97 research outputs found
Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites
We calculate the bulk contribution for the doubly degenerated largest
eigenvalue of the transfer matrix of the eight vertex model with an odd number
of lattice sites N in the disordered regime using the generic equation for
roots proposed by Fabricius and McCoy. We show as expected that in the
thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change
Increase in linear motion steadiness of tractor-trailers using stabilizing towing couplers
Travelling at higher speeds over any type of roads could disturb the stability of motion, which is manifested through lateral oscillations of the trailer in a horizontal plane - trailer wobbling. This research is aimed at building a mathematical model of tractor-trailer motion affected by the external action of lateral forces and estimating how efficient stabilizing couplers could be. A double pendulum design diagram is used to build the model. It is shown that the stability of motion is impacted at most by the ratio of the inertia radius (relative to the vertical axis passing through the center of gravity) to the base of the trailer, which depends on the type of cargo, its distribution within the trailer body, the heterogeneity of the cargo material and so on. It is demonstrated that the critical velocity of a trailer would increase when stabilizers are used. Changing the design of the trailer should also positively affect the stability of a tractor-trailer due to faster and more efficient damping of lateral oscillations impacting its movement. © Published under licence by IOP Publishing Ltd
Improving design safety of tractor-trailers by upgrading towing couplers
One major way of increasing efficiency in production, construction and agriculture industries is to use motor- and tractor-trailers for transportation needs. At the same time, a tractor-trailer is a complex and less maneuverable machine in comparison with a single vehicle. Exceeding the velocity regime, especially in the case of tractor-trailers, leads to a loss of stability during linear motion, on curvilinear sections of the trajectory or in complex traffic conditions. Speed limit is a standard prevention method; however, it does not guarantee any acceptable result. Other ways of resolving this issue have almost exhausted their potential. It should be noted that solving this problem is further complicated by a lack of a unified road-movement theory for tractor-trailers - thus, mainly restrictive measures are used. The authors suggested a hypothesis on possible improvement of tractor-trailer safety by means of increasing their motion stability via upgraded design characteristics of towing tractor-trailer couplers. The higher stability would be achieved by raising the damping factor of transverse oscillations by applying lateral disturbing forces. The authors proposed over 55 technical solutions, all protected by certificates of authorship in engineering, of upgrading the towing couplers and providing the increase of tractor-trailer operation safety in various road conditions. © Published under licence by IOP Publishing Ltd
Ground-state properties of a supersymmetric fermion chain
We analyze the ground state of a strongly interacting fermion chain with a
supersymmetry. We conjecture a number of exact results, such as a hidden
duality between weak and strong couplings. By exploiting a scale free property
of the perturbative expansions, we find exact expressions for the order
parameters, yielding the critical exponents. We show that the ground state of
this fermion chain and another model in the same universality class, the XYZ
chain along a line of couplings, are both written in terms of the same
polynomials. We demonstrate this explicitly for up to N = 24 sites, and provide
consistency checks for large N. These polynomials satisfy a recursion relation
related to the Painlev\'e VI differential equation, and using a scale-free
property of these polynomials, we derive a simple and exact formula for their
limit as N goes to infinity.Comment: v2: added more information on scaling function, fixed typo
Auxiliary matrices on both sides of the equator
The spectra of previously constructed auxiliary matrices for the six-vertex
model at roots of unity are investigated for spin-chains of even and odd
length. The two cases show remarkable differences. In particular, it is shown
that for even roots of unity and an odd number of sites the eigenvalues contain
two linear independent solutions to Baxter's TQ-equation corresponding to the
Bethe ansatz equations above and below the equator. In contrast, one finds for
even spin-chains only one linear independent solution and complete strings. The
other main result is the proof of a previous conjecture on the degeneracies of
the six-vertex model at roots of unity. The proof rests on the derivation of a
functional equation for the auxiliary matrices which is closely related to a
functional equation for the eight-vertex model conjectured by Fabricius and
McCoy.Comment: 22 pages; 2nd version: one paragraph added in the conclusion and some
typos correcte
Exact expressions for correlations in the ground state of the dense O(1) loop model
Conjectures for analytical expressions for correlations in the dense O
loop model on semi infinite square lattices are given. We have obtained these
results for four types of boundary conditions. Periodic and reflecting boundary
conditions have been considered before. We give many new conjectures for these
two cases and review some of the existing results. We also consider boundaries
on which loops can end. We call such boundaries ''open''. We have obtained
expressions for correlations when both boundaries are open, and one is open and
the other one is reflecting. Also, we formulate a conjecture relating the
ground state of the model with open boundaries to Fully Packed Loop models on a
finite square grid. We also review earlier obtained results about this relation
for the three other types of boundary conditions. Finally, we construct a
mapping between the ground state of the dense O loop model and the XXZ
spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA
Fluctuations and skewness of the current in the partially asymmetric exclusion process
We use functional Bethe Ansatz equations to calculate the cumulants of the
total current in the partially asymmetric exclusion process. We recover known
formulas for the first two cumulants (mean value of the current and diffusion
constant) and obtain an explicit finite size formula for the third cumulant.
The expression for the third cumulant takes a simple integral form in the limit
where the asymmetry scales as the inverse of the square root of the size of the
system, which corresponds to a natural separation between weak and strong
asymmetry.Comment: 21 pages, 3 figure
Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
We prove higher rank analogues of the Razumov--Stroganov sum rule for the
groundstate of the O(1) loop model on a semi-infinite cylinder: we show that a
weighted sum of components of the groundstate of the A_{k-1} IRF model yields
integers that generalize the numbers of alternating sign matrices. This is done
by constructing minimal polynomial solutions of the level 1 U_q(\hat{sl(k)})
quantum Knizhnik--Zamolodchikov equations, which may also be interpreted as
quantum incompressible q-deformations of fractional quantum Hall effect wave
functions at filling fraction nu=1/k. In addition to the generalized
Razumov--Stroganov point q=-e^{i pi/k+1}, another combinatorially interesting
point is reached in the rational limit q -> -1, where we identify the solution
with extended Joseph polynomials associated to the geometry of upper triangular
matrices with vanishing k-th power.Comment: v3: misprint fixed in eq (2.1
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
Non-local space-time supersymmetry on the lattice
We show that several well-known one-dimensional quantum systems possess a
hidden nonlocal supersymmetry. The simplest example is the open XXZ spin chain
with \Delta=-1/2. We use the supersymmetry to place lower bounds on the ground
state energy with various boundary conditions. For an odd number of sites in
the periodic chain, and with a particular boundary magnetic field in the open
chain, we can derive the ground state energy exactly. The supersymmetry thus
explains why it is possible to solve the Bethe equations for the ground state
in these cases. We also show that a similar space-time supersymmetry holds for
the t-J model at its integrable ferromagnetic point, where the space-time
supersymmetry and the Hamiltonian it yields coexist with a global u(1|2) graded
Lie algebra symmetry. Possible generalizations to other algebras are discussed.Comment: 12 page
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