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We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a "compatibility score" metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory. [ABSTRACT FROM AUTHOR]

This study explores the impact of stochastic resetting on the random walk dynamics within scale-free (u , v) -flowers. Utilizing the generating function technique, we develop a recursive relationship for the generating function of the first passage time and establish a connection between the mean first passage time with and without resetting. Our investigation spans multiple scenarios, with the random walker starting from various positions and aiming to reach different target nodes, allowing us to identify the optimal resetting probability that minimizes the mean first passage time for each case. We demonstrate that stochastic resetting significantly improves search efficiency, especially in larger networks. These findings underscore the effectiveness of stochastic resetting as a strategy for optimizing search algorithms in complex networks, offering valuable applications in domains such as biological transport, data networks, and search processes where rapid and efficient exploration is vital. [ABSTRACT FROM AUTHOR]

Transmission matrix measurements of multimode fibers are now routinely performed in numerous laboratories, enabling control of the electric field at the distal end of the fiber and paving the way for the potential application to ultrathin medical endoscopes with high resolution. The same concepts are applicable to other areas, such as space division multiplexing, targeted power delivery, fiber laser performance, and the general study of the mode coupling properties of the fiber. However, the process of building an experimental setup and developing the supporting code to measure the fiber's transmission matrix remains challenging and time consuming, with full details on experimental design, data collection, and supporting algorithms spread over multiple papers or lacking in detail. Here, we outline a complete and self-contained description of the specific experiment we use to measure fully polarization-resolved transmission matrices, which enable full control of the electric field, in contrast to the more common scalar setups. Our exact implementation of the full polarization experiment is new and is easy to align while providing flexibility to switch between full-polarization and scalar measurements if desired. We utilize a spatial light modulator to measure the transmission matrix using linear phase gratings to generate the basis functions and measure the distal electric field using phase-shifting interferometry with an independent reference beam derived from the same laser. We introduce a new method to measure and account for the phase and amplitude drift during the measurement using a Levenberg–Marquardt nonlinear fitting algorithm. Finally, we describe creating distal images through the multimode fiber using phase-to-amplitude shaping techniques to construct the correct input electric field through a superposition of the basis functions with the phase-only spatial light modulator. We show that results are insensitive to the choice of phase-to-amplitude shaping technique as quantified by measuring the contrast of a razor blade at the distal end of the fiber, indicating that the simplest but most power efficient method may be the best choice for many applications. We also discuss some of the possible variations on the setup and techniques presented here and highlight the details that we have found key in achieving high fidelity distal control. Throughout the paper, we discuss applications of our setup and measurement process to a variety of specialty fibers, including fibers with harsh environment coatings, coreless fibers, rectangular core fibers, pedestal fibers, and a pump–signal combiner based on a tapered fiber bundle. This demonstrates the usefulness of these techniques across a variety of application areas and shows the flexibility of our setup in studying various fiber types. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the new generalized stochastic fractional potential-Korteweg–de Vries equation, which describes nonlinear optical solitons and photon propagation in circuits and multicomponent plasmas. Inspired by Kolmogorov–Arnold network and our earlier work, we enhance the improved bilinear neural network method by using a large number of activation functions instead of neurons. This method incorporates the concept of simulating more complicated activation functions with fewer parameters, with more diverse activation functions to generate more complex and rare analytical solutions. On this basis, constraints are introduced into the method, reducing a significant amount of computational workload. We also construct neural network architectures, such as "2–3–1," "2–2–3–1," "2–3–3–1," and "2–3–2–1" using this method. Maple software is employed to obtain many exact analytical solutions by selecting appropriate parameters, such as the superposition of double-period lump solutions, lump–rogue wave solutions, and three interaction solutions. The results show that these solutions exhibit more complex waveforms than those obtained by conventional methods, which is of great significance for the electrical systems and multicomponent fluids to which the equation is applied. This novel method shows significant advantages when applied to fractional-order equations and is expected to be increasingly widely used in the study of nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

This article is concerned with the existence and spectral stability of pulses in singularly perturbed two-component reaction-diffusion systems with slowly mixed nonlinearity. In this paper, the slow nonlinearity is referred to be "mixed" in the sense that it is generated by a trigonometric function multiplied by a power function. We demonstrate via geometric singular perturbation theory that this model can support both the single-pulse and the double-hump solutions. The presence of the slowly mixed nonlinearity complicates the stability analysis on pulses, since the conditions that govern their stability can no longer be explicitly computed. We remove this difficulty by introducing the hypergeometric functions followed by a comparison theorem. By doing so, the "slow–fast" eigenvalues can be determined via the nonlocal eigenvalue problem method. We prove that the double-hump solution is always unstable, while the single-pulse solution can be stable under certain parameter conditions. [ABSTRACT FROM AUTHOR]

Real-world complex systems demonstrated temporal features, i.e., the network topology varies with time and should be described as temporal networks since the traditional static networks cannot accurately characterize. To describe the deliberate attack events in the temporal networks, we propose an activity-based targeted attack on the activity-driven network to investigate temporal networks' temporal percolation properties and resilience. Based on the node activity and network mapping framework, the giant component and temporal percolation threshold are solved according to percolation theory and generating function. The theoretical results coincide with the simulation results near the thresholds. We find that targeted attacks can affect the temporal network, while random attacks cannot. As the probability of a highly active node being deleted increases, the temporal percolation threshold increases, and the giant component increases, thus enhancing robustness. When the network's activity distribution is extremely heterogeneous, network robustness decreases consequently. These findings help us to analyze and understand real-world temporal networks. [ABSTRACT FROM AUTHOR]

The Weil–Petersson volumes of moduli spaces of hyperbolic surfaces with geodesic boundaries are known to be given by polynomials in the boundary lengths. These polynomials satisfy Mirzakhani's recursion formula, which fits into the general framework of topological recursion. We generalize the recursion to hyperbolic surfaces with any number of special geodesic boundaries that are required to be tight. A special boundary is tight if it has minimal length among all curves that separate it from the other special boundaries. The Weil–Petersson volume of this restricted family of hyperbolic surfaces is shown again to be polynomial in the boundary lengths. This remains true when we allow conical defects in the surface with cone angles in (0, π) in addition to geodesic boundaries. Moreover, the generating function of Weil–Petersson volumes with fixed genus and a fixed number of special boundaries is polynomial as well, and satisfies a topological recursion that generalizes Mirzakhani's formula. This work is largely inspired by recent works by Bouttier, Guitter, and Miermont [Ann. Henri Lebesgue 5, 1035–1110 (2022)] on the enumeration of planar maps with tight boundaries. Our proof relies on the equivalence of Mirzakhani's recursion formula to a sequence of partial differential equations (known as the Virasoro constraints) on the generating function of intersection numbers. Finally, we discuss a connection with Jackiw–Teitelboim (JT) gravity. We show that the multi-boundary correlators of JT gravity with defects are expressible in the tight Weil–Petersson volume generating functions, using a tight generalization of the JT trumpet partition function. [ABSTRACT FROM AUTHOR]

In a recent article [Kawamoto, J. Phys. Complexity 4, 035005 (2023)], Kawamoto evoked statistical physics methods for the problem of counting graphs with a prescribed degree sequence. This treatment involved truncating a particular Taylor expansion at the first two terms, which resulted in the Bender-Canfield estimate for the graph counts. This is surprisingly successful since the Bender-Canfield formula is asymptotically accurate for large graphs, while the series truncation does not a priori suggest a similar level of accuracy. We upgrade this treatment in three directions. First, we derive an exact formula for counting d-regular graphs in terms of a d-dimensional Gaussian integral. Second, we show how to convert this formula into an integral representation for the generating function of d-regular graph counts. Third, we perform explicit saddle point analysis for large graph sizes and identify the saddle point configurations responsible for graph count estimates. In these saddle point configurations, only two of the integration variables condense to significant values, while the remaining ones approach zero for large graphs. This provides an underlying picture that justifies Kawamoto's earlier findings. [ABSTRACT FROM AUTHOR]

Living systems are built from microscopic components that function dynamically; they generate work with molecular motors, assemble and disassemble structures such as microtubules, keep time with circadian clocks, and catalyze the replication of DNA. How do we implement these functions in synthetic nanostructured materials to execute them before the onset of dissipative losses? Answering this question requires a quantitative understanding of when we can improve performance and speed while minimizing the dissipative losses associated with operating in a fluctuating environment. Here, we show that there are four modalities for optimizing dynamical functions that can guide the design of nanoscale systems. We analyze Markov models that span the design space: a clock, ratchet, replicator, and self-assembling system. Using stochastic thermodynamics and an exact expression for path probabilities, we classify these models of dynamical functions based on the correlation of speed with dissipation and with the chosen performance metric. We also analyze random networks to identify the model features that affect their classification and the optimization of their functionality. Overall, our results show that the possible nonequilibrium paths can determine our ability to optimize the performance of dynamical functions, despite ever-present dissipation, when there is a need for speed. [ABSTRACT FROM AUTHOR]

In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and then we give the relationships between the terms of these sequences. We present some properties, such as the Binet formulas, special summation formulas, special generating functions, etc. We find the relationships between the roots of the characteristic equation of these sequences and the general terms of these sequences. What is interesting here is that the relationships obtained from that between the roots of the characteristic equation of these new sequences and the terms of the sequences are satisfied in both roots. In addition, we examine the relationships between these sequences with the classic Fibonacci and Lucas sequences. Moreover, we calculate some identities of these sequences, such as Cassini and Catalan. Then Catalan transformation is applied to these sequences, and their terms are found. Furthermore, we apply Hankel transform to the Catalan transform of these sequences. Besides, we associate the terms of the Hankel transformation of the Catalan copper Fibonacci sequence with the classical Fibonacci numbers and the terms of the Hankel transformation of the Catalan copper Lucas sequence with the terms of the copper Lucas sequence. We present the application of copper Fibonacci and copper Lucas sequences to hyperbolic quaternions. Finally, the terms of the copper Fibonacci and copper Lucas sequences are associated with their hyperbolic quaternion values. [ABSTRACT FROM AUTHOR]

Many sensors and catalysts composed of proteins immobilized on inorganic materials have been reported over the past few decades. Despite some examples of functional protein–surface and protein–nanoparticle conjugates, thorough characterization of the biological–abiological interface at the heart of these materials and devices is often overlooked in lieu of demonstrating acceptable system performance. This has resulted in a focus on generating functioning protein-based devices without a concerted effort to develop reliable tools necessary to measure the fundamental properties of the bio–abio interface, such as surface concentration, biomolecular structure, and activity. In this Perspective, we discuss current methods used to characterize these critical properties of devices that operate by integrating a protein into both flat surfaces and nanoparticle materials. We highlight the advantages and drawbacks of each method as they relate to understanding the function of the protein–surface interface and explore the manner in which an informed understanding of this complex interaction leads directly to the advancement of protein-based materials and technology. [ABSTRACT FROM AUTHOR]

When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a current or entropy production rate, has become a central problem in nonequilibrium statistical mechanics. Asymptotically, for a broad class of observables, the distribution of a given observable satisfies a large deviation principle when the dynamics is Markovian, meaning that fluctuations can be characterized in the long-time limit by computing a scaled cumulant generating function. Calculating this function is not tractable analytically (nor often numerically) for complex, interacting systems, so the development of robust numerical techniques to carry out this computation is needed to probe the properties of nonequilibrium materials. Here, we describe an algorithm that recasts this task as an optimal control problem that can be solved variationally. We solve for optimal control forces using neural network ansatz that are tailored to the physical systems to which the forces are applied. We demonstrate that this approach leads to transferable and accurate solutions in two systems featuring large numbers of interacting particles. [ABSTRACT FROM AUTHOR]

The covariance of the one-electron Schrödinger equation in a gauge transformation of electromagnetic potentials is customarily discussed, introducing the relationships that describe their changes, induced by a generating function of position coordinates and time, together with a phase transformation of the wavefunction, according to a proposal by Fock, i.e.,2 relying on three distinct hypotheses. The present note shows that (i) a single similarity transformation employing the Fock phase factor is sufficient to prove the covariance of the wave equation and (ii) the Fock transformations of the nonperturbed Hamiltonian h ̂ (0) and of the time-derivative operator determine the changes appearing in first and second-order Hamiltonians, h ̂ (1) and h ̂ (2) , a single term being obtained by Fock-transforming h ̂ (1) . [ABSTRACT FROM AUTHOR]

The transform technique applied to the analysis of doubly resonant sum-frequency generation (DR-SFG) spectra is extended to include Herzberg–Teller (HT) vibronic modes. The experimentally measured overlap spectral function generates all the energy resonant amplitudes of the DR-SFG excitation function for both Franck–Condon (FC) and HT modes. When FC modes dominate the DR-SFG spectra, a methodology is provided to perform efficient curve fitting and orientation analysis in order to extract FC activities of the various vibration modes from experimental spectra with the help of a molecular model. Determination of the FC or HT natures of the vibration modes from DR-SFG data is also shown to be possible through their visible line shapes with an appropriate choice of polarizations. As an example, experimental DR-SFG data suggest that a known HT-active mode in the vibronic structure of Rhodamine 6G monomers exhibits a FC behavior in molecular aggregates. [ABSTRACT FROM AUTHOR]

In this paper, we present the physics and design-space exploration of a novel pulse compression photoconductive switch (PCPS) using semi-insulating gallium arsenide (GaAs) operating in the negative differential mobility (NDM) regime of electron transport. We systematically quantify the relationship between the PCPS performance and various design options, including contact separation, laser energy and placement, and trap dynamics. Specifically, we report the full-width at half-maximum and the peak output current generated by the PCPS as a function of applied electrical and optical bias. We discuss the optimal spacing between the electrodes and the distance of the laser spot to the anode to achieve higher electron confinement and superior radio-frequency (RF) metrics. Reducing the laser energy is important to prevent the appearance of secondary peaks due to diffusive transport, but there exists a trade-off between the bandwidth and the maximum current of the PCPS. We also compare the PCPS response with and without trap dynamics and find that the electrostatic screening from the trap-induced space charge is time-independent when the trapping time constant is set larger than the recombination lifetime. Overall, trap dynamics are detrimental to performance, unless the compensation doping scheme to achieve semi-insulating GaAs is carefully selected. Results presented in this paper can be used by experimentalists to fine-tune the PCPS design parameters to meet the specifications of various RF applications. Moreover, our results will provide a strong theoretical basis to the measurements of PCPS devices using GaAs and other NDM materials under investigation. [ABSTRACT FROM AUTHOR]

How much time does it take for two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the time it takes for the two molecules to meet. However, this is not always the case as molecules switch stochastically between reactive and non-reactive states. The reaction is then said to be "gated" by the internal states of the molecules involved, which could have a dramatic influence on kinetics. A unified, continuous-time, approach to gated reactions on networks was presented in a recent paper [Scher and Reuveni, Phys. Rev. Lett. 127, 018301 (2021)]. Here, we build on this recent advancement and develop an analogous discrete-time version of the theory. Similar to continuous-time, we employ a renewal approach to show that the gated reaction time can always be expressed in terms of the corresponding ungated first-passage and return times, which yields formulas for the generating function of the gated reaction-time distribution and its corresponding mean and variance. In cases where the mean reaction time diverges, we show that the long-time asymptotics of the gated problem is inherited from its ungated counterpart. However, when molecules spend most of their time non-reactive, an interim regime of slower power-law decay emerges prior to the terminal asymptotics. The discretization of time also gives rise to resonances and anti-resonances, which were absent from the continuous-time picture. These features are illustrated using two case studies that also demonstrate how the general approach presented herein greatly simplifies the analysis of gated reactions. [ABSTRACT FROM AUTHOR]

Photoacoustic waves can be detected by recording optical beam deflection as a result of density gradients inherent in the waves. Beam deflection can be recorded from a single laser beam placed at a distance from the source where data are generated as a function of time, or by recording beam deflections at a single time as the position of the probe beam is varied. For either case, the deflection signal is shown to be described by an Abel transform of the pressure gradient. Here, the inversion of beam deflection data from photoacoustic sources with symmetry in one, two, and three dimensions is investigated. An iterative method based on total variation regularization and a regression procedure based on Lasso regularization are shown to result in accurate reproductions of the theoretical expressions that describe photoacoustic waves from simple sources. [ABSTRACT FROM AUTHOR]

A key step in applying the auxiliary superfield method to complex systems is the representation of the Green's function of the system as derivatives of a generating functional. This representation is known to be valid for Hermitian systems, but this precludes the application of the method to systems with fluid loading or damping. Here, it is demonstrated that the known representation continues to be valid for fluid-loaded and damped systems. Thus, the auxiliary superfield method may be applied to such systems. [ABSTRACT FROM AUTHOR]

We derive a functional relation between the generating functions of connected chord diagrams and two-connected chord diagrams. This relation enables us to calculate an asymptotic expansion for the number of two-connected chord diagrams on n chords. The asymptotic information obtained from this expansion refines the last established results and provides a simple alternative for calculating the asymptotic behaviour of the certain functions in (zero-dimensional) quantum electro-dynamics. [ABSTRACT FROM AUTHOR]

In this study, we suggest the truncated version of the inverse power Ailamujia distribution, which is more flexible than other well-known distributions. Statistical properties of the new distribution are considered, such as moments, moment generating function, incomplete moments, quantile function, order statistics, and entropy. We discuss various methods of estimation, such as the method of maximum likelihood, methods of least squares and weighted least squares, the method of the maximum product of spacings, the method of Cramer and Von-Mises, methods of Anderson and Darling and right-tail Anderson and Darling, the method of percentiles, and the Bayesian method. Simulation is implemented to study the performance of estimates. We introduce two real data applications, showing that the new distribution can provide better fits than some other corresponding distributions. [ABSTRACT FROM AUTHOR]

The motion of rigid spherical particles suspended in a low Reynolds number fluid can be related to the forces, torques, and stresslets acting upon them by 22 scalar resistance functions, commonly notated X 11 A , X 12 A , Y 11 A , etc. Near-field asymptotic forms of these resistance functions were derived in Jeffrey and Onishi ["Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow," J. Fluid Mech. 139, 261–290 (1984)] and Jeffrey ["The calculation of the low Reynolds number resistance functions for two unequal spheres," Phys. Fluids A 4, 16–29 (1992)]; these forms are now used in several numerical methods for suspension mechanics. However, the first of these important papers contains a number of small errors, which make it difficult for the reader to correctly evaluate the functions for parameters not explicitly tabulated. This short article comprehensively corrects these errors and adds formulas that were originally omitted from both papers, so that the reader can verify and implement the equations independently. The corrected expressions, rationalized and using contemporary nondimensionalization, are shown to match mid-field values of these scalars, which are calculated through an alternative method. A Python script to generate and evaluate these functions is provided. [ABSTRACT FROM AUTHOR]