Finite Length Effects Research Articles

Stacking correlation length in single-stranded DNA.

Base stacking is crucial in nucleic acid stabilization, from DNA duplex hybridization to single-stranded DNA (ssDNA) protein binding. While stacking energies are tiny in ssDNA, they are inextricably mixed with hydrogen bonding in DNA base pairing, making their measurement challenging. We conduct unzipping experiments with optical tweezers of short poly-purine (dA and alternating dG and dA) sequences of 20-40 bases. We introduce a helix-coil model of the stacking-unstacking transition that includes finite length effects and reproduces the force-extension curves. Fitting the model to the experimental data, we derive the stacking energy per base, finding the salt-independent value $\Delta G_0^{ST}=0.14(3)$ kcal/mol for poly-dA and $\Delta G_0^{ST}=0.07(3)$ kcal/mol for poly-dGdA. Stacking in these polymeric sequences is predominantly cooperative with a correlation length of ∼4 bases at zero force . The correlation length reaches a maximum of ∼10 and 5 bases at the stacking-unstacking transition force of ∼10 and 20 pN for poly-dA and poly-dGdA, respectively. The salt dependencies of the cooperativity parameter in ssDNA and the energy of DNA hybridization are in agreement, suggesting that double-helix stability is primarily due to stacking. Analysis of poly-rA and poly-rC RNA sequences shows a larger stacking stability but a lower stacking correlation length of ∼2 bases.

Microwave analogy of Förster resonance energy transfer and effect of finite antenna length

The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole–dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole–dipole energy transfer in a wider range of conditions.

Evaporation of binary liquids from a capillary tube

Evaporation of multi-component liquid mixtures in confined geometries, such as capillaries, is crucial in applications such as microfluidics, two-phase cooling devices and inkjet printing. Predicting the behaviour of such systems becomes challenging because evaporation triggers complex spatio-temporal changes in the composition of the mixture. These changes in composition, in turn, affect evaporation. In the present work, we study the evaporation of aqueous glycerol solutions contained as a liquid column in a capillary tube. Experiments and direct numerical simulations show three evaporation regimes characterised by different temporal evolutions of the normalised mass transfer rate (or Sherwood number $Sh$ ), namely $Sh (\tilde{t} ) = 1$ , $Sh \sim 1/\sqrt {\tilde{t} }$ and $Sh \sim \exp (-\tilde{t} )$ , where $\tilde {t}$ is a normalised time. We present a simplistic analytical model that shows that the evaporation dynamics can be expressed by the classical relation $Sh = \exp ( \tilde{t} )\,\mathrm {erfc} ( \sqrt {\tilde{t} })$ . For small and medium $\tilde{t}$ , this expression results in the first and second of the three observed scaling regimes, respectively. This analytical model is formulated in the limit of pure diffusion and when the penetration depth $\delta (t)$ of the diffusion front is much smaller than the length $L(t)$ of the liquid column. When $\delta \approx L$ , finite-length effects lead to $Sh \sim \exp (-\tilde{t} )$ , i.e. the third regime. Finally, we extend our analytical model to incorporate the effect of advection and determine the conditions under which this effect is important. Our results provide fundamental insights into the physics of selective evaporation from a multi-component liquid column.

Compression complexity with ordinal patterns for robust causal inference in irregularly sampled time series

Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of causality, inspired by Wiener–Granger’s idea. It estimates causality based on change in dynamical compression-complexity (or compressibility) of the effect variable, given the cause variable. CCC works with minimal assumptions on given data and is robust to irregular-sampling, missing-data and finite-length effects. However, it only works for one-dimensional time series. We propose an ordinal pattern symbolization scheme to encode multidimensional patterns into one-dimensional symbolic sequences, and thus introduce the Permutation CCC (PCCC). We demonstrate that PCCC retains all advantages of the original CCC and can be applied to data from multidimensional systems with potentially unobserved variables which can be reconstructed using the embedding theorem. PCCC is tested on numerical simulations and applied to paleoclimate data characterized by irregular and uncertain sampling and limited numbers of samples.

Development and evaluation of the sandwich open-hole compression test

An open-hole compression test method has been developed to assess the notch sensitivity of sandwich composites under compression loading. This test method, in the process of being standardized by ASTM International, utilizes end loading as well as knife-edge side supports to provide out-of-plane restraint to specimen buckling. Finite element analyses focused on identifying a sandwich specimen geometry that minimized finite-width and finite-length effects on the stress concentration produced by the centrally-located through-hole. Geometric variables included the specimen width-to-hole diameter (w/D) and length-to-hole diameter (l/D) ratios. The sandwich configurations investigated consisted of a Nomex honeycomb core and carbon/epoxy facesheet laminates with a range of material orthotropy ratios. Numerical results were used to identify a candidate sandwich specimen geometry and optimal strain gage placements for use in specimen alignment. A series of mechanical tests were performed to evaluate the proposed specimen design, the proposed test fixture, and the recommended test procedure. The first set of experiments were performed using specimens with different hole diameters but the same specimen width and length. A second set of experiments used specimens with different lengths but with the same specimen width and open-hole. In addition, the use of specimen end potting of the core region was investigated to prevent facesheet separation and end brooming.

Quantum Key Distribution Over a Channel with Scattering

Scattering of light by cloud, haze, and fog decreases the transmission efficiency of communication channels in quantum key distribution (QKD), reduces the system's practical security, and thus constrains the deployment of free-space QKD. Here, we employ wave-front shaping technology to compensate distorted optical signals in high-loss scattering quantum channels and fulfill a polarization-encoded BB84 QKD experiment. With this quantum-channel compensation technology, we achieve a typical enhancement of about 250 in transmission efficiency and build a secure communication link even considering finite key length effect, while the link is impossible to share secure keys before optimization. The method applied in the QKD system shows the potential to expand the application range of QKD systems from lossless channels to highly scattered ones and therefore enhances the deployment ability of a global quantum communication network.

Quantum corrected polymer black hole thermodynamics: mass relations and logarithmic entropy correction

In this paper, we continue the analysis of the effective model of quantum Schwarz­schild black holes recently proposed by some of the authors in [1,2]. In the resulting quantum-corrected spacetime the central singularity is resolved by a black-to-white hole bounce, quantum effects become relevant at a unique mass-independent curvature scale, while they become negligible in the low curvature region near the horizon and classical Schwarzschild geometry is approached asymptotically. This is the case independently of the relation between the black and white hole masses, which are thus freely specifiable independent observables. A natural question then arises about the phenomenological implications of the resulting non-singular effective spacetime and whether some specific relation between the masses can be singled out from a phenomenological perspective. Here we focus on the thermodynamic properties of the effective polymer black hole and analyze the corresponding quantum corrections as functions of black and white hole masses. The study of the relevant thermodynamic quantities such as temperature, specific heat, and horizon entropy reveals that the effective spacetime generically admits an extremal minimal-sized configuration of quantum-gravitational nature characterized by vanishing temperature and entropy. For large masses, the classically expected results are recovered at leading order and quantum corrections are negligible, thus providing us with a further consistency check of the model. The explicit form of the corrections depends on the specific relationship among the masses. In particular, a first-order logarithmic correction to the black hole entropy is obtained for a quadratic mass relation. The latter corresponds to the case of proper finite-length effects which turn out to be compatible with a minimal length generalized uncertainty principle associated with an extremal Planck-sized black hole.

Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals

We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liquid crystals, which can be treated like bloc birefringent media. In particular, we find that the torque deviates considerably from its usual sinusoidal behavior as a function of the misalignment angle. In the case of a birefringent crystal faced with a cholesteric liquid one, the Casimir-Lifshitz torque decreases more slowly as a function of distance than in the nematic case. In the case of two cholesteric liquid crystals, either in the homochiral or in the heterochiral configuration, the angular dependence changes qualitatively as a function of distance. In all considered cases, finite pitch length effects are most pronounced at distances of about 10 nm.

Comment on "Flexibility of short DNA helices with finite-length effect: From base pairs to tens of base pairs" [J. Chem. Phys. 142, 125103 (2015)

First Page

High-spatial-resolution nuclear-magnetic-resonance method for investigation of fluid distribution in whole cores

Low field Nuclear Magnetic Resonance (NMR) has been widely used in laboratories to investigate hydrocarbon and water in small core plugs to provide accurate petrophysical measurements and for calibration of downhole NMR logs. One fundamental limiting factor of current NMR technologies on large whole core is that the spatial resolution is limited by the length of the radio-frequency (r.f.) detection coil. In addition, the end effects of finite coil length can compromise the accuracy of NMR measurement when the core is longer than the coil. Herein a method is developed to overcome these problems to acquire high-spatial-resolution (HSR-) NMR data of the fluid in the long rock samples. The method is implemented by first conducting a series of NMR measurements in synchronization with a stepwise movement of the long sample through the NMR r.f. coil with the step increment equal to the desired spatial resolution. It then inverts the acquired data to obtain HSR-NMR results using a robust inversion algorithm. This new method provides a non-destructive measurement of fluid content with any desired spatial resolution and is especially useful for tight rock samples with short NMR relaxation times. The method is tested on 23 preserved whole cores from a source rock reservoir. The measured fluid distribution from the HSR-NMR method matches well with the fluid content from GRI method on the same sections of the preserved cores. In addition, the measured fluid distribution correlates well with the kerogen content along the cores with obvious lamination in the samples.

Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA.

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length.

Quasi-3D Analytic Method of the Single-Sided Linear Induction Motor With the Ladder Secondary

A quasi-three-dimensional (3-D) analytic method is presented for calculating the performance of single-sided linear induction motor with the ladder secondary. To simplify the analytic model, the ladder aluminum plate is equivalent to the flat-solid one, and the equivalent conductivity is derived and given. In the direction of the motion, the finite primary length and end effect are considered by the method of the Fourier transform and Residue theorem. In the transverse direction, considering finite width of the primary core and the region between the overhang of the primary windings and the secondary, the equivalent integral length is given. Finally, the thrust, vertical force and secondary efficiency are calculated and compared with the results of the 3-D finite-element method and experiment, it is shown that the method presented in the paper is much simpler and the accuracy of the analytic method is verified.

Finite Length Effects on Switching Mechanisms in Chains of Magnetic Particles

Periodic systems of magnetic nanoparticles are now of interest as they support GHz spin waves. Their equilibrium configurations, switchable with the external magnetic field, are crucial for such applications. We study infinite and finite chains of particles of two shapes (i) ellipsoidal and (ii) rectangular stripes with long axes perpendicular to the chain axis. A variable magnetic field is applied parallel to the long axes. Micromagnetic simulations are compared with the corresponding discrete spin models (Stoner-Wohlfarth model, S-W). An antiferromagnetic configuration is the ground state for all the systems at vanishing field but a ferromagnetic configuration occurs when the field is strong enough. The switching of the infinite chains to the reversed ferromagnetic configuration proceeds directly for the ellipsoids and by an intermediate configuration, in which the magnetization within the particle is non-uniform, in the case of the stripes. The non-uniform configurations are well represented by tilted states in S-W model. Important differences are found in the finite analogs: the switching of ellipsoids becomes multistage and starts from the innermost particles relatively well reproduced with S-W model, whereas the reversal of the stripes, starts from the outermost particles and has no analog in S-W model. Practical consequences of the findings are discussed.

On the applicability limits of a model of the magnetic field of a long straight wire

We discuss the influence of two factors on the deviations from the model of the magnetic field of a long straight wire. Firstly, we derive the magnetostatic analogue of McCullagh’s formula for the case of the infinitely long straight conductor with an arbitrary cross-section. Using this equation on the basis of its practical significance, we find that the greatest deviations from the long straight wire model should be observed for a system of two parallel and infinitely long straight wires, equal in absolute value and direction currents. In this case the extremal direction of the magnetic field deviations respectively passes through these wires or is perpendicular to the plane passing through them. Our numerical estimations show that any infinitely long straight conductor with a cross-section having dihedral group symmetry can be considered with reasonable accuracy (the relative error in the determination of the magnetic flux density is less than 5%) as the infinite straight wire, if the distance to the observation point is approximately more than half order of magnitude larger than its maximum transverse size. We also analyse the effect of finite length of the carrying wire on the magnitudes of the magnetic field. We show that in this case, the smallest deviations from the infinite straight wire model should be observed for points belonging to the perpendicular plane passing through the midpoint of a wire.

Acoustic radiation efficiency of a submerged periodic ring-stiffened cylindrical shell with finite vibration loading

The acoustic radiation efficiency of a cylindrical shell is an important parameter in estimating the sound radiation emitted by a structure. However, many of the relevant previous studies have approached acoustic radiation problem by employing numerical methods, requiring large computational resources. In this study, an analytical method is developed to calculate the acoustic radiation efficiency of a finite-length, submerged, periodically stiffened cylindrical shell excited by a radial line force. Using the Flügge shell equations and Helmholtz equation, the motions of the shell wall and the acoustic pressure field in the outer fluid can be expressed analytically. Furthermore, to investigate the effects of finite length on the acoustic radiation efficiency, a stiffened cylindrical shell of infinite length is assumed to have a finite-length vibration distribution and to be constrained by simply supported boundary conditions. Numerical simulations are performed to investigate the acoustic radiation efficiency’s dependency on the finite-length vibration and the presence of stiffeners.

Convergence analysis of iterative learning control using pseudospectra

Iterative learning control (ILC) is an approach to improve the performance of a system that repeats the same operation. In this paper, we apply the theory of pseudospectra to transient analysis of ILC. The focus of this paper is on frequency-domain analysis of filter-based ILC. Moreover, the effect of finite trial length on the transient growth is discussed.

Exclusive photoproduction of excited quarkonia in ultraperipheral collisions

In this paper, we discuss the exclusive photoproduction of ground and excited states of $\psi(1S,2S)$ and $\Upsilon(1S,2S)$ in ultraperipheral collisions (UPCs). Using the potential model in order to obtain the vector meson wave function, we find a good agreement of our calculations with data from the LHC and HERA colliders for $J/\psi (1S,2S) $ and $\Upsilon(1S)$ in $\gamma p$ collisions. We extend the calculations to the nuclear target case applying them to $AA$ UPCs with the use of the shadowing and finite coherence length effects fitted to the data. Our results are compared to the recent LHC data, in both incoherent ($J/\Psi(1S)$ at 2.76 TeV) and coherent ($J/\Psi(1S)$ at 2.76 and 5.02 TeV) processes. We also show the corresponding predictions for the excited states, in the hope that future measurements could provide more detailed information about the vector meson wave functions and nuclear effects.

Finite-length effects on cylindrical Langmuir probes

This work uses self-consistent 3D kinetic simulations to quantify and profile currents collected along a Langmuir probe. These results can be used to design optimal probes for a wide range of parameters relevant to the ionosphere, and low density laboratory plasma experiments.

Cylindrical shells under uniform bending in the framework of Reference Resistance Design

The resistance of cylindrical shells and tubes under uniform bending has received significant research attention in recent times, with a number of major projects aiming to characterise their strength through both experimental and numerical studies. However, the investigated cross-section slenderness ranges have mostly addressed low radius to thickness ratios where buckling occurs after significant plasticity and the influence of geometric imperfections is relatively minor. The behaviour under uniform bending of thinner imperfection-sensitive cylinders that fail by elastic buckling was largely omitted, as was the influence of finite length effects. The value of such resistance models that are only useful for thicker cylinders is therefore somewhat limited.This paper offers the most comprehensive known characterisation of the buckling and collapse resistance of isotropic cylindrical shells and tubes under uniform bending. Expressed within the modern framework of Reference Resistance Design (RRD), it holistically incorporates the effects of material plasticity, geometric nonlinearity and sensitivity to realistic and damaging weld depression imperfections. The characterisation was made possible by the authors' recently-developed novel methodology for mass automation of nonlinear shell buckling finite element analyses. A modification of the RRD formulation is proposed which facilitates its application to systems of low slenderness, and offers a compact algebraic characterisation of all potential imperfection amplitudes for this common shell structural condition. A reliability analysis is also performed.

Memory effects in quantum processes

Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics that define a stochastic process lies at the heart of any proper treatment of memory effects. This is well understood in classical theory, where a hierarchy of joint probability distributions completely characterizes the process at hand. However, attempting to generalize this notion to quantum mechanics is problematic: observing realizations of a quantum process necessarily disturbs the state of the system, breaking an implicit, and crucial, assumption in the classical setting. This issue can be overcome by separating the experimental interventions from the underlying process, enabling an unambiguous description of the process itself and accounting for all possible multi-time correlations for any choice of interrogating instruments. In this paper, using a novel framework for the characterization of quantum stochastic processes, we first solve the long standing question of unambiguously describing the memory length of a quantum processes. This is achieved by constructing a quantum Markov order condition, which naturally generalizes its classical counterpart for the quantification of finite-length memory effects. As measurements are inherently invasive in quantum mechanics, one has no choice but to define Markov order with respect to the interrogating instruments that are used to probe the process at hand: different memory effects are exhibited depending on how one addresses the system, in contrast to the standard classical setting. We then fully characterize the structural constraints imposed on quantum processes with finite Markov order, shedding light on a variety of memory effects that can arise through various examples. Finally, we introduce an instrument-specific notion of memory strength that allows for a meaningful quantification of the temporal correlations between the history and the future of a process for a given choice of experimental intervention. These findings are directly relevant to both characterizing and exploiting memory effects that persist for a finite duration. In particular, immediate applications range from developing efficient compression and recovery schemes for the description of quantum processes with memory to designing coherent control protocols that efficiently perform information-theoretic tasks, amongst a plethora of others.