# Category Archives: PHYSICS

# Dimensionless Units in the SI

**Peter J. Mohr** and **William D. Phillips**

The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor.

Here we consider dimensionless units as defined in the SI, * e.g.* angular units like radians or steradians and counting units like radioactive decays or molecules.

We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit “one”, and suggest how to properly include such units into the SI in order to remove the incoherence.

In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.

Read more at http://arxiv.org/pdf/1409.2794v1.pdf

# Information Theory And The Origin of Life

**Christoph Adami**

Research investigating the origins of life usually focuses on exploring possible life-bearing chemistries in the pre-biotic Earth, or else on synthetic approaches.

Little work has been done exploring fundamental issues concerning the spontaneous emergence of life using only concepts (such as information and evolution) that are divorced from any particular chemistry.

Here, I advocate studying the probability of spontaneous molecular self-replication as a function of the information contained in the replicator, and the environmental conditions that might enable this emergence.

I show that (under certain simplifying assumptions) the probability to discover a self-replicator by chance depends exponentially on the rate of formation of the monomers.

If the rate at which monomers are formed is somewhat similar to the rate at which they would occur in a self-replicating polymer, the likelihood to discover such a replicator by chance is increased by many orders of magnitude.

I document such an increase in searches for a self-replicator within the digital life system avida …

… Read more at arxiv.org/pdf/

Read also medium.com/the-physics-arxiv-blog

# Van der Pol and the history of relaxation oscillations

Jean-Marc Ginoux, Christophe Letellier

Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit.

Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed:

i) the series dynamo machine conducted by Gerard-Lescuyer (1880),

ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905),

iii) the triode invented by de Forest (1907)

and, iv) the multivibrator elaborated by Abraham and Bloch (1917).

The differential equation describing such a self-oscillating system was proposed by Poincare for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol’s contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller’s help, he popularized the “relaxation oscillations” using the previous experiments as examples and, turned them into a concept….

… Read more at http://arxiv.org/pdf/1408.4890v1.pdf

# Freezing droplet

A droplet on a deep-frozen surface turns into a conical shape. Scientists of the University of Twente (Physics of Fluids) found out why, by looking into the droplet. Their results are also important for other processes where liquid droplets solidify ‘from the bottom’, like 3D printing.

**Universality of Tip Singularity Formation in Freezing Water Drops**

**A. G. Marín, O. R. Enríquez, P. Brunet, P. Colinet,** and **J. H. Snoeijer**

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip.

While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation.

We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry.

It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification.

We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with the experiments….

Read more at arxiv.org/pdf and phys.org

# New Physics of Metamaterials

**Z.Y.Wang**

Einstein utilized Lorentz invariance from Maxwell’s equations to modify mechanical laws and establish the special theory of relativity.

Similarly, we may have a different theory if there exists another covariance of Maxwell’s equations. In this paper, we find such a new transformation where Maxwell’s equations are still unchanged.

Consequently, Veselago’s metamaterial and other systems have negative phase velocities without double negative permittivity and permeability can be described by a unified theory.

People are interested in the application of metamaterials and negative phase velocities but do not appreciate the magnitude and significance to the spacetime conception of modern physics and philosophy….

… Read more at http://arxiv.org/ftp/arxiv/papers/1404/1404.5255.pdf

# A multiple of 12 for Avogadro

Carbon, Avogadro’s Constant and the Importance of the Number 12

**Materials scientists have decided to define, rather than measure, Avogadro’s constant, triggering a lengthy debate over what number to choose. Now one physicist thinks he has the answer.**

The International System of Units (with the abbreviation of SI units) is one of the foundations of modern science. It consists of seven base units from which all others can be derived.

These are the meter for length; the kilogram for mass; the second for time; the ampere for electric current; Kelvin for thermodynamic temperature; candela for luminous intensity, and mole for the amount of substance. This is a coӧrdinated system of units that allows scientific results to be compared relatively easily, regardless of where they are made.

However, the SI system is far from perfect. One of the problems is that some of the units have values based on arbitrary objects, such as the kilogram. There is general agreement that this should be changed so that the units are based on the fundamental constants of nature and on specific numbers that are defined and therefore constant.

One of these numbers is Avogadro’s constant. This is currently defined as the number of atoms in 12 grams of carbon-12 and is known to be about 6.02214129 ×10^23. But the exact number depends on the definition of a kilogram, which for the moment is the mass of an arbitrary bar of platinum-iridium alloy hidden in a safe somewhere in Paris.

The general consensus is that it would be better to define Avogadro’s constant and let this determine the mass of the kilogram. But what number should serve? Continue reading A multiple of 12 for Avogadro