Macroscopic Research Articles

Global existence and decay estimates of the classical solution to the compressible Navier-Stokes-Smoluchowski equations in ℝ3

Abstract The compressible Navier-Stokes-Smoluchowski equations under investigation concern the behavior of the mixture of fluid and particles at a macroscopic scale. We devote to the existence of the global classical solution near the stationary solution based on the energy method under weaker conditions imposed on the external potential compared with Chen et al. (Global existence and time–decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations, Discrete Contin. Dyn. Syst. 36 (2016), no. 10, 5287–5307). Under further assumptions that the stationary solution ( ρ s ( x ) , 0 , 0 ) T {\left({\rho }_{s}\left(x),0,0)}^{T} is in a small neighborhood of the constant state ( ρ ¯ , 0 , 0 ) T {\left(\bar{\rho },0,0)}^{T} at infinity, we also obtain the time decay rates of the solution by the combination of the energy method and the linear L p {L}^{p} - L q {L}^{q} decay estimates.

Measuring gravity with milligram levitated masses.

Gravity differs from all other known fundamental forces because it is best described as a curvature of space-time. For that reason, it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here, we show gravitational coupling between a levitated submillimeter-scale magnetic particle inside a type I superconducting trap and kilogram source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors.

Fluid-mineral Equilibrium Under Nonhydrostatic Stress: Insight From Molecular Dynamics

The interpretation of phase equilibria and reactions in geological materials is based on standard thermodynamics that assumes hydrostatic and homogeneous stress conditions. However, rocks and minerals in the lithosphere can support stress gradients and nonhydrostatic stresses. Currently, there is still not an accepted macroscopic thermodynamic theory to include the effect of nonhydrostatic stress on mineral reactions, and the use of several thermodynamic potentials in stressed geological system remains under debate. In experiments under nonhydrostatic stress, it is often difficult to resolve the direct effect of differential stress on phase equilibria because pressure gradients may be developed. Such gradients can affect the metamorphic equilibria at the local scale. Here, we investigate the direct effect of a homogeneous, nonhydrostatic stress field on the solid-fluid equilibrium using molecular dynamics simulations at non-zero pressure and elevated temperature conditions. Our results show that, for simple single-component systems at constant temperature, the equilibrium fluid pressure of a stressed system is always larger than the value of fluid pressure at hydrostatic stress conditions. The displacement of the equilibrium value of the fluid pressure is about an order of magnitude smaller compared to the level of differential stress in the solid crystal. Thus, phase equilibria can be accurately predicted by taking the fluid pressure as a proxy of the equilibration pressure. On the contrary, the mean stress of the solid can deviate substantially from the pressure of the fluid in stressed systems at thermodynamic equilibrium. This has implications on the use of thermodynamic pressure in geodynamic models since the fluid pressure is a more accurate proxy for predicting the location of metamorphic reactions, while the equilibrium density of the solid has to be determined from its mean stress.

Investigation on form-preserving polishing of side-wall surfaces via an active fluid jet.

In recent years, extensive research and development have been conducted on an active fluid jet (AFJ) polishing-based post-polishing process aimed at removing periodic marks from diamond-turned surfaces. This cost-effective method demonstrates its machining capability across a wide range of materials. Notably, it excels in preserving the form accuracy during the post-polishing process for traditional optics, allowing for the attainment of high-precision shape and an ultra-smooth texture. However, the challenge arises when attempting to maintain form preservation on diamond-cut surfaces located on the side-walls of structures due to non-uniform material removal. This limitation significantly restricts its application in advanced opto-mechanical systems, including monolithic multi-surface workpieces. Therefore, this paper systematically investigates the form-preserving capability of AFJ polishing for side-wall surfaces through multi-scale analysis. The micromachining characteristics of the diamond-cut surface are elaborated upon using elastic-plastic theory, and the impact of polishing parameters on form preservation is studied at the microscopic scale. Furthermore, at the macroscopic scale, a simulation model of the AFJ polishing process is established based on fluid-structure interaction (FSI) analysis and rigid dynamic analysis. To validate the proposed theory, a series of tests are conducted. Theoretical and experimental results indicate that non-uniform material removal occurs in the contact area between the tool and the workpiece due to the influence of gravity, thereby hindering the form-preservation polishing process. Building upon the simulation model, a new AFJ tool is designed and optimized to enhance the form-preserving capability of AFJ post-polishing for side-wall surfaces. Experimental results confirm that the innovative AFJ tool uniformly eliminates the periodic marks on diamond-cut surfaces. The theory and methodology presented in this work have broad applicability to various form-preservation post-polishing processes on diamond-cut surfaces.

On a Class of Solvable Stationary Non Equilibrium States for Mass Exchange Models

We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of reversible models for which the product invariant measure is known and the gradient condition is satisfied so that we can explicitly compute the transport coefficients associated to the diffusive hydrodynamic rescaling. Based on the Macroscopic Fluctuation Theory (Bertini et al. in Rev Mod Phys 87:593–636, 2015) we have that the large deviations rate functional for a stationary non equilibrium state can be computed solving a Hamilton–Jacobi equation depending only on the transport coefficients and the details of the boundary sources. Thus, we are able to identify a class of models having transport coefficients for which the Hamilton–Jacobi equation can indeed be solved. We give a complete characterization in the case of generalized zero range models and discuss several other cases. For the generalized zero range models we identify a class of discrete models that, modulo trivial extensions, coincides with the class discussed in Frassek and Giardinà (J Math Phys 63(10):103301–103335, 2022) and a class of continuous dynamics that coincides with the class in Franceschini et al. (J Math Phys 64(4): 043304–043321, 2023). Along the discussion we obtain a complete characterization of reversible misanthrope processes solving the discrete equations in Cocozza-Thivent (Z Wahrsch Verw Gebiete 70(4):509–523, 1985).

Probing the large deviations for the beta random walk in random medium.

We consider a discrete-time random walk on a one-dimensional lattice with space- and time-dependent random jump probabilities, known as the beta random walk. We are interested in the probability that, for a given realization of the jump probabilities (a sample), a walker starting at the origin at time t=0 is at position beyond ξsqrt[T/2] at time T. This probability fluctuates from sample to sample and we study the large-deviation rate function, which characterizes the tails of its distribution at large time T≫1. It is argued that, up to a simple rescaling, this rate function is identical to the one recently obtained exactly by two of the authors for the continuum version of the model. That continuum model also appears in the macroscopic fluctuation theory of a class of lattice gases, e.g., in the so-called KMP model of heat transfer. An extensive numerical simulation of the beta random walk, based on an importance sampling algorithm, is found in good agreement with the detailed analytical predictions. A first-order transition in the tilted measure, predicted to occur in the continuum model, is also observed in the numerics.

Aouelloul impact crater, Mauritania: New structural, lithological, and petrographic data

The Aouelloul circular structure (Mauritania), 0.4 km in diameter, is a simple impact crater, which formed approximately 3 Myr ago. The Aouelloul crater was confirmed to be an impact crater based on the presence of an extraterrestrial component in glass fragments found around the crater, but so far, no convincing evidence of shock metamorphism in minerals, such as shocked quartz grains, is reported. The crater has been visited by a small number of geologists and limited information is available on deformations and impact-related effects at the macroscopic and microscopic scales. Detailed petrographic investigations of eight sandstone samples, all collected at the rim of Aouelloul during a 2019's field campaign, show that tectonic deformation lamellae occur in a number of quartz grains, but did not reveal any evidence of shock metamorphism. New observations on the distribution of the impact glass at the Aouelloul crater, exclusively located in the southern and eastern outer parts of the crater, suggest an oblique impact, from possible directions ranging from south-west to north (clockwise). Geological and lithostructural data are also presented and show that the rim of the crater is characterized by more or less disturbed metric to pluri-metric blocks of rocks showing fracturing and dipping toward either the interior or the exterior of the crater. This study confirms previous works conducted at the Aouelloul crater and illustrates the difficulty in demonstrating the impact origin of relatively small craters.

DNA Cryogels with Anisotropic Mechanical and Responsive Properties for Specific Cell Capture and Release.

Due to their programmable stimuli-responsiveness, excellent biocompatibility, and water-rich and soft structures similar to biological tissues, smart DNA hydrogels hold great promise for biosensing and biomedical applications. However, most DNA hydrogels developed to date are composed of randomly oriented and isotropic polymer networks, and the resulting slow response to biotargets and lack of anisotropic properties similar to those of biological tissues have limited their extensive applications. Herein, anisotropic DNA hydrogels consisting of unidirectional void channels internally oriented up to macroscopic length scales were constructed by a directional cryopolymerization method, as exemplified by a DNA-incorporated covalently cross-linked DNA cryogel and a DNA duplex structure noncovalently cross-linked DNA cryogel. Results showed that the formation of unidirectional channels significantly improved the responsiveness of the gel matrix to biomacromolecular substances and further endowed the DNA cryogels with anisotropic properties, including anisotropic mechanical properties, anisotropic swelling/shrinking behaviors, and anisotropic responsiveness to specific biotargets. Moreover, the abundant oriented and long macroporous channels in the gel matrix facilitated the migration of cells, and through the introduction of aptamer structures and thermosensitive polymers, an anisotropic DNA cryogel-based platform was further constructed to achieve the highly efficient capture and release of specific cells. These anisotropic DNA hydrogels may provide new opportunities for the development of anisotropic separation and biosensing systems.

Post-clustering Prioritization Framework for Autonomous Decision Making in the Absence of Ground Truth via Hypothetical Probing

A generic prioritization framework is introduced for addressing the problem of automated prioritization of region of interest or target selection. The framework is based on the assumption that clustering of preliminary data for preidentified regions or targets of interest within an operational area has already occurred, i.e., post-classification, and that the clustering quality can be expressed as an energy/objective function. Region or target of interest prioritization then means to rank regions or targets of interest according to their probability of changing the energy/objective function value upon subsequent hypothetical probing as opposed to actually conducted reexamination, i.e., thorough follow-up or in-situ measurements. The mathematical formalism for calculating these probabilities to contribute to this change of the energy/objective function value is introduced and validated through numerical simulations. Moreover, these probabilities can also be understood as a confidence-check of the classification, i.e., the pre-clustering of the preliminary data. The operation of the prioritization framework is independent of the algorithm used to pre-cluster the preliminary data, and supports autonomous decision-making. It is widely applicable across many scientific disciplines and areas, ranging from the microscopic to the macroscopic scale. Due to its ability to help maximize scientific return while optimizing resource utilization, it is particularly relevant in the context of resource-constrained autonomous robotic planetary exploration as it may extend the Remaining Useful Lifetime (RUL) – a key aspect in Prognostics and Health Management (PHM) – of space missions. On a more general, PHM-relevant level, the prioritization framework may provide an additional mechanism of identifying and correcting the maintenance status of system components to assist predictive maintenance or condition-based maintenance.

Macroscopic fluctuation theory of local time in lattice gases

The local time in an ensemble of particles measures the amount of time the particles spend in the vicinity of a given point in space. Here we study fluctuations of the empirical time average R=T−1∫0Tρx=0,tdt of the density ρx=0,t at the origin (so that R is the local time spent at the origin, rescaled by T) for an initially uniform one-dimensional diffusive lattice gas. We consider both the quenched and annealed initial conditions and employ the Macroscopic Fluctuation Theory (MFT). For a gas of non-interacting random walkers (RWs) the MFT yields exact large-deviation functions of R, which are closely related to the ones recently obtained by Burenev et al. (2023) using microscopic calculations for non-interacting Brownian particles. Our MFT calculations, however, additionally yield the most likely history of the gas density ρ(x,t) conditioned on a given value of R. Furthermore, we calculate the variance of the local time fluctuations for arbitrary particle- or energy-conserving diffusive lattice gases. Better known examples of such systems include the simple symmetric exclusion process, the Kipnis-Marchioro-Presutti model and the symmetric zero-range process. Our results for the non-interacting RWs can be readily extended to a step-like initial condition for the density.

Microstructure of electronic-grade polycrystalline silicon core-matrix interface

This paper focuses on the problems encountered in the production process of electronic-grade polycrystalline silicon. It points out that the characterization of electronic-grade polycrystalline silicon is mainly concentrated at the macroscopic scale, with relatively less research at the mesoscopic and microscopic scales. Therefore, we utilize the method of physical polishing to obtain polysilicon characterization samples and then the paper utilizes metallographic microscopy, scanning electron microscopy-electron backscatter diffraction technology, and aberration-corrected transmission electron microscopy technology to observe and characterize the interface region between silicon core and matrix in the deposition process of electronic-grade polycrystalline silicon, providing a full-scale characterization of the interface morphology, grain structure, and orientation distribution from macro to micro. Finally, the paper illustrates the current uncertainties regarding polycrystalline silicon.

Averaging on Macroscopic Scales with Application to Smoluchowski–Kramers Approximation

Averaging on Macroscopic Scales with Application to Smoluchowski–Kramers Approximation

‘Typical container’ of Chinese civilisation: ‘Yellow-Canal-Yangtze’ watershed community

The watershed is the earliest geographical unit of human activity and the tensest area in terms of human–land relations. Focussing solely on individual watershed spaces makes it difficult to comprehensively reflect and address complex human–land issues. For the complex processes of the origin, dissemination, communication and integration of civilisations, a more macroscopic scale is also needed for systematic understanding and analysis. The exchange and mutual learning amongst the Yellow River Basin, Yangtze River Basin and Grand Canal region promote the diversity and innovation of culture, making them the ‘typical containers’ of Chinese civilisation. Based on the uniqueness and correlation of regions such as the Yellow River Basin, Yangtze River Basin and Grand Canal, this study constructs the concept of a ‘Yellow-Canal-Yangtze’ watershed community, combining existing disciplinary advances and summarizing its spatial, temporal and elemental characteristics. This research is conducive to promoting the creative transformation and innovative development of excellent traditional culture, assisting in the protection of watershed cultural heritage systems and the governance of watershed ecosystems, and promoting regional coordinated and interconnected development.

Optimal design and experimental validation of emulsified cosmetic products: A multiscale approach

There is an increasing demand for sustainable and cost-effective chemical products, such as eco-friendly emulsified products, contributing to a resource-efficient economy and a reduction in our ecological footprint. This new paradigm challenges the chemical industry due to a lack of accurate predictive models and understanding of emulsified systems. This study presents an optimization strategy to design cosmetic emulsions through a multiscale approach, which represents an opportunity to boost and improve the design of these products. The study employs a model-based design approach considering operating conditions, product formulation, economic performance, consumer preference, and the emulsions properties at different scales. At the macroscopic scale, rheological and textural properties are considered and coupled with a Population Balance Model, which estimates the drop size distribution (i.e., microscopic scale). The optimal emulsion formulation is established for consumer preference and product profit maximization scenarios. According to the economic model, a higher level of consumer preference is expected to lead to increased product sales. However, the results also indicate that consumer preference maximization may not necessarily correlate with higher profits. Thus, the profit maximization scenario offers a better balance between consumer preference and economic performance. Also, experimental validation was performed for the product properties and operating conditions.

Intrinsic dichroism in amorphous and crystalline solids with helical light

Amorphous solids do not exhibit long-range order due to the disordered arrangement of atoms. They lack translational and rotational symmetry on a macroscopic scale and are therefore isotropic. As a result, differential absorption of polarized light, called dichroism, is not known to exist in amorphous solids. Using helical light beams that carry orbital angular momentum as a probe, we demonstrate that dichroism is intrinsic to both amorphous and crystalline solids. We show that in the nonlinear regime, helical dichroism is responsive to the short-range order and its origin is explained in terms of interband multiphoton assisted tunneling. We also demonstrate that the helical dichroism signal is sensitive to chirality and its strength can be controlled and tuned using a superposition of OAM and Gaussian beams. Our research challenges the conventional knowledge that dichroism does not exist in amorphous solids and enables to manipulate the optical properties of solids.

Geometry-Dependent Elastic Flow Dynamics in Micropillar Arrays.

Regular device-scale DNA waves for high DNA concentrations and flow velocities have been shown to emerge in quadratic micropillar arrays with potentially strong relevance for a wide range of microfluidic applications. Hexagonal arrays constitute another geometry that is especially relevant for the microfluidic pulsed-field separation of DNA. Here, we report on the differences at the micro and macroscopic scales between the resulting wave patterns for these two regular array geometries and one disordered array geometry. In contrast to the large-scale regular waves visible in the quadratic array, in the hexagonal arrays, waves occur in a device-scale disordered zig-zag pattern with fluctuations on a much smaller scale. We connect the large-scale pattern to the microscopic flow and observe flow synchronization that switches between two directions for both the quadratic and hexagonal arrays. We show the importance of order using the disordered array, where steady-state stationary and highly fluctuating flow states persist in seemingly random locations across the array. We compare the flow dynamics of the arrays to that in a device with sparsely distributed pillars. Here, we observe similar vortex shedding, which is clearly observable in the quadratic and disordered arrays. However, the shedding of these vortices couples only in the flow direction and not laterally as in the dense, ordered arrays. We believe that our findings will contribute to the understanding of elastic flow dynamics in pillar arrays, helping us elucidate the fundamental principles of non-Newtonian fluid flow in complex environments as well as supporting applications in engineering involving e.g., transport, sorting, and mixing of complex fluids.

Real-time and quantitative investigation of zwitterionic surfactant interaction at oil-water interface: Interferometry experimental and MD simulation insights

In this work, the interaction performances at octadecane oil–water interface were investigated for zwitterionic surfactants of dodecyl dimethyl hydroxypropyl sulfobetaine (HSB-12) and hexadecyl dimethyl hydroxypropyl sulfobetaine (HSB-16) from both experimental and simulation insights. For macroscopic experiment, optical interferometry methodology was developed to real-time measure the interfacial interaction process and obtain the quantitative interfacial thickness and mass results. The four-step dynamic process (diffusion, adsorption, arrangement and aggregation) was characterized by kinetic analysis, indicating arrangement process as slow-limiting step. The rate of the four step process (diffusion rate k1(dif), adsorption rate k2(ads), arrangement rate k3(arr), and aggregation rate k4(agg)) is represented as k3(arr)<k1(dif),k2(ads),k4(agg). The Langmuir model was characterized by thermodynamic analysis, deducing the aggregation spontaneity of HSB-16 > HSB-12. The free energy of the aggregation stages of HSB-16 and HSB-12 was expressed as ΔGagg(HSB16)=-3.95 kJ/mol < ΔGagg(HSB12)=-3.13kJ/mol. For microscopic simulation, the interaction configurations and interaction energies were obtained through molecular dynamics simulation (MDS) calculation. The interaction stability and interaction strength were indicated to be HSB-16 > HSB-12. The interaction mechanism was explained by proposing molecular-orientation model below critical micelle concentration (CMC) and layer-interaction model above CMC. The different mechanisms were attributed to electronic attraction between surfactant molecules and hydrophobic interaction between surfactant and oil molecules. This work successfully constructs the interfacial platform for oil–water interface analysis, which not only elucidate the surfactant-oil intermolecular interactions but also provide mechanism understanding from macroscopic and microscopic scales.

Constructing universal phenomenology for biological cellular systems: an idiosyncratic review on evolutionary dimensional reduction

The possibility of establishing a macroscopic phenomenological theory for biological systems, akin to the well-established framework of thermodynamics, is briefly reviewed. We introduce the concept of an evolutionary fluctuation–response relationship, which highlights the tight correlation between the variance in phenotypic traits caused by genetic mutations and by internal noise. We provide a distribution theory that allows us to derive these relationships, which suggests that the changes in traits resulting from adaptation and evolution are considerably constrained within a lower-dimensional space. We explore the reasons behind this dimensional reduction, focusing on the constraints posed by the requirements for steady growth and robustness achieved through the evolutionary process. We draw support from recent laboratory and numerical experiments to substantiate our claims. The universality of evolutionary dimensional reduction is presented and potential theoretical formulations for it are discussed. We conclude by briefly considering the prospects of establishing a macroscopic framework that characterizes biological robustness and irreversibility in cell differentiation, as well as an ideal cell model.

Exploring Transformation in Flux-Like Pattern – A Review of The Chinese Biantong in Yijing

One of the central features of the _Yijing_ is its use of 陰陽 _yin-yang_ correlative cosmology, a fundamental concept in traditional Chinese philosophy. This cosmology involves the idea that all things in the universe are interconnected and interdependent, each possessing _yin_ (negative, feminine) and _yang_ (positive, masculine) energies. Moreover, these energies are constantly in flux and transformation, with their balance continually shifting. Bohm's wholeness, also known as Bohm's holomovement, is a concept developed by physicist David Bohm as part of his interpretation of quantum mechanics. According to Bohm, the universe is fundamentally interconnected and interdependent, with all aspects of the universe influencing and being influenced by one another. This interconnectedness is reflected in the behaviour of subatomic particles, which can exhibit non-local correlations that classical physics cannot explain. Bohm's wholeness is similar to other physics and philosophy theories that emphasise the universe's interconnectedness. For example, one such theory is non-dualism, which posits that there is no fundamental separation between the self and the universe and that the self is an expression of the underlying unity of all things. Finally, the concept of entanglement in quantum mechanics also suggests a fundamental interconnectedness between particles, with changes in the state of one particle instantaneously affecting the state of another particle, regardless of their spatial separation. The significance of 變通 _biantong_ in Chinese philosophy is explored in relation to _yin_ and _yang_ energies constantly transforming and balancing each other in a continuous cycle. Similarly, Bohm's holomovement concept highlights the universe's interconnectedness and constant flux. The flux-like variables provide insights into the system's macroscopic and microscopic details, where transformation and change are fundamental aspects of reality. The probabilistic nature of human affairs and subatomic particles implies that their properties continually change and transform in response to the surrounding environment, reflecting the integral interdependence of all things. This paper emphasizes the significance of transformation and changes in comprehending reality by examining the concepts of yin and yang energies, Bohm's wholeness, and flux-like variables. The dynamic and interconnected nature of the universe necessitates an understanding of this constant state of flux, whether on a macroscopic or microscopic scale. This knowledge is vital for understanding the behaviour of subatomic particles and the natural world.

Zigzag optical cavity for sensing and controlling torsional motion

Precision sensing and manipulation of milligram-scale mechanical oscillators has attracted growing interest in the fields of table-top explorations of gravity and tests of quantum mechanics at macroscopic scales. Torsional oscillators present an opportunity in this regard due to their remarked isolation from environmental noise. For torsional motion, an effective employment of optical cavities to enhance optomechanical interactions—as already established for linear oscillators—so far faced certain challenges. Here, we propose a concept for sensing and manipulating torsional motion, where exclusively the torsional rotations of a pendulum are mapped onto the path length of a single two-mirror optical cavity. The concept inherently alleviates many limitations of previous approaches. A proof-of-principle experiment is conducted with a rigidly controlled pendulum to explore the sensing aspects of the concept and to identify practical limitations in a potential state-of-the art setup. Based on this study, we anticipate development of precision torque sensors utilizing torsional pendulums that can support sensitivities below 10−19Nm/Hz, while the motion of the pendulums are dominated by quantum radiation pressure noise at sub-microwatts of incoming laser power. These developments will provide horizons for experiments at the interface of quantum mechanics and gravity. Published by the American Physical Society 2024