Explanatory Information in Mathematical Explanations of Physical Phenomena

2019 ◽  
Vol 98 (3) ◽  
pp. 590-603
Author(s):  
Manuel Barrantes
Author(s):  
Gabriel Tȃrziu

Can mathematics contribute to our understanding of physical phenomena? One way to try to answer this question is by getting involved in the recent philosophical dispute about the existence of mathematical explanations of physical phenomena. If there is such a thing, given the relation between explanation and understanding, we can say that there is an affirmative answer to our question. But what if we do not agree that mathematics can play an explanatory role in science? Can we still consider that the above question can have an affirmative answer? My main aim here is to give an account that takes mathematics, in some of the cases discussed in the literature, as contributing to our understanding of physical phenomena despite not being explanatory.


Synthese ◽  
2021 ◽  
Author(s):  
Mary Leng

AbstractAre there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue of their form, establish that, given the mathematical structure instantiated in the physical system under consideration, the explanandum had to occur. Against the claims of platonists such as Alan Baker and Mark Colyvan, I argue that formulating mathematical explanations as structural explanations in this way shows that we can accept that mathematics can play an indispensable explanatory role in empirical science without committing to the existence of any abstract mathematical objects.


1977 ◽  
Vol 36 ◽  
pp. 191-215
Author(s):  
G.B. Rybicki

Observations of the shapes and intensities of spectral lines provide a bounty of information about the outer layers of the sun. In order to utilize this information, however, one is faced with a seemingly monumental task. The sun’s chromosphere and corona are extremely complex, and the underlying physical phenomena are far from being understood. Velocity fields, magnetic fields, Inhomogeneous structure, hydromagnetic phenomena – these are some of the complications that must be faced. Other uncertainties involve the atomic physics upon which all of the deductions depend.


Author(s):  
George C. Ruben ◽  
Merrill W. Shafer

Traditionally ceramics have been shaped from powders and densified at temperatures close to their liquid point. New processing methods using various types of sols, gels, and organometallic precursors at low temperature which enable densificatlon at elevated temperatures well below their liquidus, hold the promise of producing ceramics and glasses of controlled and reproducible properties that are highly reliable for electronic, structural, space or medical applications. Ultrastructure processing of silicon alkoxides in acid medium and mixtures of Ludox HS-40 (120Å spheres from DuPont) and Kasil (38% K2O &62% SiO2) in basic medium have been aimed at producing materials with a range of well defined pore sizes (∼20-400Å) to study physical phenomena and materials behavior in well characterized confined geometries. We have studied Pt/C surface replicas of some of these porous sol-gels prepared at temperatures below their glass transition point.


2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.


Author(s):  
Christian Devereux ◽  
Justin Smith ◽  
Kate Davis ◽  
Kipton Barros ◽  
Roman Zubatyuk ◽  
...  

<p>Machine learning (ML) methods have become powerful, predictive tools in a wide range of applications, such as facial recognition and autonomous vehicles. In the sciences, computational chemists and physicists have been using ML for the prediction of physical phenomena, such as atomistic potential energy surfaces and reaction pathways. Transferable ML potentials, such as ANI-1x, have been developed with the goal of accurately simulating organic molecules containing the chemical elements H, C, N, and O. Here we provide an extension of the ANI-1x model. The new model, dubbed ANI-2x, is trained to three additional chemical elements: S, F, and Cl. Additionally, ANI-2x underwent torsional refinement training to better predict molecular torsion profiles. These new features open a wide range of new applications within organic chemistry and drug development. These seven elements (H, C, N, O, F, Cl, S) make up ~90% of drug like molecules. To show that these additions do not sacrifice accuracy, we have tested this model across a range of organic molecules and applications, including the COMP6 benchmark, dihedral rotations, conformer scoring, and non-bonded interactions. ANI-2x is shown to accurately predict molecular energies compared to DFT with a ~10<sup>6</sup> factor speedup and a negligible slowdown compared to ANI-1x. The resulting model is a valuable tool for drug development that can potentially replace both quantum calculations and classical force fields for myriad applications.</p>


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