On certain homological invariant and its relation with Poincaré duality pairs

Let G be a group, S = {Sᵢ, i ∊ I} a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a Z₂G-module. In [4] the authors defined a homological invariant E*(G, S,M), which is “dual” to the cohomological invariant E(G, S,M), defined in [1]. In this paper we present a more general treatment of the invariant E*(G, S,M) obtaining results and properties, under a homological point of view, which are dual to those obtained by Andrade and Fanti with the invariant E(G, S,M). We analyze, through the invariant E*(G, S,M), properties about groups that satisfy certain finiteness conditions such as Poincaré duality for groups and pairs

Theoretical framework of radiation force in surface acoustic waves for modulated particle sorting

Sorting specific target entities from sample mixtures is commonly used in many macroscale laboratory processing, such as disease diagnosis or treatment. Downscaling of sorting systems enables less laboratory space and fewer quantities of sample and reagent. Such lab-on-a-chip devices can perform separation functions using passive or active sorting methods. Such a method, acoustic sorting, when used in microfluidics, offers contactless, label-free, non-invasive manipulation of target cells or particles and is therefore the topic of active current research. Our phase-modulated sorting technique complements traditional time-of-flight techniques and offers higher sensitivity separation using a periodic signal. By cycling of this periodic signal, the target entities are gradually displaced compared to the background debris, thereby achieving sorting. In this paper, we extend the knowledge on phase-modulated sorting techniques. Firstly, using numerical simulations, we confirm the sorting role of our proposed primary acoustic radiation force within surface wave devices. Secondly, a threefold agreement between analytical, numerical and experimental sorting trajectories is presented

Generating airborne ultrasonic amplitude patterns using an open hardware phased array

Holographic methods from optics can be adapted to acoustics for enabling novel applications in particle manipulation or patterning by generating dynamic custom-tailored acoustic fields. Here, we present three contributions towards making the field of acoustic holography more widespread. Firstly, we introduce an iterative algorithm that accurately calculates the amplitudes and phases of an array of ultrasound emitters in order to create a target amplitude field in mid-air. Secondly, we use the algorithm to analyse the impact of spatial, amplitude and phase emission resolution on the resulting acoustic field, thus providing engineering insights towards array design. For example, we show an onset of diminishing returns for smaller than a quarter-wavelength sized emitters and a phase and amplitude resolution of eight and four divisions per period, respectively. Lastly, we present a hardware platform for the generation of acoustic holograms. The array is integrated in a single board composed of 256 emitters operating at 40 kHz. We hope that the results and procedures described within this paper enable researchers to build their own ultrasonic arrays and explore novel applications of ultrasonic holograms.This research was funded by the Government of Navarre (FEDER) 0011-1365-2019-000086 and from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 101017746, TOUCHLESS

Monte-Carlo based sensitivity analysis of acoustic sorting methods

Separation in microfluidic devices is a crucial enabling step for many industrial, biomedical, clinical or chemical applications. Acoustic methods offer contactless, biocompatible, scalable sorting with high degree of reconfigurability and are therefore favored techniques. The literature reports on various techniques to achieve particle separation, but these do not investigate the sensitivity of these methods or are difficult to compare due to the lack of figures of merit. In this paper, we present analytical and numerical sensitivity analysis of the time-of-flight and a phase-modulated sorting scheme against various extrinsic and intrinsic properties. The results reveal great robustness of the phase-modulated sorting method against variations of the flow rate or acoustic energy density, while the time-of-flight method shows lower efficiency drop against size and density variations. The results presented in this paper provide a better understanding of the two sorting methods and offer advice on the selection of the right technique for a given sorting application

Estimation of loan portfolio risk on the basis of Markov chain model

A change of shares of credits portfolio is described by Markov chain with discrete time. A credit state is determined on as an accessory to some group of credits depending on presence of indebtedness and its terms. We use a model with discrete time and fix the system state through identical time intervals - once a month. It is obvious that the matrix of transitive probabilities is known incompletely. Various approaches to the matrix estimation are studied and methods of forecast the portfolio risk are proposed. The portfolio risk is set as a share of problematic loans. We propose a method to calculate necessary reserves on the base of the considered model. © 2013 IFIP International Federation for Information Processing.German Sci. Found. (DFG) Eur. Sci. Found. (ESF);Natl. Inst. Res. Comput. Sci. Control France (INRIA);DFG Research Center MATHEON;Weierstrass Institute for Applied Analysis and Stochastics (WIAS);European Patent Offic

Particle separation in surface acoustic wave microfluidic devices using reprogrammable, pseudo-standing waves

We report size and density/compressibility-based particle sorting using on-off quasi-standing waves based on the frequency difference between two ultrasonic transducers. The 13.3 MHz fundamental operating frequency of the surface acoustic wave microfluidic device allows the manipulation of particles on the micrometer scale. Experiments, validated by computational fluid dynamics, were carried out to demonstrate size-based sorting of 5–14.5 μm diameter polystyrene (PS) particles and density/compressibility-based sorting of 10 μm PS, iron-oxide, and poly(methyl methacrylate) particles, with densities ranging from 1.05 to 1.5 g/cm3. The method shows a sorting efficiency of >90% and a purity of >80% for particle separation of 10 μm and 14.5 μm, demonstrating better performance than similar sorting methods recently published (72%–83% efficiency). The sorting technique demonstrates high selectivity separation of particles, with the smallest particle ratio being 1.33, compared to 2.5 in previous work. Density/compressibility-based sorting of polystyrene and iron-oxide particles showed an efficiency of 97 ± 4% and a purity of 91 ± 5%. By varying the sign of the acoustic excitation signal, continuous batch acoustic sorting of target particles to a desired outlet was demonstrated with good sorting stability against variations of the inflow rates

Universal Critical Behavior of Aperiodic Ferromagnetic Models

We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of $q$-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a non-trivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent $\alpha$ of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free-energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of $q$). The critical exponents do not depend on the strengths of the exchange interactions.Comment: 4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communicatio

Dynamic Scaling in Diluted Systems Phase Transitions: Deactivation trough Thermal Dilution

Activated scaling is confirmed to hold in transverse field induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold but well bellow and above it including the Griffiths-McCoy phase. A novel deactivation phenomena in the Griffiths-McCoy phase is observed using a thermal (in contrast to random) dilution of the system.Comment: 4 pages, 4 figures, RevTe

On the critical behavior of disordered quantum magnets: The relevance of rare regions

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered non-perturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.Comment: 16 pp., REVTeX, epsf, 2 figs, final version as publishe