Exact derivation of a finite-size-scaling law and corrections to scaling in the geometric Galton-Watson process

The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary.Comment: 21 pages, 4 figure

Field theories of active particle systems and their entropy production

Active particles that translate chemical energy into self-propulsion can maintain a far-from-equilibrium steady state and perform work. The entropy production measures how far from equilibrium such a particle system operates and serves as a proxy for the work performed. Field theory offers a promising route to calculating entropy production, as it allows for many interacting particles to be considered simultaneously. Approximate field theories obtained by coarse-graining or smoothing that draw on additive noise can capture densities and correlations well, but they generally ignore the microscopic particle nature of the constituents, thereby producing spurious results for the entropy production. As an alternative we demonstrate how to use Doi-Peliti field theories, which capture the microscopic dynamics, including reactions and interactions with external and pair potentials. Such field theories are in principle exact, while offering a systematic approximation scheme, in the form of diagrammatics. We demonstrate how to construct them from a Fokker-Planck equation (FPE) of the single-particle dynamics and show how to calculate entropy production of active matter from first principles. This framework is easily extended to include interaction. We use it to derive exact, compact and efficient general expressions for the entropy production for a vast range of interacting particle systems. These expressions are independent of the underlying field theory and can be interpreted as the spatial average of the local entropy production. They are readily applicable to numerical and experimental data. In general, any pair interaction draws at most on the three point, equal time density and an n-point interaction on the (2n-1)-point density. We illustrate the technique in a number of exact, tractable examples, including some with pair-interaction.Comment: 10 page main text, no figures; 49 pages supplement, two figure

Entropy production of non-reciprocal interactions

Non-reciprocal interactions, in general, break detailed balance. We study an active particle system where activity originates from asymmetric, pairwise interaction forces that result in an injection of energy at the microscopic scale. Using a field theory that captures microscopic dynamics, we calculate correlation functions and the entropy production to characterise the non-equilibrium properties of this many-particle active system in the stationary state. We support our analytical results with numerical simulations.Comment: 15 pages, 5 figure

Shannon entropy and particle decays

We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to the already known ones. Because the entropy is additive, one can subdivide the set of channels and discuss, for example, how much information the discovery of a new decay branching would add; or subdivide the decay distribution down to the level of individual quantum states (which can be quickly counted by the phase space). We illustrate the concept with some examples of experimentally known particle decay distributions.Comment: 12 pages, 18 plots; to appear in Nuclear Physics

The individual BSC for executives: An application of Balanced Scorecard including Total Leadership method

The use of an Individual BSC that includes metrics from both business and Total Leadership experiments it is proposed as a suitable tool to monitor the execution of executive’s personal strategy for those who want to become total leaders by fully integrating the four-way-view in an individual internal BSC perspective to get better results in both all four domains and business. When integrating the four domains: work, family, community and self, executives will improve their role as a leader and, consequently, their business performance, what is specially appreciated in highly competitive environment

Non-linear response of single-molecule magnets: field-tuned quantum-to-classical crossovers

Quantum nanomagnets can show a field dependence of the relaxation time very different from their classical counterparts, due to resonant tunneling via excited states (near the anisotropy barrier top). The relaxation time then shows minima at the resonant fields H_{n}=n D at which the levels at both sides of the barrier become degenerate (D is the anisotropy constant). We showed that in Mn12, near zero field, this yields a contribution to the nonlinear susceptibility that makes it qualitatively different from the classical curves [Phys. Rev. B 72, 224433 (2005)]. Here we extend the experimental study to finite dc fields showing how the bias can trigger the system to display those quantum nonlinear responses, near the resonant fields, while recovering an classical-like behaviour for fields between them. The analysis of the experiments is done with heuristic expressions derived from simple balance equations and calculations with a Pauli-type quantum master equation.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B, brief report

Imaging the asymmetric dust shell around CI Cam with long baseline optical interferometry

We present the first high angular resolution observation of the B[e] star/X-ray transient object CI Cam, performed with the two-telescope Infrared Optical Telescope Array (IOTA), its upgraded three-telescope version (IOTA3T) and the Palomar Testbed Interferometer (PTI). Visibilities and closure phases were obtained using the IONIC-3 integrated optics beam combiner. CI Cam was observed in the near-infrared H and K spectral bands, wavelengths well suited to measure the size and study the geometry of the hot dust surrounding CI Cam. The analysis of the visibility data over an 8 year period from soon after the 1998 outburst to 2006 shows that the dust visibility has not changed over the years. The visibility data shows that CI Cam is elongated which confirms the disc-shape of the circumstellar environment and totally rules out the hypothesis of a spherical dust shell. Closure phase measurements show direct evidence of asymmetries in the circumstellar environment of CI Cam and we conclude that the dust surrounding CI Cam lies in an inhomogeneous disc seen at an angle. The near-infrared dust emission appears as an elliptical skewed Gaussian ring with a major axis a = 7.58 +/- 0.24 mas, an axis ratio r = 0.39 +/- 0.03 and a position angle theta = 35 +/- 2 deg.Comment: 9 pages, 5 figures, accepted MNRA

A mathematical model for the optimization of e-commerce logistics operations in the face of the spread of COVID-19

In this work, it was carry out a new model of attention to product orders in e-commerce operations in a pandemic situation. The model was evaluated in situations that require capacity and flexibility for companies when the forecast presents a high level of uncertainty. A two-echelon multi-period MIP model was used. It was shown from a case example the model's behavior in stressful situations, which represent a pandemic moment or high demand, and a case in which companies can use the model for decision-making when demand is lower or stable. It is proposed to use a productivity factor and extra hours to decide to hire permanent or temporary employees to take the best strategies in its logistics operations. The results show the usability of the model for decisions and the flexibility obtained for better productivity in e-commerce operations. © 2021 IEEE