1,466 research outputs found

### How does gravity save or kill Q-balls?

We explore stability of gravitating Q-balls with potential
$V_4(\phi)={m^2\over2}\phi^2-\lambda\phi^4+\frac{\phi^6}{M^2}$ via catastrophe
theory, as an extension of our previous work on Q-balls with potential
$V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$. In flat spacetime
Q-balls with $V_4$ in the thick-wall limit are unstable and there is a minimum
charge $Q_{{\rm min}}$, where Q-balls with $Q<Q_{{\rm min}}$ are nonexistent.
If we take self-gravity into account, on the other hand, there exist stable
Q-balls with arbitrarily small charge, no matter how weak gravity is. That is,
gravity saves Q-balls with small charge. We also show how stability of Q-balls
changes as gravity becomes strong.Comment: 10 pages, 10 figure

### Unified pictures of Q-balls and Q-tubes

While Q-balls have been investigated intensively for many years, another type
of nontopological solutions, Q-tubes, have not been understood very well. In
this paper we make a comparative study of Q-balls and Q-tubes. First, we
investigate their equilibrium solutions for four types of potentials. We find,
for example, that in some models the charge-energy relation is similar between
Q-balls and Q-tubes while in other models the relation is quite different
between them. To understand what determines the charge-energy relation, which
is a key of stability of the equilibrium solutions, we establish an analytical
method to obtain the two limit values of the energy and the charge. Our
prescription indicates how the existent domain of solutions and their stability
depends on their shape as well as potentials, which would also be useful for a
future study of Q-objects in higher-dimensional spacetime.Comment: 11 pages, 14 figure

### Unified picture of Q-balls and boson stars via catastrophe theory

We make an analysis of Q-balls and boson stars using catastrophe theory, as
an extension of the previous work on Q-balls in flat spacetime. We adopt the
potential $V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$ for Q-balls and
that with $\mu =0$ for boson stars. For solutions with $|g^{rr}-1|\sim 1$ at
its peak, stability of Q-balls has been lost regardless of the potential
parameters. As a result, phase relations, such as a Q-ball charge versus a
total Hamiltonian energy, approach those of boson stars, which tell us an
unified picture of Q-balls and boson stars.Comment: 10 pages, 13 figure

### Fuzzy geometry

The concept of fuzzy space is due independently to
PoincarÃ© and Zeeman. (PoincarÃ©
used the term "physical continuum", Zeeman the term
"tolerance space". I have reluctantly introduced a
third expression since my attempts to generate a
vocabulary from either of these have all proved
impossibly unwieldy.) Both were led to it by the
nature of our perception of space, and both adapted to
it tools current in topology. Unfortunately, neither
examined the application of these tools in complete
detail, and as a result the argument from analogy
was somewhat over-extended by both. The resemblances
to topology are strong; the differences are sometimes
glaring and sometimes subtle. In the latter case the
difficulties produced by a topologically-conditioned
intuition can be severe obstacles to progress.
(Certainly, having been reared mathematically as a
topologist I have found it necessary to distrust any
conclusion whose proof is not painfully precise. )
For this reason many of the proofs in this paper are
set out in somewhat more detail than would be natural
in a more established field. For this reason also I
have here not only set out the positive results I
have so far obtained in the subject but, for the
benefit of topologists, elaborated on the failures of
analogy with topology where a more succinct exposition
would have ignored them as dead ends (e.g., in Chap. I, Â§2)

### Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

We investigate a Bose-Einstein condensate with additional long-range dipolar
interaction in a cylindrically symmetric trap within a variational framework.
Compared to the ground state of this system, little attention has as yet been
payed to its unstable excited states. For thermal excitations, however, the
latter is of great interest, because it forms the "activated complex" that
mediates the collapse of the condensate. For a certain value of the s-wave
scatting length our investigations reveal a bifurcation in the transition
state, leading to the emergence of two additional and symmetry-breaking excited
states. Because these are of lower energy than their symmetric counterpart, we
predict the occurrence of a symmetry-breaking thermally induced collapse of
dipolar condensates. We show that its occurrence crucially depends on the trap
geometry and calculate the thermal decay rates of the system within leading
order transition state theory with the help of a uniform rate formula near the
rank-2 saddle which allows to smoothly pass the bifurcation.Comment: 6 pages, 3 figure

### Overheating in Scotland : lessons from 26 monitored low energy homes

There is growing awareness in the UK that overheating is a significant problem and one that is likely to intensify with climate change, increasing urbanisation, an ageing population and the move towards ?low energy? buildings. Recent research suggested that while overheating may be an issue in the South of England, particularly in urban areas, it was not likely to be an issue for Scotland and the North of the UK in the medium term. This notion is reflected in the lack of awareness of the issue in Scotland. Monitoring of 26 new-build low energy and Passivhaus homes across Scotland over a two year period indicates overheating is prevalent in living areas and in particular in bedrooms where it is acknowledged that respite from high temperatures is important. This paper describes the quantitative and qualitative results, assesses relevant factors, comments on predictive tools used and seeks a robust series of measures to avoid overheating in future low energy homes in Scotland

### Thermodynamic phase transitions and shock singularities

We show that under rather general assumptions on the form of the entropy
function, the energy balance equation for a system in thermodynamic equilibrium
is equivalent to a set of nonlinear equations of hydrodynamic type. This set of
equations is integrable via the method of the characteristics and it provides
the equation of state for the gas. The shock wave catastrophe set identifies
the phase transition. A family of explicitly solvable models of
non-hydrodynamic type such as the classical plasma and the ideal Bose gas are
also discussed.Comment: revised version, 18 pages, 6 figure

### Generation of scalar-tensor gravity effects in equilibrium state boson stars

Boson stars in zero-, one-, and two-node equilibrium states are modeled
numerically within the framework of Scalar-Tensor Gravity. The complex scalar
field is taken to be both massive and self-interacting. Configurations are
formed in the case of a linear gravitational scalar coupling (the Brans-Dicke
case) and a quadratic coupling which has been used previously in a cosmological
context. The coupling parameters and asymptotic value for the gravitational
scalar field are chosen so that the known observational constraints on
Scalar-Tensor Gravity are satisfied. It is found that the constraints are so
restrictive that the field equations of General Relativity and Scalar-Tensor
gravity yield virtually identical solutions. We then use catastrophe theory to
determine the dynamically stable configurations. It is found that the maximum
mass allowed for a stable state in Scalar-Tensor gravity in the present
cosmological era is essentially unchanged from that of General Relativity. We
also construct boson star configurations appropriate to earlier cosmological
eras and find that the maximum mass for stable states is smaller than that
predicted by General Relativity, and the more so for earlier eras. However, our
results also show that if the cosmological era is early enough then only states
with positive binding energy can be constructed.Comment: 20 pages, RevTeX, 11 figures, to appear in Class. Quantum Grav.,
comments added, refs update

### Pulsive feedback control for stabilizing unstable periodic orbits in a nonlinear oscillator with a non-symmetric potential

We examine a strange chaotic attractor and its unstable periodic orbits in
case of one degree of freedom nonlinear oscillator with non symmetric
potential. We propose an efficient method of chaos control stabilizing these
orbits by a pulsive feedback technique. Discrete set of pulses enable us to
transfer the system from one periodic state to another.Comment: 11 pages, 4 figure

### Mode Bifurcation and Fold Points of Complex Dispersion Curves for the Metamaterial Goubau Line

In this paper the complex dispersion curves of the four lowest-order
transverse magnetic modes of a dielectric Goubau line ($\epsilon>0, \mu>0$) are
compared with those of a dispersive metamaterial Goubau line. The vastly
different dispersion curve structure for the metamaterial Goubau line is
characterized by unusual features such as mode bifurcation, complex fold
points, both proper and improper complex modes, and merging of complex and real
modes

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