381 research outputs found
Discrete Formulation for the dynamics of rods deforming in space
We describe the main ingredients needed to create, from the smooth lagrangian
density, a variational principle for discrete motions of a discrete rod, with
corresponding conserved Noether currents. We describe all geometrical objects
in terms of elements on the linear Atiyah bundle, using a reduced forward
difference operator. We show how this introduces a discrete lagrangian density
that models the discrete dynamics of a discrete rod. The presented tools are
general enough to represent a discretization of any variational theory in
principal bundles, and its simplicity allows to perform an iterative
integration algorithm to compute the discrete rod evolution in time, starting
from any predefined configurations of all discrete rod elements at initial
times
Emitter-site selective photoelectron circular dichroism of trifluoromethyloxirane
The angle-resolved inner-shell photoionization of R-trifluoromethyloxirane,
C3H3F3O, is studied experimentally and theoretically. Thereby, we investigate
the photoelectron circular dichroism (PECD) for nearly-symmetric O 1s and F 1s
electronic orbitals, which are localized on different molecular sites. The
respective dichroic and angular distribution parameters
are measured at the photoelectron kinetic energies from 1 to 16 eV by using
variably polarized synchrotron radiation and velocity map imaging spectroscopy.
The present experimental results are in good agreement with the outcome of ab
initio electronic structure calculations. We report a sizable chiral asymmetry
of up to about 9% for the K-shell photoionization of oxygen atom.
For the individual fluorine atoms, the present calculations predict asymmetries
of similar size. However, being averaged over all fluorine atoms, it drops down
to about 2%, as also observed in the present experiment. Our study demonstrates
a strong emitter- and site-sensitivity of PECD in the one-photon inner-shell
ionization of this chiral molecule
A New Biology: A Modern Perspective on the Challenge of Closing the Gap between the Islands of Knowledge
This paper discusses the rebirth of the old quest for the principles of biology along the discourse line of machine-organism disanalogy and within the context of biocomputation from a modern perspective. It reviews some new attempts to revise the existing body of research and enhance it with new developments in some promising fields of mathematics and computation. The major challenge is that the latter are expected to also answer the need for a new framework, a new language and a new methodology capable of closing the existing gap between the different levels of complex system organization
Groupoids and Wreath Products of Musical Transformations: a Categorical Approach from poly-Klumpenhouwer Networks
Transformational music theory, pioneered by the work of Lewin, shifts the
music-theoretical and analytical focus from the "object-oriented" musical
content to an operational musical process, in which transformations between
musical elements are emphasized. In the original framework of Lewin, the set of
transformations often form a group, with a corresponding group action on a
given set of musical objects. Klumpenhouwer networks have been introduced based
on this framework: they are informally labelled graphs, the labels of the
vertices being pitch classes, and the labels of the arrows being
transformations that maps the corresponding pitch classes. Klumpenhouwer
networks have been recently formalized and generalized in a categorical
setting, called poly-Klumpenhouwer networks. This work proposes a new
groupoid-based approach to transformational music theory, in which
transformations of PK-nets are considered rather than ordinary sets of musical
objects. We show how groupoids of musical transformations can be constructed,
and an application of their use in post-tonal music analysis with Berg's Four
pieces for clarinet and piano, Op. 5/2. In a second part, we show how groupoids
are linked to wreath products (which feature prominently in transformational
music analysis) through the notion of groupoid bisectionsComment: 16 pages, 9 figures; comments welcom
MacDowell-Mansouri gravity and Cartan geometry
The geometric content of the MacDowell-Mansouri formulation of general
relativity is best understood in terms of Cartan geometry. In particular,
Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick
of combining the Levi-Civita connection and coframe field, or soldering form,
into a single physical field. The Cartan perspective allows us to view physical
spacetime as tangentially approximated by an arbitrary homogeneous "model
spacetime", including not only the flat Minkowski model, as is implicitly used
in standard general relativity, but also de Sitter, anti de Sitter, or other
models. A "Cartan connection" gives a prescription for parallel transport from
one "tangent model spacetime" to another, along any path, giving a natural
interpretation of the MacDowell-Mansouri connection as "rolling" the model
spacetime along physical spacetime. I explain Cartan geometry, and "Cartan
gauge theory", in which the gauge field is replaced by a Cartan connection. In
particular, I discuss MacDowell-Mansouri gravity, as well as its more recent
reformulation in terms of BF theory, in the context of Cartan geometry.Comment: 34 pages, 5 figures. v2: many clarifications, typos correcte
Hyper-domains in exchange bias micro-stripe pattern
A combination of experimental techniques, e.g. vector-MOKE magnetometry, Kerr microscopy and polarized neutron reflectometry, was applied to study the field induced evolution of the magnetization distribution over a periodic pattern of alternating exchange bias (EB) stripes. The lateral structure is imprinted into a continuous ferromagnetic/antiferromagnetic EB bilayer via laterally selective exposure to He-ion irradiation in an applied field. This creates an alternating frozen-in interfacial EB field competing with the external field in the course of the re-magnetization. It was found that in a magnetic field applied at an angle with respect to the EB axis parallel to the stripes the re-magnetization process proceeds via a variety of different stages. They include coherent rotation of magnetization towards the EB axis, precipitation of small random (ripple) domains, formation of a stripe-like alternation of the magnetization, and development of a state in which the magnetization forms large hyper-domains comprising a number of stripes. Each of those magnetic states is quantitatively characterized via the comprehensive analysis of data on specular and off-specular polarized neutron reflectivity. The results are discussed within a phenomenological model containing a few parameters, which can readily be controlled by designing systems with a desired configuration of magnetic moments of micro- and nano-elements
Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra
We study the basic features of BPS quiver mutations in 4D
supersymmetric quantum field theory with gauge symmetries.\ We show,
for these gauge symmetries, that there is an isotropy group
associated to a set of quiver mutations capturing
information about the BPS spectra. In the strong coupling limit, it is shown
that BPS chambers correspond to finite and closed groupoid orbits with an
isotropy symmetry group isomorphic to the discrete
dihedral groups contained in Coxeter with the
Coxeter number of G. These isotropy symmetries allow to determine the BPS
spectrum of the strong coupling chamber; and give another way to count the
total number of BPS and anti-BPS states of gauge theories. We
also build the matrix realization of these mutation groups from which we read directly the electric-magnetic
charges of the BPS and anti-BPS states of QFT as well as
their matrix intersections. We study as well the quiver mutation symmetries in
the weak coupling limit and give their links with infinite Coxeter groups. We
show amongst others that is contained in
; and isomorphic to the infinite Coxeter
. Other issues such as building
and are also
studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde
Observation of enhanced chiral asymmetries in the inner-shell photoionization of uniaxially oriented methyloxirane enantiomers
Most large molecules are chiral in their structure: they exist as two
enantiomers, which are mirror images of each other. Whereas the rovibronic
sublevels of two enantiomers are almost identical, it turns out that the
photoelectric effect is sensitive to the absolute configuration of the ionized
enantiomer - an effect termed Photoelectron Circular Dichroism (PECD). Our
comprehensive study demonstrates that the origin of PECD can be found in the
molecular frame electron emission pattern connecting PECD to other fundamental
photophysical effects as the circular dichroism in angular distributions
(CDAD). Accordingly, orienting a chiral molecule in space enhances the PECD by
a factor of about 10
Stepping Beyond the Newtonian Paradigm in Biology. Towards an Integrable Model of Life: Accelerating Discovery in the Biological Foundations of Science
The INBIOSA project brings together a group of experts across many disciplines
who believe that science requires a revolutionary transformative
step in order to address many of the vexing challenges presented by the
world. It is INBIOSA’s purpose to enable the focused collaboration of an
interdisciplinary community of original thinkers.
This paper sets out the case for support for this effort. The focus of the
transformative research program proposal is biology-centric. We admit
that biology to date has been more fact-oriented and less theoretical than
physics. However, the key leverageable idea is that careful extension of the
science of living systems can be more effectively applied to some of our
most vexing modern problems than the prevailing scheme, derived from
abstractions in physics. While these have some universal application and
demonstrate computational advantages, they are not theoretically mandated
for the living. A new set of mathematical abstractions derived from biology
can now be similarly extended. This is made possible by leveraging
new formal tools to understand abstraction and enable computability. [The
latter has a much expanded meaning in our context from the one known
and used in computer science and biology today, that is "by rote algorithmic
means", since it is not known if a living system is computable in this
sense (Mossio et al., 2009).] Two major challenges constitute the effort.
The first challenge is to design an original general system of abstractions
within the biological domain. The initial issue is descriptive leading to the
explanatory. There has not yet been a serious formal examination of the
abstractions of the biological domain. What is used today is an amalgam;
much is inherited from physics (via the bridging abstractions of chemistry)
and there are many new abstractions from advances in mathematics (incentivized
by the need for more capable computational analyses). Interspersed
are abstractions, concepts and underlying assumptions “native” to biology
and distinct from the mechanical language of physics and computation as
we know them. A pressing agenda should be to single out the most concrete
and at the same time the most fundamental process-units in biology
and to recruit them into the descriptive domain. Therefore, the first challenge
is to build a coherent formal system of abstractions and operations
that is truly native to living systems.
Nothing will be thrown away, but many common methods will be philosophically
recast, just as in physics relativity subsumed and reinterpreted
Newtonian mechanics.
This step is required because we need a comprehensible, formal system to
apply in many domains. Emphasis should be placed on the distinction between
multi-perspective analysis and synthesis and on what could be the
basic terms or tools needed.
The second challenge is relatively simple: the actual application of this set
of biology-centric ways and means to cross-disciplinary problems. In its
early stages, this will seem to be a “new science”.
This White Paper sets out the case of continuing support of Information
and Communication Technology (ICT) for transformative research in biology
and information processing centered on paradigm changes in the epistemological,
ontological, mathematical and computational bases of the science
of living systems. Today, curiously, living systems cannot be said to
be anything more than dissipative structures organized internally by genetic
information. There is not anything substantially different from abiotic
systems other than the empirical nature of their robustness. We believe that
there are other new and unique properties and patterns comprehensible at
this bio-logical level. The report lays out a fundamental set of approaches
to articulate these properties and patterns, and is composed as follows.
Sections 1 through 4 (preamble, introduction, motivation and major biomathematical
problems) are incipient. Section 5 describes the issues affecting
Integral Biomathics and Section 6 -- the aspects of the Grand Challenge
we face with this project. Section 7 contemplates the effort to
formalize a General Theory of Living Systems (GTLS) from what we have
today. The goal is to have a formal system, equivalent to that which exists
in the physics community. Here we define how to perceive the role of time
in biology. Section 8 describes the initial efforts to apply this general theory
of living systems in many domains, with special emphasis on crossdisciplinary
problems and multiple domains spanning both “hard” and
“soft” sciences. The expected result is a coherent collection of integrated
mathematical techniques. Section 9 discusses the first two test cases, project
proposals, of our approach. They are designed to demonstrate the ability
of our approach to address “wicked problems” which span across physics,
chemistry, biology, societies and societal dynamics. The solutions
require integrated measurable results at multiple levels known as “grand
challenges” to existing methods. Finally, Section 10 adheres to an appeal
for action, advocating the necessity for further long-term support of the
INBIOSA program.
The report is concluded with preliminary non-exclusive list of challenging
research themes to address, as well as required administrative actions. The
efforts described in the ten sections of this White Paper will proceed concurrently.
Collectively, they describe a program that can be managed and
measured as it progresses
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