How narrow can a meniscus be?

A water meniscus naturally forms in air between an atomic force microscope (AFM) tip and a substrate. This nanoscale meniscus produces a capillary force on the AFM, and also serves as a molecular transport channel in dip-pen nanolithography (DPN). A stable meniscus is a necessary condition for DPN and for the validity of the Kelvin equation commonly applied to AFM experiments. Lattice gas Monte Carlo simulations show that, due to thermal fluctuation, a stable meniscus has a lower limit in width. We find a minimum width of 5 molecular diameters (1.9 nm) when the tip becomes atomically sharp (terminated by a single atom).     

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen; (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes.     

How entangled can a multi-party system possibly be?

The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of pure product (separable) states. Given an n-partite system composed of subsystems of dimensions $d_1,\dots ,d_n$, an upper bound for maximally allowable entanglement is derived in terms of geometric measure of entanglement. This upper bound is characterized exclusively by the dimensions $d_1,\dots ,d_n$ of composite subsystems. Numerous examples demonstrate that the upper bound appears to be reasonably tight.     

How thin can a microfiber be and still guide light?

For the adiabatically deformed optical fiber the intermode transmission amplitudes and loss vanish exponentially with the characteristic length of the fiber's nonuniformity. For this reason smoothly deformed optical fiber tapers can have very small losses. However, losses dramatically increase with a thinning of the microfiber down to a diameter much smaller than the radiation wavelength. The theory of nonadiabatic intermode transitions is briefly discussed and, by using this theory, the problem of the smallest diameter of a microfiber that can transmit evanescent radiation is studied. It is shown that even for an extremely high uniformity of microfiber the ability of light transmission does not leave much space for microfiber thinning: the propagating mode vanishes at a threshold value of the microfiber's diameter, that is smaller than the radiation wavelength by only an order of magnitude.     

How far can one send a photon?

The answer to the question How far can one send a photon? depends heavily on what one means by a photon and on what one intends to do with that photon. For direct quantum communication, the limit is approximately 500 km. For terrestrial quantum communication, near-future technologies based on quantum teleportation and quantum memories will soon enable quantum repeaters that will turn the development of a world-wide-quantum-web (WWQW) into a highly non-trivial engineering problem. For Device-Independent Quantum Information Processing, near-future qubit amplifiers (i.e., probabilistic heralded amplification of the probability amplitude of the presence of photonic qubits) will soon allow demonstrations over a few tens of kilometers.     

How can automotive friction-induced noises be related to physical mechanisms?

Three main physical mechanisms are found in the literature to explain the occurrence of friction-induced noises: the stick–slip, the sprag-slip and the mode-coupling instabilities. In order to improve the understanding of the automotive friction-induced noises and regarding the variety of these noises and the systems concerned, the consideration of these three physical mechanisms in a unique model, called phenomenological model, is proposed. The relationships between the mechanisms at the origin of friction-induced noises and the different kinds of friction-induced noises that can be perceived in a vehicle are particularly investigated. First, a simple classification of automotive-friction induced noises is proposed and highlights three noise categories: squeal, squeak and creak noises. Time simulations carried out on the phenomenological model show the qualitative reproduction of the vibrational behaviors at the origin of these three noise categories. Conditions are then proposed to define the three noise categories, based on the contact states ratios encountered in the time response. In order to understand the relationships between the three physical mechanisms and the three noise categories, a fullfact design of experiments is carried out with the phenomenological model. A system with realistic dynamic properties is used and submitted to a large number of conditions of use, allowing the appearance of a wide diversity of responses. The results show that the three mechanisms as well as the three noise categories can be obtained on a same dynamic system. They also show that creak is caused by a stick–slip phenomenon, squeal is mainly due to a mode-coupling phenomenon, while squeak can be caused either by mode-coupling or stick–slip phenomena. Finally, the occurrence of each mechanism and noise category is independently analyzed for the given dynamic system, giving quite significant trends towards model parameters. These trends highlight some interesting design levers to reduce the propensity of noise for an automotive structure.     

How small can thermal machines be? The smallest possible refrigerator

We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.     

Will a large complex system with time delays be stable?

In 1972 May showed that for a large linear system with random coupling the system size and the average coupling strength must together satisfy a simple inequality to ensure the stability of the equilibrium point. Here we extend the analysis to delay coupled systems. Our calculations establish that the same inequality obtained by May constrains the stability for systems randomly coupled through discrete and distributed delays.     

How many parameters can be identified by adaptive synchronization in chaotic systems?

Five interesting experiments have been done for a class of chaos synchronization systems with unknown parameters and unknown control directions. And three important conclusions about parameters identification have been made. First, a necessary and sufficient condition for parameters identification is obtained. Second, a Nussbaum method is proposed to solve the problem of unknown control direction. Third, the adaptive method is not infinitely effective considered for our current ability of computation and simulation algorithm.     

How much entanglement can be generated between two atoms by detecting photons?

It is possible to achieve an arbitrary amount of entanglement between two atoms using only spontaneously emitted photons, linear optics, single-photon sources, and projective measurements. This is in contrast to all current experimental proposals for entangling two atoms, which are fundamentally restricted to one entanglement bit or "ebit."     

How fast can cracks propagate?

We have performed atomic simulations of crack propagation along a weak interface joining two harmonic crystals. The simulations show that a mode II shear dominated crack can accelerate to the Rayleigh wave speed and then nucleate an intersonic daughter that travels at the longitudinal wave speed. This contradicts the general belief that a crack can travel no faster than the Rayleigh speed.     

How much information can one store in a nonequilibrium medium?

It has recently been emphasized again that the very existence of stationary stable localized structures with short-range interactions might allow one to store information in nonequilibrium media, opening new perspectives on information storage. We show how to use generalized topological entropies to measure aspects of the quantities of storable and nonstorable information. This leads us to introduce a measure of the long-term stably storable information. As a first example to illustrate these concepts, we revisit a mechanism for the appearance of stationary stable localized structures that is related to the stabilization of fronts between structured and unstructured states (or between differently structured states).     

How large is “large N c ” for nuclear matter?

We argue that a so far neglected dimensionless scale, the number of neighbors in a closely packed system, is relevant for the convergence of the large-N _c expansion at high chemical potential. It is only when the number of colors is large w.r.t. this new scale $( \sim \mathcal{O}(10))$ that a convergent large-N _c limit is reached. This provides an explanation as to why the large-N _c expansion, qualitatively successful in vacuum QCD, fails to describe high baryo-chemical potential systems, such as nuclear matter. It also means that phenomenological claims about high-density matter based on large-N _c extrapolations should be treated with caution. This work is based on [1].