2,127 research outputs found
Modeling of ground excavation with the particle finite element method
The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it. The method has a high versatility and a reasonable computational cost. The obtained results are really promising.Postprint (published version
Origins of Mass
Newtonian mechanics posited mass as a primary quality of matter, incapable of
further elucidation. We now see Newtonian mass as an emergent property. Most of
the mass of standard matter, by far, arises dynamically, from back-reaction of
the color gluon fields of quantum chromodynamics (QCD). The equations for
massless particles support extra symmetries - specifically scale, chiral, and
gauge symmetries. The consistency of the standard model relies on a high degree
of underlying gauge and chiral symmetry, so the observed non-zero masses of
many elementary particles ( and bosons, quarks, and leptons) requires
spontaneous symmetry breaking. Superconductivity is a prototype for spontaneous
symmetry breaking and for mass-generation, since photons acquire mass inside
superconductors. A conceptually similar but more intricate form of
all-pervasive (i.e. cosmic) superconductivity, in the context of the
electroweak standard model, gives us a successful, economical account of
and boson masses. It also allows a phenomenologically successful, though
profligate, accommodation of quark and lepton masses. The new cosmic
superconductivity, when implemented in a straightforward, minimal way, suggests
the existence of a remarkable new particle, the so-called Higgs particle. The
mass of the Higgs particle itself is not explained in the theory, but appears
as a free parameter. Earlier results suggested, and recent observations at the
Large Hadron Collider (LHC) may indicate, the actual existence of the Higgs
particle, with mass GeV. In addition to consolidating our
understanding of the origin of mass, a Higgs particle with
GeV could provide an important clue to the future, as it is consistent with
expectations from supersymmetry.Comment: Invited review for the Central European Journal of Physics. This is
the supplement to my 2011 Solvay Conference talk promised there. It is
adapted from an invited talk given at the Atlanta APS meeting, April 2012. 33
pages, 6 figures. v2: Added update section bringing in the CERN discovery
announcemen
Concepts for modeling impacts without friction
Summary.: There are three basic equations in mechanics for treating collisions: the law of impact, kinematic compatibility, and energetic consistency. In this paper, the conditions are examined under which a natural extension of the dynamics at an impact is possible without taking additional impact laws, and which additional assumptions have to be made to solve the impact for different classes of systems. It will be shown that Newton's law of impact for two colliding point masses can be derived from the concept of energy conservation and the principle of maximum dissipation, and has therefore not to be regarded as an independent equation. Moreover, it can be assigned to single-contact impacts in multibody systems as soon as the classical definition of perfect constraints is being extended to impulsive dynamics and unilateral contacts. It will further be shown that the principle of maximum dissipation leads to a unique post-impact velocity in the case of multi-contact collisions. In all other cases, however, the velocities remain undetermined, and laws of impact have to be postulated as additional and independent equations, whereas the classic definition of the restitution coefficient as a dissipation parameter can still be kep
Accurate Prediction of Core Properties for Chiral Molecules using Pseudo Potentials
Pseudo potentials (PPs) constitute perhaps the most common way to treat relativity, often in a formally non-relativistic framework, and reduce the electronic
structure to the chemically relevant part. The drawback is that orbitals obtained
in this picture (called pseudo orbitals (POs)) show a reduced nodal structure
and altered amplitude in the vicinity of the nucleus, when compared to the
corresponding molecular orbitals (MOs). Thus expectation values of operators
localized in the spatial core region that are calculated with POs, deviate significantly from the same expectation values calculated with all-electron (AE)
MOs. This study describes the reconstruction of AE MOs from POs, with a
focus on POs generated by energy consistent pseudo Hamiltonians. The method
reintroduces the nodal structure into the POs, thus providing an inexpensive
and easily implementable method that allows to use nonrelativistic, efficiently
calculated POs for good estimates of expectation values of core-like properties.
The discussion of the method proceeds in two parts: Firstly, the reconstruction scheme is developed for atomic cases. Secondly, the scheme is discussed in
the context of MO reconstruction and successfully applied to numerous numerical examples.
Starting from the equations of the state-averaged multi-configuration self-
consistent field method, used for the generation of energy consistent pseudo
potentials, the electronic spectrum of the many-electron Hamiltonian is linked
to the spectrum of the effective one-electron Fock operator by means of various
models systems. This relation and the Topp–Hopfield–Kramers theorem, are
used to show the shape-consistency of energy-consistent POs for atomic systems.
Shape-consistency describes POs that follow distinct AOs exactly outside a core-radius r_core . In the cases presented here, shape-consistency holds to a high degree
and it follows that in atomic systems every PO has one distinct partner in the
set of AOs. The overlap integral between these two orbitals is close to one, as it
is determined mainly by the spatial orbital parts outside r_core . Expanding, e.g.,
a 5s PO in occupied AOs, the 5s AOs will have the highest contribution. The
POs itself contains contributions from high-energy unoccupied AOs as well (e.g.
15s), which damp the nodal structure of the POs near the nucleus. Consequently,
neglecting contributions from unoccupied orbitals in a projection of the POs
reintroduces the nodal structure.
This approach is not directly suitable for the reconstruction of MOs, as they
often need to be expanded in a full set of AOs at each atomic center, including all
unoccupied orbitals, to properly account for the electron density distribution in
the molecule. However, it is shown that the occupied MOs are well described by
occupied and low-energy unoccupied AOs only and a mapping of the POs onto
a basis containing only these orbitals reconstructs the nodal structure of the MO.
The approach uses only standard integrals available in most quantum chemistry
programs. The computational cost of these integrals scales with N^2 , where N is
the number of basis functions. The most time consuming step is a Gram-Schmidt
orthogonalization, which scales in this implementation with MN^2 , M being the
number of reconstructed orbitals.
The reconstruction method is subsequently tested: Valence orbitals of atomic,
closed-shell systems were reconstructed numerically exactly. The influence of
numerical parameters is investigated using the molecule BaF . It is shown that
the method is basis set dependent: One has to ensure that the PO basis can be
expanded exactly in the basis of AOs. Violating this rule of thumb may degrade
the quality of reconstructed orbitals. Additionally, the representation of MOs by
a linear combination of occupied and unoccupied AOs is investigated. For the
exemplary systems, the shells included in the fitting procedure of the PP were
sufficient.
Reconstruction of the alkaline earth monofluorides showed that periodic
trends can be reconstructed as well. Scaling of hyperfine structure parameters
with increasing atomic number is discussed. For hydrogenic atoms, the scaling should be linear, whereas small deviations from the linear behavior were
observed for molecules. The scaling laws computed from reconstructed and
reference orbitals were almost identical. In this context, the failure of commonly
used relativistic enhancement factors beyond atomic number 100 is discussed.
Applicability of the method is also tested on parity violating properties for which
the main contribution is generated by the valence orbitals near the nucleus.
Symmetry-independence of the method is shown by successful reconstruction of
orbitals of the tetrahedral PbCl_4 and chiral NWHClF. The reliable reconstruction
of chemical trends is shown with the help of the NWHClF derivatives NWHBrF
and NWHFI.
The study of chiral compounds as, e.g., NWHClF and its group 17 derivatives, which have been proposed as paradigm for the detection of parity-violation
in chiral molecules, remains of great importance. Especially the direct determination of absolute configuration of chiral centers is still non-trivial. The author
contributed to this field with a self-written molecular dynamics (MD) program
to simulate Coulomb explosions and thus to provide an insight especially into
the early explosion stages directly after an instantaneous multi-ionization of
the molecule CHBrClF, comparable to experiments using the Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) technique. An algorithm for
the determination of the investigated molecule’s absolute configuration from
time-of-flight data and detection locations of molecular fragments is included
in the program. The program was used to generate experiment-equivalent data
which allowed for the first time the investigation of non-racemic mixtures by
the analysis routines of the experiment. The MD program includes harmonic
and anharmonic bond potentials. A charge-exchange model can model partial
charges in early phases of the Coulomb explosion.
Furthermore, Born–Oppenheimer MD simulations and statistical models
are used to explain the relative abundance of products belonging to competing
reaction channels, as obtained by photoion coincidence measurements. Additionally, qualitative statements about reaction branching ratios are made by
comparing the partition functions of involved degrees of freedom. Analytic
equations for partition functions of simple models are used to provide a simple
formula allowing fast estimates of reaction branching ratios
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