Phycomyces

This monographic review on a fungus is not addressed to mycologists. None of the authors has been trained or has otherwise acquired a general proficiency in mycology. They are motivated by a common interest in the performances of signal handling exhibited by the sense organs of all organisms and by the desire to attack these as yet totally obscure aspects of molecular biology by the study of a microorganism with certain desirable properties. The sporangiophore of the fungus Phycomyces is a gigantic, single-celled, erect, cylindrical, aerial hypha. It is sensitive to at least four distinct stimuli: light, gravity, stretch, and some unknown stimulus by which it avoids solid objects. These stimuli control a common output, the growth rate, producing either temporal changes in growth rate or tropic responses. We are interested in the output because it gives us information about the reception of the various signals. In the absence of external stimuli, the growth rate is controlled by internal signals keeping the network of biochemical processes in balance. The external stimuli interact with the internal signals. We wish to inquire into the early steps of this interaction. For light, for instance, the cell must have a receptor pigment as the first mediator. What kind of a molecule is this pigment? Which organelle contains it? What chemical reaction happens after a light quantum has been absorbed? And how is the information introduced by this primary photochemical event amplified in a controlled manner and processed in the next step? How do a few quanta or a few molecules trigger macroscopic responses? Will we find ourselves confronted with devices wholly distinct from anything now known in biology

The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

Enhancement of vacuum polarization effects in a plasma

The dispersive effects of vacuum polarization on the propagation of a strong circularly polarized electromagnetic wave through a cold collisional plasma are studied analytically. It is found that, due to the singular dielectric features of the plasma, the vacuum effects on the wave propagation in a plasma are qualitatively different and much larger than those in pure vacuum in the regime when the frequency of the propagating wave approaches the plasma frequency. A possible experimental setup to detect these effects in plasma is described.Comment: 33 pages, 3 figure

On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

The knotting probability is defined by the probability with which an $N$-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of $N$. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be $2.5 \times 10^5$ on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure

Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure

Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well-known to Einstein from earlier work on Wien's displacement law, Planck's radiation theory, and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory.Comment: 57 pp

The Generalized Second Law implies a Quantum Singularity Theorem

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose's original singularity theorem, it implies that spacetime is null geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. An introductory section describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.) A proof of the coarse-grained ordinary second law is given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised (4.1, 5.2), more comments on AdS. v3: major revisions including change of title. v4: similar to published version, but with corrections to plan of paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new footnote

International organisations and anti-terrorist sanctions: no accountability for human rights violations?

The targeted sanctions adopted by the UN Security Council against individuals and entities suspected of association with terrorism are managed through procedures that infringe fundamental human rights, and there are no mechanisms for actual accountability. With the exception of the ECJ in Kadi, municipal and regional courts tend to consider the UN Security Council's resolutions and domestic measures implementing them outside the scope of judicial review. This article argues that the Security Council is bound to observe human rights even in the context of international security action, and that States are not exonerated from international responsibility for violations committed under the umbrella of Chapter VII resolutions