5,455 research outputs found

### Microscopic dissipation in a cohesionless granular jet impact

Sufficiently fine granular systems appear to exhibit continuum properties,
though the precise continuum limit obtained can be vastly different depending
on the particular system. We investigate the continuum limit of an unconfined,
dense granular flow. To do this we use as a test system a two-dimensional dense
cohesionless granular jet impinging upon a target. We simulate this via a
timestep driven hard sphere method, and apply a mean-field theoretical approach
to connect the macroscopic flow with the microscopic material parameters of the
grains. We observe that the flow separates into a cone with an interior cone
angle determined by the conservation of momentum and the dissipation of energy.
From the cone angle we extract a dimensionless quantity $A-B$ that
characterizes the flow. We find that this quantity depends both on whether or
not a deadzone --- a stationary region near the target --- is present, and on
the value of the coefficient of dynamic friction. We present a theory for the
scaling of $A-B$ with the coefficient of friction that suggests that
dissipation is primarily a perturbative effect in this flow, rather than the
source of qualitatively different behavior.Comment: 9 pages, 11 figure

### Approximately multiplicative maps from weighted semilattice algebras

We investigate which weighted convolution algebras $\ell^1_\omega(S)$, where
$S$ is a semilattice, are AMNM in the sense of Johnson (JLMS, 1986). We give an
explicit example where this is not the case. We show that the unweighted
examples are all AMNM, as are all $\ell^1_\omega(S)$ where $S$ has either
finite width or finite height. Some of these finite-width examples are
isomorphic to function algebras studied by Feinstein (IJMMS, 1999).
We also investigate when $(\ell^1_\omega(S),{\bf M}_2)$ is an AMNM pair in
the sense of Johnson (JLMS, 1988), where ${\bf M}_2$ denotes the algebra of
2-by-2 complex matrices. In particular, we obtain the following two contrasting
results: (i) for many non-trivial weights on the totally ordered semilattice
${\bf N}_{\min}$, the pair $(\ell^1_\omega({\bf N}_{\min}),{\bf M}_2)$ is not
AMNM; (ii) for any semilattice $S$, the pair $(\ell^1(S),{\bf M}_2)$ is AMNM.
The latter result requires a detailed analysis of approximately commuting,
approximately idempotent $2\times 2$ matrices.Comment: AMS-LaTeX. v3: 31 pages, additional minor corrections to v2. Final
version, to appear in J. Austral. Math. Soc. v4: small correction of
mis-statement at start of Section 4 (this should also be fixed in the journal
version

### Submodule Categories of Wild Representation Type

Let $\Lambda$ be a commutative local uniserial ring of length at least seven
with radical factor ring $k$. We consider the category $S(\Lambda)$ of all
possible embeddings of submodules of finitely generated $\Lambda$-modules and
show that $S(\Lambda)$ is controlled $k$-wild with a single control object
$I\in S(\Lambda)$. In particular, it follows that each finite dimensional
$k$-algebra can be realized as a quotient \End(X)/\End(X)_I of the
endomorphism ring of some object $X\in S(\Lambda)$ modulo the ideal \End(X)_I
of all maps which factor through a finite direct sum of copies of $I$.Comment: 13 page

### Combinatorial Topology Of Multipartite Entangled States

With any state of a multipartite quantum system its separability polytope is
associated. This is an algebro-topological object (non-trivial only for mixed
states) which captures the localisation of entanglement of the state.
Particular examples of separability polytopes for 3-partite systems are
explicitly provided. It turns out that this characterisation of entanglement is
associated with simulation of arbitrary unitary operations by 1- and 2-qubit
gates. A topological description of how entanglement changes in course of such
simulation is provided.Comment: 14 pages, LaTeX2e. Slightly revised version of the poster resented on
the International Conference on Quantum Information, Oviedo, Spain, 13-18
July, 2002. To appear in the special issue of Journal of Modern Optic

### Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene

We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene.
We derive analytic low energy expressions for the spectrum, the validity of
which is confirmed by comparison to a \pi -band tight-binding calculation of
the density of states on the honeycomb lattice. We further study the effect of
a perpendicular electric field on the spectrum, where a zero-energy plateau
appears for ABC stacking order, due to the opening of a gap at the Dirac point,
while the ABA-stacked trilayer graphene remains metallic. We discuss our
results in the context of recent electronic transport experiments. Furthermore,
we argue that the expressions obtained can be useful in the analysis of future
measurements of cyclotron resonance of electrons and holes in trilayer
graphene.Comment: 10 pages, 8 figure

### Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism

We develop the idea of employing localization systems of Boolean coverings,
associated with measurement situations, in order to comprehend structures of
Quantum Observables. In this manner, Boolean domain observables constitute
structure sheaves of coordinatization coefficients in the attempt to probe the
Quantum world. Interpretational aspects of the proposed scheme are discussed
with respect to a functorial formulation of information exchange, as well as,
quantum logical considerations. Finally, the sheaf theoretical construction
suggests an opearationally intuitive method to develop differential geometric
concepts in the quantum regime.Comment: 25 pages, Late

### Classification of finite congruence-simple semirings with zero

Our main result states that a finite semiring of order >2 with zero which is
not a ring is congruence-simple if and only if it is isomorphic to a `dense'
subsemiring of the endomorphism semiring of a finite idempotent commutative
monoid.
We also investigate those subsemirings further, addressing e.g. the question
of isomorphy.Comment: 16 page

### Chromatic Polynomials for Families of Strip Graphs and their Asymptotic Limits

We calculate the chromatic polynomials $P((G_s)_m,q)$ and, from these, the
asymptotic limiting functions $W(\{G_s\},q)=\lim_{n \to \infty}P(G_s,q)^{1/n}$
for families of $n$-vertex graphs $(G_s)_m$ comprised of $m$ repeated subgraphs
$H$ adjoined to an initial graph $I$. These calculations of $W(\{G_s\},q)$ for
infinitely long strips of varying widths yield important insights into
properties of $W(\Lambda,q)$ for two-dimensional lattices $\Lambda$. In turn,
these results connect with statistical mechanics, since $W(\Lambda,q)$ is the
ground state degeneracy of the $q$-state Potts model on the lattice $\Lambda$.
For our calculations, we develop and use a generating function method, which
enables us to determine both the chromatic polynomials of finite strip graphs
and the resultant $W(\{G_s\},q)$ function in the limit $n \to \infty$. From
this, we obtain the exact continuous locus of points ${\cal B}$ where
$W(\{G_s\},q)$ is nonanalytic in the complex $q$ plane. This locus is shown to
consist of arcs which do not separate the $q$ plane into disconnected regions.
Zeros of chromatic polynomials are computed for finite strips and compared with
the exact locus of singularities ${\cal B}$. We find that as the width of the
infinitely long strips is increased, the arcs comprising ${\cal B}$ elongate
and move toward each other, which enables one to understand the origin of
closed regions that result for the (infinite) 2D lattice.Comment: 48 pages, Latex, 12 encapsulated postscript figures, to appear in
Physica

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