Random Collisions Research Articles

Equilibrium Dynamics of Mutually Confined Waves with Signed Analogous Masses.

We report the first experimental realization of equilibrium dynamics of mutually confined waves with signed analogous masses in an optical fiber. Our Letter is mainly demonstrated by considering a mutual confinement between a soliton pair and a dispersive wave experiencing opposite dispersion. The resulting wave-packet complex is found robust upon random perturbation and collision with other waves. The equilibrium dynamics are also extended to scenarios of more than three waves. Our finding may trigger fundamental interest in the dynamics of many-body systems arising from the concept of negative mass, which is promising for new applications based on localized nonlinear waves.

Identification of Ballast Fouling Status and Mechanized Cleaning Efficiency Using FDTD Method

Systematic assessment of ballast fouling and mechanized cleaning efficiency through ground penetrating radar (GPR) is vital to ensure track stability and safe train transportation. Nevertheless, conventional methods of ballast fouling inspection and evaluation impede construction progress and escalate the cost of maintenance. This paper proposes a novel method using random irregular polygons and collision detection algorithms to model the ballast layer and simulated using the finite-difference time-domain (FDTD) algorithm. Hilbert transform energy, S-transform, and energy integration curve are employed to identify ballast fouling and cleaning efficiency. The highly fouled ballast exhibits concentrated Hilbert transform energy, increased energy attenuation rate in S-transform with depth in the 1.0-3.0 GHz, along with a stronger energy integration curve. Clean or post-cleaning ballast shows opposite results. Experiments on a passenger trunk line in southern China validated the method’s accuracy after mechanized ballast cleaning. This approach guides GPR-based detection and supports railway maintenance. Future studies will consider heterogeneous properties and the three-dimensional structure of the ballast layer.

Formation of the Transition Region for the Quiet Sun

We propose a partially ionized collisional two-fluid model of the formation of the transition region between the cool dense chromosphere and hot tenuous corona for the quiet Sun. The chromosphere is treated as an isothermal gravity-bound two-fluid stratified atmosphere without appreciable vertical flow, on average. The different scale heights of the two fluids result in vertical evolution of the ionization state, and the transition region can be defined according to the ionization fraction. The transition region starts at the altitude where the ionization fraction reaches 0.5, the demarcation between the weakly and strongly ionized gas. The upper border of the region is defined as the temperature at which the particles possess enough energy for ionization, i.e., the first ionization potential. Within the transition region is a diffusion process in which the cold chromospheric particles gain energy and ionize through random collisions with hot coronal particles diffusing upward into the corona, whereas, when colliding with cold chromospheric particles, hot coronal particles lose energy, recombine, and fall into the chromosphere. The type II spicules can be generated when and where the local heating rate is so high that the conditions for a stratified chromosphere are not satisfied; upward flow is formed, penetrating the corona where the chromospheric gas in the spicule is ionized and dispersed. The enhanced radiation via those chromospheric neutral particles cools the coronal gas, and more recombination occurs, producing enhanced downward diffusion. The model reproduces key structural features of the transition region from first principles and a minimum of arbitrary parameters.

The research on interfacial area transport equation in rectangular channels: Experimental research and models development of sink and source terms

Interfacial area concentration is a crucial constitutive parameter to close the two-fluid model, the accuracy of whose prediction is vital, so the interfacial area transport equation (IATE) has been proposed. According to the analysis of experimental results involving bubble interaction mechanisms in the rectangular channel from the bubbly-to-slug flow, new sink and source terms in a one-group IATE are put forward in this study. The new source term aroused by random collision is considered with relative velocity inducing collision and the effect of gap size on coalescence efficiency. Besides, the number density of small and large bubbles is considered respectively to model the source term of wake entrainment. Combined with the source terms of break up brought by turbulent impact and expansion caused by the pressure gradient, a new one-group IATE applicable to rectangular channels are completed. The coefficients in the newly-derived model are determined by experimental results of 4 × 66 mm and 8 × 66 mm vertical rectangular channels under co-current upward air-water two-phase flow, and the average relative error is 11.9%. Furthermore, the new model is also testified by the experimental result in the 6 × 66 mm rectangular channel independently, and the average relative error is 14.4%. Generally, the new model is feasible to predict the change of the interfacial area concentration in different rectangular channels.

The research on the interfacial area transport equation in rectangular channels: Interfacial characteristics distribution and bubbles interaction mechanism

The interfacial area transport equation (IATE) is employed to describe the evolution of interfacial structure and evaluate the interfacial area concentration of two-phase flow. However, the interaction mechanisms among bubbles change in different rectangular channels, significantly impacting interfacial characteristics and source terms in IATE. In order to study the interface characteristics and mechanism of bubble interaction in rectangular channels with different gap sizes, an experimental study was conducted on the upward mixture flow of air and water in an adiabatic vertical channel under atmospheric pressure. Two channels with cross-sections of 4 × 66 mm and 8 × 66 mm were selected. The superficial velocities of water and air were 0.5–3 and 0–1.12 m/s, respectively, almost at the transitional region of bubbly to slug flow. Flat electrodes and the four-sensor probes measured the interfacial characteristics. This study analyzes the development of interface and mechanism of interaction among bubbles. The result shows that the evolution in the distribution of void fraction and interfacial area concentration significantly depends on the flow regime, flow rate, and cross-sectional geometric size of channels. Under the condition of a lower liquid flow rate, the gap size of the channel plays a vital role in the efficiency of bubble coalescence, influencing the mechanisms of the random collision and wake entrainment among bubbles. However, the interfacial parameter distribution under higher liquid rate conditions is dominated by turbulence intensity and flow regime, and the mechanisms of bubble interaction become identical. Finally, the mechanisms of interaction among bubbles (random collision and wake entrainment) are analyzed based on the development of interfacial characteristics. In a word, based on the conclusions specified in this research, the new models of source terms of ITAE in rectangular channels will be predictably established in the future.

Calculation of Concentration Distribution of Steady Flow Aerosol by Langevin Dynamics Method

Langevin dynamics (LD) method is a modelling technique using pseudo-random numbers to reproduce the acceleration of aerosol particles due to random collisions of gas molecules onto the particles. Although the LD method can reproduce the Brownian motion of particles and motion due to inertial force and/or external force, it is difficult to understand the behavior of aerosol, which is group of particles, from the information on the motion of individual particles. In this study, a novel calculation method was developed to obtain the concentration distribution of aerosol by accumulating the information of position of particles calculated by the LD method, and it was applied to the diffusion of aerosol flowing steadily in a cylindrical tube. The concentration distribution obtained by this method agreed well with that obtained by solving the conventional convective-diffusion equation. Furthermore, change in cup-mixing concentration of aerosol in axial direction calculated from the concentration distribution agreed well also with the penetration expressed by Gormley & Kennedy.

A Monte Carlo code for the collisional evolution of porous aggregates (CPA)

Context. The collisional evolution of submillimeter-sized porous dust aggregates is important in many astrophysical fields. Aims. We have developed a Monte Carlo code to study the processes of collision between mass-asymmetric, spherical, micron-sized porous silica aggregates that belong to a dust population. Methods. The Collision of Porous Aggregates (CPA) code simulates collision chains in a population of dust aggregates that have different sizes, masses, and porosities. We start from an initial distribution of granular aggregate sizes and assume some collision velocity distribution. In particular, for this study we used a random size distribution and a Maxwell-Boltzmann velocity distribution. A set of successive random collisions between pairs of aggregates form a single collision chain. The mass ratio, filling factor, and impact velocity influence the outcome of the collision between two aggregates. We averaged hundreds of thousands of independent collision chains to obtain the final, average distributions of aggregates. Results. We generated and studied four final distributions (F), for size (n), radius (R), porosity, and mass-porosity distributions, for a relatively low number of collisions. In general, there is a profuse generation of monomers and small clusters, with a distribution F (R) ∝ R−6 for small aggregates. Collisional growth of a few very large clusters is also observed. Collisions lead to a significant compaction of the dust population, as expected. Conclusions. The CPA code models the collisional evolution of a dust population and incorporates some novel features, such as the inclusion of mass-asymmetric aggregates (covering a wide range of aggregate radii), inter-granular friction, and the influence of porosity.

MATHEMATICS AS AN ORGANIZING PRINCIPLE OF THE SYSTEM OF CHARACTERS IN A. BELY’S NOVEL PETERSBURG

The paper attempts to prove that mathematics is not just one of the keys to comprehending the conceptosphere of A. Bely’s novel Petersburg, but the basis of his poetics, including the character sphere. It is the mathematical approach to the ways of grouping characters, as well as to the types of psychological analysis, that ensures the compositional unity of the chaotic, ‘unassembled’, at fi rst sight, text. Th e ‘brain game’ of the characters and the author-narrator, which reveals the textgenerating algorithm of the novel and provides seemingly unlimited freedom to its creator, turns out to be a carefully adjusted ‘program’ based on a system of binary oppositions. A. Bely’s Petersburg, for all its ornamental ‘motleyness’, is one of the most well-ordered texts of Russian literature: random encounters and collisions of characters, their chaotic movements around the city, strange actions, as well as ‘disorderly’ thoughts, have a strict ‘mathematical foundation’. At the same time, the principle of binary oppositions as the organizing principle of the system of characters corresponds to the logic of the neo-mythological text, which is characterized by the mutual refl ection of characters into each other, as well as the division of a single ‘pro-hero’ into novel doubles. The philosophical ideas of Vyach. Ivanov, dating back to the teachings of the Pythagoreans and their interpretation of the monad and dyad (as the essence of Apollo and Dionysus), are correlated in the novel with the scientific discoveries of Professor N.V. Bugaev (arrhythmology, the doctrine of ‘continuity’ and ‘discontinuity’). Moreover, it is emphasized that Bely’s interest in the categories of singularity and multiplicity, which sets the mathematically visual vector of perception of the text — and above all its system of characters — reveals a typological relationship with other areas of mathematical knowledge (in particular, with the Banach—Tarski paradox).

Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices

Let X = { X ( t ) , t ∈ R N } X= \{X(t), t \in \mathbb {R}^N\} be a centered Gaussian random field with values in R d \mathbb {R}^d satisfying certain conditions and let F ⊂ R d F \subset \mathbb {R}^d be a Borel set. In our main theorem, we provide a sufficient condition for F F to be polar for X X , i.e. P ( X ( t ) ∈ F for some t ∈ R N ) = 0 \mathbb P\big ( X(t) \in F \text { for some } t \in \mathbb {R}^N\big ) = 0 , which improves significantly the main result in Dalang et al. [Ann. Probab. 45 (2017), pp. 4700–4751], where the case of F F being a singleton was considered. We provide a variety of examples of Gaussian random field for which our result is applicable. Moreover, by using our main theorem, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries that was left open in Jaramillo and Nualart [Random Matrices Theory Appl. 9 (2020), p. 26] and Song et al. [J. Math. Anal. Appl. 502 (2021), p. 22].

INFLUENCE OF ELECTROMAGNETIC RADIATION ON RESISTANCE OF SEMICONDUCTOR DEVICES

The subject matter is the processes of analysis and mechanisms of appearance of instabilities of natural vibrations of semiconductor structures., due to their interaction with flows of charged particles under the influence of external electromagnetic radiation. It is shown that the influence of pulsed electromagnetic radiation is accompanied by the appearance of currents in the conductive elements of products that are capable of exciting natural oscillations of semiconductor components and are the cause of failures of radio products. The aim is to develop the theory of collisionless damping of surface polaritons in the classical approximation, as well as to study the mechanisms of collisionless damping of surface plasmons at the boundaries of semiconductor components of radio products under conditions when the temperature of carriers of conducting solids is much lower than the plasmon energy (quantum approximation). The objectives are: a kinetic equation describing the change in the number of surface plasmons as a result of their interaction with conduction electrons; obtaining its solution, which determine the decrement of oscillations and the power of spontaneous emission of particles. The methods used are: a method of successive approximations for solving the kinetic equations of the charged particle flux - semiconductor structure system within the framework of the quantum approach, when the interaction of waves and particles is in the nature of random collisions and is described by the method of secondary quantization of the system (representation of occupation numbers). The following results are obtained: Expressions are obtained for the decrements of surface plasmons in the presence of an infinitely high and infinitely small potential barrier at the interface between media. A kinetic equation is obtained that describes the change in the number surface plasmons as a result of their interaction with conduction electrons; his decisions are given, which determine oscillation decrement. Expressions are obtained for the decrements of surface plasmons at presence of infinitely high and infinitely small potential barrier at the interface between A physical model of the occurrence of reversible failures (effects induced by electromagnetic radiation currents per volt - ampere characteristics of semiconductor devices). The ranges of parameters of the external electromagnetic radiation at which this physical model is realized. Conclusion. Calculated relations are obtained that relate the parameters of semi-conductor structures: the concentration of free carriers, permittivity, carrier temperature with the value oscillation decrement in the classical and quantum approximations. The comparative analysis of quantitative estimates of the increments of oscillation instabilities carried out in the work makes it possible to solve the problems of optimizing the operating characteristics of active devices in the microwave range. The results of the work can be used in the development of microwave devices designed to amplify, generate and convert electromagnetic oscillations in the millimeter and submillimeter ranges.

Nucleic Acid Amplification by Template-Dominated Click Chemistry for Ultrasensitive DNA/RNA Detection on an Electrochemical Readout Platform.

As an enzyme-free exponential nucleic acid amplification method, the click chemistry-mediated ligation chain reaction (ccLCR) has shown great prospects in the molecular diagnosis. However, the current optics-based ccLCR is challenged by remarkable nonspecific amplification, severely hindering its future application. This study demonstrated that the severe nonspecific amplification was generated probably due to high random collision in the high DNA probe concentration (μM level). To solve this hurdle, a nucleic acid template-dominated ccLCR was constructed using nM-level DNA probes and read on an electrochemical platform (cc-eLCR). Under the optimal conditions, the proposed cc-eLCR detected a low-level nucleic acid target (1 fM) with a single-base resolution. Furthermore, this assay was applied to detect the target of interest in cell extracts with a satisfactory result. The proposed cc-eLCR offers huge possibility for click chemistry-mediated enzyme-free exponential nucleic acid amplification in the application of medical diagnosis and biomedical research.

Vibration-collision mechanism of dual-stabilizer bottom hole assembly system in vertical wellbore trajectory

The lateral vibration of drill string causes well deviation and the collision between drill collar and sidewall, and severe lateral vibration even affects the drilling safety or reliability. In view of the problems above, the lateral vibration characteristics of drill string need to be analyzed. Therefore, a newly vibration-collision model of BHA (bottom hole assembly) with random collision characteristics is proposed in this paper. Firstly, the dynamic model of drill collar with double stabilizer is presented by utilizing the Lagrange equations. Secondly, the dynamic characteristics of drill collar in air and mud drilling is analyzed with different collision frequencies. Subsequently, the displacement and motion trajectory of drill collar under different structure parameters of BHA and mechanical parameters of system are investigated by numerical simulation. Finally, the influence of rotation speed of BHA and length of drill collar on lateral vibration of drill collar is discussed. The results indicate that the lateral vibration of drill collar in air drilling is more serious than that in mud drilling; and the higher the collision frequency, the more severe the lateral vibration. Improving rotation speed of BHA, length of drill collar and WOB (weight on bit) have promoting influence on lateral vibration of drill collar; however, increasing stabilizer diameter has suppressing influence on lateral vibration of drill collar. The research findings give reasonable guidance for structure design of BHA and selection of mechanical parameters of system.

Deep Learning Based Double-Contention Random Access for Massive Machine-Type Communication

With the rapid development of 5G, massive machine-type communication is expected to experience significant growth, leading to severe random access collisions. To address this issue, we first adopt deep neural networks to detect random access collisions by learning the features of the received signals. Based on the collision-detection results, we propose a double-contention random access (DCRA) scheme, with which the base station can schedule one more contention process for devices experiencing collisions. To fully harness the collision-resolution capability of the proposed DCRA scheme, we further analyze its performance and illustrate how to tune the backoff parameters to optimize the network throughput. It is revealed that the maximum throughput of the DCRA scheme depends on the number of random access preambles and the collision recognition accuracy. The corresponding optimal backoff parameters are then obtained, which greatly facilitates implementations in practice. Simulation results show that with a high collision recognition accuracy, the proposed scheme can achieve significant throughput improvement.

Deep Reinforcement Learning-Based Grant-Free NOMA Optimization for mURLLC

Grant-free non-orthogonal multiple access (GF-NOMA) is a potential technique to support massive Ultra-Reliable and Low-Latency Communication (mURLLC) service. However, the dynamic resource configuration in GF-NOMA systems is challenging due to random traffics and collisions, that are unknown at the base station (BS). Meanwhile, joint consideration of the latency and reliability requirements makes the resource configuration of GF-NOMA for mURLLC more complex. To address this problem, we develop a novel learning framework for signature-based GF-NOMA in mURLLC service taking into account the multiple access signature collision, the UE detection, as well as the data decoding procedures for the K-repetition GF and the Proactive GF schemes. The goal of our learning framework is to maximize the long-term average number of successfully served users (UEs) under the latency constraint. We first perform a real-time repetition value configuration based on a double deep Q-Network (DDQN) and then propose a Cooperative Multi-Agent learning technique based DQN (CMA-DQN) to optimize the configuration of both the repetition values and the contention-transmission unit (CTU) numbers. Our results show the superior performance of CMA-DQN over the conventional load estimation-based uplink resource configuration approach (LE-URC) in heavy traffic and demonstrate its capability in dynamically configuring in long term for mURLLC service. In addition, with our learning optimization, the Proactive scheme always outperforms the K-repetition scheme in terms of the number of successfully served UEs, especially under the high backlog traffic scenario.

Binary collisions of dark matter blobs

We describe the model-independent mechanism by which dark matter and dark matter structures heavier than ~ 8 × 1011 GeV form binary pairs in the early Universe that spin down and merge both in the present and throughout the Universe’s history, producing potentially observable signals. Sufficiently dense dark objects will dominantly collide through binary mergers instead of random collisions. We detail how one would estimate the merger rate accounting for finite size effects, multibody interactions, and friction with the thermal bath. We predict how mergers of dark dense objects could be detected through gravitational and electromagnetic signals, noting that such mergers could be a unique source of high frequency gravitational waves. We rule out objects whose presence would contradict observations of the CMB and diffuse gamma-rays.

Modeling of turbulent diffusion terms for one-dimensional interfacial area transport equation in vertical round channels

The two-fluid model is comprised of the mass, momentum, and energy equations for liquid and gas phases separately. The terms of interfacial transfer govern mass, momentum, and energy transfer across the gas-liquid interface. The interfacial area concentration is critical to formulating the interfacial transfer terms. The one-dimensional Interfacial Area Transport Equation (IATE) has excellent potential in dynamically predicting the interfacial area concentration. The sink and source terms modeling for the interfacial area concentration is vital in the successful IATE development. The current IATE in bubbly flows considers the sink terms caused by bubble coalescence owing to random bubble collision and wake entrainment. The source term is caused by bubble breakup owing to turbulent impact. The turbulent diffusion term has not been considered in the current practice of one-dimensional IATE. This study developed the equation to predict the turbulent diffusion terms in the one-dimensional IATE for bubbly flow in vertical round channels. The predictive capability of the developed equation was validated with the collected database. The non-dimensionalized turbulent diffusion terms predicted by the developed equation agreed with those directly calculated by the experimental data. The developed turbulent diffusion term was also implemented in the one-dimensional IATE. The interfacial area concentrations predicted by the one-dimensional IATE with the turbulent diffusion term had a satisfactory agreement with the experimental results by the statistical parameters of the mean relative deviation of 3.76% and the mean absolute relative deviation of 10.1%.

Simulation study of membrane bending by protein crowding: a case study with the epsin N-terminal homology domain.

The mechanisms by which peripheral membrane proteins generate curvature is currently an active area of research. One of the proposed mechanisms is amphipathic insertion or the 'wedge' mechanism in which the protein shallowly inserts an amphipathic helix inside the membrane to drive the curvature. However, recent experimental studies have challenged the efficiency of the 'wedge' mechanism as it requires unusual protein densities. These studies proposed an alternative mechanism, namely 'protein-crowding', in which the lateral pressure generated by the random collisions among the membrane bound proteins drives the bending. In this study, we employ atomistic and coarse-grained molecular dynamics simulations to investigate the effects of amphipathic insertion and protein crowding on the membrane surface. Considering epsin N-terminal homology (ENTH) domain as a model protein, we show that amphipathic insertion is not essential for membrane bending. Our results suggest that ENTH domains can aggregate on the membrane surface by employing another structured region (H3 helix). And this protein crowding decreases the cohesive energy of the lipid tails which causes a significant decrease in the membrane bending rigidity. The ENTH domain can generate a similar degree of membrane curvature irrespective of the activity of its H0 helix. Our results are consistent with the recent experimental results.

Experimental confirmation of the formation of a spin polariton in dilute solutions of paramagnetic particles.

Spin exchange during random bimolecular collisions of paramagnetic particles in dilute solutions leads to a surprising effect. Collective modes of motion of the average values of the transverse magnetization components (spin coherences) of subensembles of radicals with different resonant frequencies are formed. The elementary excitations of these modes can be considered as quasiparticles. As a result of interactions with the microwave field, these quasiparticles form spin polaritons. The theoretical prediction for the formation of spin polaritons was made on the basis that the resonance frequencies observed in the EPR experiment depend on the power of the microwave field. In this work, we present an experimental confirmation of the resonant frequency dependence of the spin ensemble on the microwave power for nitroxide radical [15N]-4-hydroxy-2,2,6,6-tetramethylpiperidine-1-oxyl in toluene.

Detection of Recombinant Proteins SOX2 and OCT4 Interacting in HEK293T Cells Using Real-Time Quantitative PCR.

In vivo biotinylation using wild-type and mutants of biotin ligases is now widely applied for the study of cellular proteomes. The commercial availability of kits for the highly efficient purification of biotinylated proteins and their excellent compatibility with LC-MS/MS protocols are the main reasons for the choice of biotin ligases. Since they are all enzymes, however, just a very low expression in cells is required for experiments. Therefore, it can be difficult to perform the quantifications of these enzymes in various samples. Traditional methods, such as western blotting, are not always fit for the detection of the expression levels. Therefore, real-time qRT-PCR, a technology that is more sensitive, was used in this study to quantify the expression of BirA fusions. Using this method, we detected high expression levels of BirA fusions in models of interactions of pluripotency transcription factors to carry out their relative quantification. We also found the absence of the competing endogenous proteins SOX2 and OCT4, as well as no cross-reactivity between BAP/BirA and the endogenous biotinylation system in HEK293T cells. Thus, these data indicated that the high level of biotinylation is due to the in vivo interaction of BAP-X and BirA-Y (X,Y = SOX2, OCT4) in the cell rather than their random collision, a big difference in the expression level of BirA fusions across samples or endogenous biotinylation.

The Boltzmann Brains Puzzle

AbstractLeading cosmological theories engender a controversial puzzle which has prompted philosophers to propose competing epistemological solutions and physicists to propose methodological changes to cosmology. The puzzle arises from the prediction that every brain on Earth will eventually be vastly outnumbered by physical duplicates formed by random collisions of particles in outer space. Supposing that this prediction is correct, shouldn't you believe that your brain is probably one of these vastly more typical extraterrestrial brains, since you cannot infer your brain's origin from your experiential state? But supposing that your brain is one of these extraterrestrial brains, why be confident in the cosmological theories, since you never actually received testimony supporting these theories? Proposals in the literature either deny the rationality of believing theories that make the prediction or deny the typicality of your brain among its duplicates. This paper argues that these proposals are not entirely satisfactory. Instead, one should be confident in theories making the prediction on the supposition that your brain is one of the extraterrestrial brains. The upshots include that it may be rational to believe that your brain is probably an extraterrestrial brain and that cosmologists should not alter their methodology in response to the puzzle.