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The article presents a summarised history of the equations governing fluid motion, known as the Navier–Stokes equations. It starts with the work of Castelli, who established the continuity equation in 1628. The determination of fluid flow resistance was a topic that involved the brightest minds of the 17th and 18th centuries. Navier's contribution consisted of the incorporation of molecular attraction effects into Euler's equation, giving rise to an additional term associated with resistance. However, his analysis was not the only one. This continued until 1850, when Stokes firmly established the boundary conditions that must be applied to the differential equations of motion, specifically stating the non-slip condition of the fluid in contact with a solid surface. With this article, the author wants to commemorate the bicentennial of the publication of "Sur les Lois du Mouvement des Fluides" by Navier in the Mémoires de l'Académie Royale des Sciences de l'Institut de France. [ABSTRACT FROM AUTHOR]

In this paper, physics-based numerical simulation (PBS) is employed to render a broad-band (0–10 Hz) realization of the near-field seismic response of the experimental nuclear site of Cadarache, located nearby the active Middle Durance Fault (southeastern France). The sensitivity of the earthquake numerical model to geological features is investigated by comparison with geophysical measurements and past aftershock and by highlighting the amplification induced by the soft sediments below Cadarache. The blind prediction of an M W6 target earthquake is approached by synthesizing four different finite-fault scenarios. The outcome is compared to the standard ground motion prediction equations (GMPEs), unveiling a possible GMPE overestimation of the pseudospectral acceleration ordinates at short natural periods, supporting the actual need to integrate synthetic and empirical predictions when direct observations are not available. [ABSTRACT FROM AUTHOR]

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter μ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including μ , similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion (EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including μ. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature. [ABSTRACT FROM AUTHOR]

This paper presents the development of a probabilistic seismic hazard analysis (PSHA) model to compute seismic hazard maps for the French territory taking into account 15 years of research and development in the area. Since 2002, when the first probabilistic hazard map was computed for France, many new data became available leading to new studies and experience gained. This 2017 PSHA version for France incorporates significant improvements over previous version. In particular, the recent SIGMA project 2010–2016 produced a number of outputs which are used in the present analysis: a homogenized earthquake catalogue in moment magnitude (Mw), a Bayesian methodology to compute distributions of maximum magnitudes, ground motion prediction equations specifically developed for the French territory, new seismotectonic analysis conducted based on geological, structural, geophysical, neotectonic and seismological data. Preliminary comparison of median PGA values at 475 years return period with results obtained independently for neighboring countries (Germany, Switzerland, and Italy) reveals a fair agreement. Comparison with the 2013 European Seismic Hazard Model (ESHM13, SHARE project) and the model for France developed in 2002 indicates that 2017 PSHA version leads to lower hazard. [ABSTRACT FROM AUTHOR]

The development of linear elastodynamics in pure stress-based formulation began over half-a-century ago as an alternative to the classical displacement-based treatment that came into existence two centuries ago in the school of mathematical physics in France. While the latter approach – fundamentally based on the Navier displacement equation of motion – remains the conventional setting for analysis of wave propagation in elastic bodies, the stress-based formulation and the advantages it offers in elastodynamics and its various extensions remain much less known. Since the key mathematical results of that formulation, as well as a series of applications, originated with J. Ignaczak in 1959 and 1963, the key relation is named the Ignaczak equation of elastodynamics. This review article presents the main ideas and results in the stress-based formulation from a common perspective, including (i) a history of early attempts to find a pure stress language of elastodynamics, (ii) a proposal to use such a language in solving the natural traction initial-boundary value problems of the theory, and (iii) various applications of the stress language to elastic wave propagation problems. Finally, various extensions of the Ignaczak equation of elastodynamics focused on dynamics of solids with interacting fields of different nature (classical or micropolar thermoelastic, fluid-saturated porous, piezoelectro-elastic) as well as nonlinear problems are reviewed. [ABSTRACT FROM AUTHOR]

Abstract: We use the Papapetrou method of multipole expansion to show that a Dirac field in the Einstein–Cartan–Kibble–Sciama (ECKS) theory of gravity cannot form singular configurations concentrated on one- or two-dimensional surfaces in spacetime. Instead, such a field describes a nonsingular particle whose spatial dimension is at least on the order of its Cartan radius. In particular, torsion modifies Burinskii''s model of the Dirac electron as a Kerr–Newman singular ring of the Compton size, by replacing the ring with a toroidal structure with the outer radius of the Compton size and the inner radius of the Cartan size. We conjecture that torsion produced by spin prevents the formation of singularities from matter composed of quarks and leptons. We expect that the Cartan radius of an electron, , introduces an effective ultraviolet cutoff in quantum field theory for fermions in the ECKS spacetime. We also estimate a maximum density of matter to be on the order of the corresponding Cartan density, , which gives a lower limit for black-hole masses . This limit corresponds to energy which is 39 orders of magnitude larger than the maximum beam energy currently available at the LHC. Thus, if torsion exists and the ECKS theory of gravity is correct, the LHC cannot produce micro black holes. [Copyright &y& Elsevier]