Is the Hamiltonian geometrical criterion for chaos always reliable?

It is found that the application of a newly developed geometrical criterion, in which negative eigenvalues of the associated matrix determined by the dynamical curvature of a conformal metric for a Hamiltonian system are used to identify the onset of local instability or chaos, is somewhat problematic in some circumstances. In fact, this criterion is neither necessary nor sufficient for the prediction of instability of orbits on a same energy hypersurface because it is not in good agreement with information on unstable or chaotic behavior given by the maximal Lyapunov exponent in general.     

Is the “missing mass” really missing?

We have no experimental evidence for the validity of the inverse square law for gravitation at distances significantly larger than the diameter of the solar system. This raises the very real possibility that the missing mass (dark matter) may not exist. Instead, the inverse square law may be breaking down at distances of the order of tens of kiloparsecs. I discuss this possibility within the framework of Scalar-Vector-Tensor (SVT) theories of gravity. It appears to be relatively easy to account for up to approximately 10% of the galactic halo dark matter via SVT theories of gravity. With some fine-tuning of parameters, it is conceivable that all of the dark matter can be accounted for in this way.This essay received an honorable mention from the Gravity Research Foundation for the year 1987.Supported by the U.S. Department of Energy under grant #DE-FG03-84ER-40168.     

Some Comments on “The Mathematical Universe”

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed “shut-up-and-calculate” approach to physics (Tegmark in Found. Phys. 38:101, 2008; New Sci., September 15th, 2007). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this—at first sight purely philosophical—difference in point of view.     

Is the “drunken sinusoid” a soliton solution?

A family of functions f_α(x) = sin(x + α) exp(cos(x)) is analysed. Explicit formulae for the Fourier and Maclaurin expansion of f_α are calculated and a hierarchy of algebraic differential equations admitting some f_α as solutions is presented. A few problems concerning analytic and algebraic properties of f_α are mentioned as well as natural wave features of f_α are regarded.     

Some Remarks on the Smoluchowski–Kramers Approximation

According to the Smoluchowski–Kramers approximation, solution q _t of the equation , where is the White noise, converges to the solution of equation as µ 0. Many asymptotic problems for the last equation were studied in recent years. We consider relations between asymptotics for the first order equation and the original second order equation. Homogenization, large deviations and stochastic resonance, approximation of Brownian motion W _t by a smooth stochastic process, stationary distributions are considered.     

Some remarks on the Dirac–Witten operator on pseudo-Riemannian manifolds

In this paper, we get optimal lower bounds for the eigenvalues of the Dirac–Witten operator. These estimates are given in terms of the intrinsic and extrinsic curvature expressions. In the limiting case, we prove that the spacelike submanifold is Einstein if the normal bundle is flat.     

What Is Temperature? Modern Outlook on the Concept of Temperature

The meaning and evolution of the notion of “temperature” (which is a key concept for the condensed and gaseous matter theories) are addressed from different points of view. The concept of temperature has turned out to be much more fundamental than conventionally thought. In particular, the temperature may be introduced for systems built of a “small” number of particles and particles at rest. The Kelvin temperature scale may be introduced into quantum and relativistic physics due to the fact that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of temperature with the metrics of the configurational space describing the behavior of systems built from non-interacting particles is demonstrated. The role of temperature in constituting inertia and gravity forces treated as entropy forces is addressed. The Landauer principle asserts that the temperature of a system is the only physical value defining the energy cost of the isothermal erasure of a single bit of information. The fundamental role of the temperature of the cosmic microwave background in modern cosmology is discussed. The range of problems and controversies related to the negative absolute temperature is treated.     

Some comments on the effectiveness of the therapy for Β-thalassemia

In the present study, twenty-five samples of red blood cells (RBCs) and two samples of lyophilized serum, drawn from thirteen patients with -thanassemia major, have been examined by Mössbauer spectroscopy. All these patients undergo long-term therapy by regular blood transfusion and deferoxamine. The samples were obtained at the end of one cycle of treatments, before the successive blood transfusion. The results show, within the experimental errors, that the ferritin-like iron appears to be absent in the RBCs of the patients but it is still present in the serum.On leave from Tsinghua University, Beijing, PR China.On leave fro East China Normal University, Shanghai, PR China.     

Is graphene on copper doped?

Angle‐resolved photoemission spectroscopy (ARPES) and X‐ray photoemission spectroscopy have been used to characterise epitaxially ordered graphene grown on copper foil by low‐pressure chemical vapour deposition. A short vacuum anneal to 200 °C allows observation of ordered low energy electron diffraction patterns. High quality Dirac cones are measured in ARPES with the Dirac point at the Fermi level (undoped graphene). Annealing above 300 °C produces n‐type doping in the graphene with up to 350 meV shift in Fermi level, and opens a band gap of around 100 meV.

     

What do we learn from the CMB observations?

We give an account, at nonexpert and quantitative level, of physics behind the CMB temperature anisotropy and polarization and their peculiar features. We discuss, in particular, how cosmological parameters are determined from the CMB measurements and their combinations with other observations. We emphasize that CMB is the major source of information on the primordial density perturbations and, possibly, gravitational waves, and discuss the implication for our understanding of the extremely early Universe.     

Some remarks about the “efficiency” of polyautomata

A proposal is made to measure the efficiency of cellular algorithms, implemented in cellular automata, roughly speaking by the ratio of the number of proper state changes and the product of time, and number of single automata. Such a definition is discussed in some detail. For some cellular algorithms lower bounds for their efficiency are given.     

Transient chaos in a generalized Hénon map on the torus

A generalized Hénon system on a torus is considered to investigate some phenomena of transient chaos in weakly dissipative systems. A simple relationship is numerically verified between the life time of chaos and other parameters of the model.     

Some minimal notes on notation and minima: A comment on “How particular is the physics of the free energy principle?” by Aguilera,Millidge, Tschantz,and Buckley

We comment on a technical critique of the free energy principle in linear systems by Aguilera, Millidge, Tschantz, and Buckley, entitled “How Particular is the Physics of the Free Energy Principle?” Aguilera and colleagues identify an ambiguity in the flow of the mode of a system, and we discuss the context for this ambiguity in earlier papers, and their proposal of a more adequate interpretation of these equations. Following that, we discuss a misinterpretation in their treatment of surprisal and variational free energy, especially with respect to their gradients and their minima. In sum, we argue that the results in the target paper are accurate and stand up to rigorous scrutiny; we also highlight that they, nonetheless, do not undermine the FEP.     

A golden age of general relativity? Some remarks on the history of general relativity

This article deals with the concepts “renaissance” and “low water mark between 1925 and 1955” of general relativity suggested in the literature. By empirical data, it is shown that no such period did exist. Research on general relativity continued continuously since the 1920s interrupted only by the second world war. On a broad scale, research on general relativity started only after 1945.     

Some Remarks on the Cohomology of Krichever–Novikov Algebras

We calculate the continuous cohomology of the Lie algebra of meromorphic vector fields on a compact Riemann surface from the cohomology of the holomorphic vector fields on the open Riemann surface pointed in the poles. This cohomology has been given by Kawazumi. Our result shows the Feigin–Novikov conjecture.     

Oscillons: an encounter with dynamical chaos in 1953?

We discuss the works of one of electronic art pioneers, Ben F. Laposky (1914-2000), and argue that he might have been the first to create a family of essentially nonlinear analog circuits that allowed him to observe chaotic attractors.