tissue mechanics." Physical Biology 19, no. 2 (2022): 021001. http://dx.doi.org/10.1088/1478-3975/ac42b8.

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Abstract Living tissue is able to withstand large stresses in everyday life, yet it also actively adapts to dynamic loads. This remarkable mechanical behaviour emerges from the interplay between living cells and their non-living extracellular environment. Here we review recent insights into the biophysical mechanisms involved in the reciprocal interplay between cells and the extracellular matrix and how this interplay determines tissue mechanics, with a focus on connective tissues. We first describe the roles of the main macromolecular components of the extracellular matrix in regards to tissu

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17

Yang, Chun, Frank W. DelRio, Hao Ma, et al. "Spatially patterned matrix elasticity directs stem cell fate." Proceedings of the National Academy of Sciences 113, no. 31 (2016): E4439—E4445. http://dx.doi.org/10.1073/pnas.1609731113.

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There is a growing appreciation for the functional role of matrix mechanics in regulating stem cell self-renewal and differentiation processes. However, it is largely unknown how subcellular, spatial mechanical variations in the local extracellular environment mediate intracellular signal transduction and direct cell fate. Here, the effect of spatial distribution, magnitude, and organization of subcellular matrix mechanical properties on human mesenchymal stem cell (hMSCs) function was investigated. Exploiting a photodegradation reaction, a hydrogel cell culture substrate was fabricated with r

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18

Copeland, E. "Quantum Mechanics in Simple Matrix Form." Physics Bulletin 37, no. 11 (1986): 465. http://dx.doi.org/10.1088/0031-9112/37/11/035.

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19

Masters, Barry R. "Werner Heisenberg’s Path to Matrix Mechanics." Optics and Photonics News 25, no. 7 (2014): 42. http://dx.doi.org/10.1364/opn.25.7.000042.

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20

Varlamov, V. V. "Algebraic quantum mechanics: II. S-matrix." Mathematical structures and modeling, no. 1 (2021): 3–24. http://dx.doi.org/10.24147/2222-8772.2021.1.3-24.

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21

Jordan, Thomas F., and Kannan Jagannathan. "Quantum Mechanics in Simple Matrix Form." American Journal of Physics 54, no. 12 (1986): 1154–55. http://dx.doi.org/10.1119/1.14691.

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22

Dietz, B., and F. Haake. "Random Matrix Theory as Statistical Mechanics." Europhysics Letters (EPL) 9, no. 1 (1989): 1–6. http://dx.doi.org/10.1209/0295-5075/9/1/001.

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23

Yukalov, V. I. "Matrix order indices in statistical mechanics." Physica A: Statistical Mechanics and its Applications 310, no. 3-4 (2002): 413–34. http://dx.doi.org/10.1016/s0378-4371(02)00783-5.

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24

Dai, Jian, and Yong-Shi Wu. "Quiver mechanics for deconstructed matrix string." Physics Letters B 576, no. 1-2 (2003): 209–18. http://dx.doi.org/10.1016/j.physletb.2003.09.083.

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25

Angerer, Wolfgang P., and Adolfo Zamora. "Eigenvalues of a statistical mechanics matrix." Journal of Mathematical Chemistry 50, no. 6 (2012): 1411–19. http://dx.doi.org/10.1007/s10910-012-9980-2.

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26

Kawamura, Y. "Cubic Matrix, Nambu Mechanics and Beyond." Progress of Theoretical Physics 109, no. 2 (2003): 153–68. http://dx.doi.org/10.1143/ptp.109.153.

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27

Dr., Ismail Abbas. "FALL and RISE of Matrix Mechanics." FALL and RISE of Matrix Mechanics 9, no. 1 (2024): 8. https://doi.org/10.5281/zenodo.10539186.

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Abstract (sommario):

In 1925, W. Heisenberg, Max Born and Pascual Jordan introduced the first so-called matrix mechanics (HMJ theory) to study the fine structure of the Bohr hydrogen atom. However, in the early 1930s, the equivalence between the HMJ theory and the Schrödinger equation was denied and the HMJ theory fell. In 2020, a new theory of matrix mechanics emerged, called b-matrix chains, and has been successfully applied to different 3D situations in classical physics as well as quantum mechanics. In this paper we study the application of new matrix theory to the initial value problem in the 3D heat dif

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28

Chen, Hui, Folian Yu, Bing Wang, et al. "Elastic Fibre Prestressing Mechanics within a Polymeric Matrix Composite." Polymers 15, no. 2 (2023): 431. http://dx.doi.org/10.3390/polym15020431.

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The elastic fibre prestressing (EFP) technique has been developed to balance the thermal residual stress generated during curing of a polymeric composite. The continuous fibre reinforcements are prestressed and then impregnated into a polymeric matrix, where the prestress load is only removed after the resin is fully cured in order to produce an elastically prestressed polymeric matrix composite (EPPMC). Although the EFP is active in improving the static mechanical performance of a composite, its mechanics on dynamic mechanical performance and viscoelasticity of a composite is still limited. H

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29

Lee, Stacey, and Sanjay Kumar. "Actomyosin stress fiber mechanosensing in 2D and 3D." F1000Research 5 (September 7, 2016): 2261. http://dx.doi.org/10.12688/f1000research.8800.1.

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Mechanotransduction is the process through which cells survey the mechanical properties of their environment, convert these mechanical inputs into biochemical signals, and modulate their phenotype in response. These mechanical inputs, which may be encoded in the form of extracellular matrix stiffness, dimensionality, and adhesion, all strongly influence cell morphology, migration, and fate decisions. One mechanism through which cells on planar or pseudo-planar matrices exert tensile forces and interrogate microenvironmental mechanics is through stress fibers, which are bundles composed of acti

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30

Rothschilds, R. J., L. B. Ilcewicz, P. Nordin, and S. H. Applegate. "The Effect of Hygrothermal Histories on Matrix Cracking in Fiber Reinforced Laminates." Journal of Engineering Materials and Technology 110, no. 2 (1988): 158–68. http://dx.doi.org/10.1115/1.3226025.

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Environmental factors that affect matrix cracking in composite laminates include temperature, moisture content, and hygrothermal history. Matrix cracking in laminates exposed to aircraft environments was modelled using a fracture mechanics approach based on strain energy release rates. Residual stress relaxation due to hygrothermal history was found to alter the static mechanical strain necessary to cause matrix cracking in experiments. Depending on material type and hygrothermal history, this effect was shown to either increase or decrease the resistance to matrix cracking. Close agreement be

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31

Bеlovol, Oleksandr. "Benefits of using matrix methods in teach-ing mechanics in higher education institu-tions." Bulletin of Kharkov National Automobile and Highway University 1, no. 101 (2023): 183. http://dx.doi.org/10.30977/bul.2219-5548.2023.101.0.183.

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Abstract (sommario):

Problem. Basic concepts, concepts, principles of mechanics are mainly taught from simple to complex in institutions of higher technical education, which to some extent resembles a course on the history of mechanics. In today's conditions, the education system is required to take into account current trends in scientific and engineering fields. The use of inherently geometric methods of vector algebra and vector analysis as a basis for studying mechanics is losing its relevance. To a certain extent, this approach interferes with the use of multidimensional spaces (configurational and phase), te

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32

Chiang, Y. C. "Mechanics of Matrix Cracking in Bonded Composites." Journal of Mechanics 23, no. 2 (2007): 95–106. http://dx.doi.org/10.1017/s172771910000112x.

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AbstractIn this paper, a general matrix cracking model including the effect of fiber/matrix debonding in the crack wake is developed for a unidirectional fiber reinforced composite. The debonding mechanics is incorporated into matrix cracking model by treating the crack-wake debonding as a particular crack propagation problem along the interface. Then, the closed-form analytical solution of the critical stress for the onset of widespread matrix cracking is derived, based on the analysis of steady state crack growth in the matrix. The fracture mechanics approach adopted in the present analysis

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33

Qiu, Ke, and Feng Luo. "Research of Several Quantities of Mechanics." Advanced Materials Research 651 (January 2013): 673–77. http://dx.doi.org/10.4028/www.scientific.net/amr.651.673.

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This paper expresses several quantities of Mechanics that can be solved using eigen value and eigen vector of matrix in a unified expression. It revealed and discussed the mathematical nature of these quantities of Mechanics. The eigen matrix diagonalization method that can be used to easily solve all the eigen values and orthogonal eigen vectors of a matrix is given. This method is liberation from the difficulties of solving these quantities traditionally.

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34

黄, 永义. "The Dirac-Jordan Transformation Theory—From Matrix Mechanics to Wave Mechanics." Modern Physics 11, no. 02 (2021): 15–20. http://dx.doi.org/10.12677/mp.2021.112003.

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35

Sherlock, B. E., J. Chen, J. C. Mansfield, E. Green, and C. P. Winlove. "Biophotonic tools for probing extracellular matrix mechanics." Matrix Biology Plus 12 (December 2021): 100093. http://dx.doi.org/10.1016/j.mbplus.2021.100093.

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36

Sun, Bo. "The mechanics of fibrillar collagen extracellular matrix." Cell Reports Physical Science 2, no. 8 (2021): 100515. http://dx.doi.org/10.1016/j.xcrp.2021.100515.

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37

Majji, Manoranjan. "Regular Celestial Mechanics and the Matrix Exponential." Journal of Guidance, Control, and Dynamics 43, no. 11 (2020): 2127–32. http://dx.doi.org/10.2514/1.g005237.

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38

More, Richard M. "Semiclassical matrix-mechanics. II. Angular momentum operators." Journal de Physique II 1, no. 2 (1991): 97–121. http://dx.doi.org/10.1051/jp2:1991150.

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39

Bender, Carl M., L. M. Simmons, and Richard Stong. "Matrix methods in discrete-time quantum mechanics." Physical Review D 33, no. 8 (1986): 2362–66. http://dx.doi.org/10.1103/physrevd.33.2362.

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40

More, R. M. "Semiclassical matrix mechanics. I. The harmonic oscillator." Journal de Physique 51, no. 1 (1990): 47–58. http://dx.doi.org/10.1051/jphys:0199000510104700.

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41

Conlon, J. G. "A matrix diagonalisation problem in quantum mechanics." Journal of Physics A: Mathematical and General 20, no. 18 (1987): 6281–91. http://dx.doi.org/10.1088/0305-4470/20/18/028.

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42

Savvidy, George K. "Loop transfer matrix and loop quantum mechanics." Journal of High Energy Physics 2000, no. 09 (2000): 044. http://dx.doi.org/10.1088/1126-6708/2000/09/044.

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43

Berg, J., and A. Engel. "Matrix Games, Mixed Strategies, and Statistical Mechanics." Physical Review Letters 81, no. 22 (1998): 4999–5002. http://dx.doi.org/10.1103/physrevlett.81.4999.

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44

Suki, Béla, and Jason H. T. Bates. "Extracellular matrix mechanics in lung parenchymal diseases." Respiratory Physiology & Neurobiology 163, no. 1-3 (2008): 33–43. http://dx.doi.org/10.1016/j.resp.2008.03.015.

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45

Anglès d'Auriac, J. Ch, and J. M. Maillard. "Random matrix theory in lattice statistical mechanics." Physica A: Statistical Mechanics and its Applications 321, no. 1-2 (2003): 325–33. http://dx.doi.org/10.1016/s0378-4371(02)01756-9.

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46

HALPERN, M. B., and C. SCHWARTZ. "THE ALGEBRAS OF LARGE N MATRIX MECHANICS." International Journal of Modern Physics A 14, no. 19 (1999): 3059–119. http://dx.doi.org/10.1142/s0217751x99001482.

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Abstract (sommario):

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: the Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the ro

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47

Djemai, A. E. F. "Quantum mechanics as a matrix symplectic geometry." International Journal of Theoretical Physics 36, no. 2 (1997): 571. http://dx.doi.org/10.1007/bf02435751.

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48

Pandey, Mahul, and Sachindeo Vaidya. "Yang–Mills matrix mechanics and quantum phases." International Journal of Geometric Methods in Modern Physics 14, no. 08 (2017): 1740009. http://dx.doi.org/10.1142/s0219887817400096.

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The [Formula: see text] Yang–Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The [Formula: see text] Yang–Mills matrix mo

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49

Sergi, Alessandro. "Matrix Algebras in Non-Hermitian Quantum Mechanics." Communications in Theoretical Physics 56, no. 1 (2011): 96–98. http://dx.doi.org/10.1088/0253-6102/56/1/18.

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Djemai, A. E. F. "Quantum mechanics as a matrix symplectic geometry." International Journal of Theoretical Physics 35, no. 3 (1996): 519–56. http://dx.doi.org/10.1007/bf02082821.

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