Carving entangled multiparticle states with exponentially improved fidelity
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Ramette, Joshua (ORCID:0000000247096236)↗
SEARCH · Engineering Papers
Results for “exponential”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Natural inflation with exponentially small tensor-to-scalar ratio
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Astronomy & Astrophysics↗
JCZ3: An Equation of State Based on the Exponential-Six Intermolecular Potential – Update: Formulation
This report presents a comprehensive analysis of the JCZ3 equation of state (EOS) as implemented in the TIGER code, focusing on its thermodynamic framework, mathematical formulations, and implications for modeling gas phase behavior under varying conditions. Overall, the report affirms the TIGER code's foundational robustness and its potential as a valuable tool for simulating high-pressure, high-temperature gas mixtures, while also highlighting areas for further refinement and validation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Exponential Backoff and Its Security Implications for Safety-Critical OT Protocols over TCP/IP Networks
The convergence of Operational Technology (OT) and Information Technology (IT) networks has become increasingly prevalent with the growth of Industrial Internet of Things (IIoT) applications. This shift, while enabling enhanced automation, remote monitoring, and data sharing, also introduces new challenges related to communication latency and cybersecurity. Oftentimes, legacy OT protocols were adapted to the TCP/IP stack without an extensive review of the ramifications to their robustness, performance, or safety objectives. To further accommodate the IT/OT convergence, protocol gateways were introduced to facilitate the migration from serial protocols to TCP/IP protocol stacks within modern IT/OT infrastructure. However, they often introduce additional vulnerabilities by exposing traditionally isolated protocols to external threats. This study investigates the security and reliability implications of migrating serial protocols to TCP/IP stacks and the impact of protocol gateways, utilizing two widely used OT protocols: Modbus TCP and DNP3. Our protocol analysis finds a significant safety-critical vulnerability resulting from this migration, and our subsequent tests clearly demonstrate its presence and impact. A multi-tiered testbed, consisting of both physical and emulated components, is used to evaluate protocol performance and the effects of device-specific implementation flaws. Through this analysis of specifications and behaviors during communication interruptions, we identify critical differences in fault handling and the impact on time-sensitive data delivery. The findings highlight how reliance on lower-level IT protocols can undermine OT system resilience, and they inform the development of mitigation strategies to enhance the robustness of industrial communication networks.
DNP3↗
Mathematical Analysis and Proof of Existence of The Photovoltaic Exponential Model
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Ortiz-Rivera, Eduardo Ivan [Sandia National Labora↗
ORMATEX
The Oak Ridge Matrix Exponential (ORMATEX) software library contains methods to compute the matrix exponential and the action of the matrix exponential on a vector. Additionally, this package contains the related methods for the phi-functions which commonly appear in a wide class of exponential time integration methods. Krylov methods are provided to evaluate the matrix exponential-vector and phi-vector products for cases where the matrix is large and sparse. Utilizing these methods, ORMATEX implements performant exponential integrators for large systems of coupled ordinary differential equations (ODEs). The exponential time integration routines in ORMATEX are particularly suitable to large, stiff systems of equations. These routines may be utilized as a competitive alternative to classical implicit and explicit time integration schemes for certain classes of differential equations where the problem stiffness can be predominately explained by the linear terms.
Gurecky, William [Oak Ridge National Laboratory (O↗
Primordial black hole dark matter: A quantitative parameter sensitivity comparison across formation mechanisms and particle candidates
Primordial black holes (PBHs) in the asteroid-mass window ( 10 17 – 10 22 g ) can account for all of the dark matter without violating any observational constraint, yet are routinely dismissed as fine-tuned. I put that dismissal to the test by applying three complementary sensitivity measures uniformly across a broad landscape: three noninflationary PBH production mechanisms, six classes of inflationary PBH models, and seven particle dark matter benchmarks, all evaluated against the same observable target. Three distinct naturalness universality classes emerge, determined entirely by the analytic structure of the abundance map rather than by the nature of the dark matter candidate. Biased-domain-wall PBHs, in their least model-dependent (free- V b ) form, have the same low sensitivity, Δ = 4.5 , as off-resonance weakly interacting massive particles and freeze-in particles ( Δ = 2 ), a sensitivity that, because it is constant over the entire parameter space of the construction, also coincides trivially with its own Wilson-normalized average within that parameter space (Section Definition and conventions), an equivalence that concerns only the space over which Δ is computed and is not a naturalness statement about the construction as a whole; a further reduction to Δ = 2 is possible only under the additional, independently motivated but not required, assumption that the domain-wall bias is generated by Planck-suppressed operators; early matter-domination PBHs occupy an intermediate tier alongside coannihilating weakly interacting massive particles (WIMPs), unified by a structural identity in which the sensitivity measure equals the logarithm of the ratio of the formation scale to the matter–radiation equality scale; first-order phase transition PBHs, once the more accurate super-exponential collapse probability is used in place of the single-exponential approximation, instead belong to the same highly sensitive tier as resonant WIMP annihilation and single-field inflationary collapse, for a structurally distinct reason; single-field ultraslow-roll inflationary collapse is severely tuned for a distinct reason: a double exponential in which the power spectrum amplitude is itself exponentially sensitive to the inflaton potential coefficients, on top of the exponential collapse sensitivity of the abundance map. My main conclusion is that the claim that PBH dark matter is generically fine-tuned conflates the worst case with a landscape spanning every naturalness tier. The Barbieri-Giudice sensitivity computed here and the Wilson-normalized measure of Iovino and Riotto answer distinct and mutually consistent questions about the same construction, a distinction I clarify within the two-layer decomposition.
Profumo, Stefano [University of California, Santa ↗
Triangle Method for Dense ReLU Layers [SWR-25-72]
This software is an implementation of the methods for initializing and training neural networks to be more efficient per parameter, described more fully below and in the related publication: In theory, depth should make a ReLU network EXPONENTIALLY more efficient by enabling it to produce an exponential number of piecewise linear sections in its output. This reasoning is largely based on the work of mathematicians that have hand-constructed networks that make good use of depth. In practice however, even very deep ReLU networks that have been randomly initialized will behave identically to their shallow counterparts - missing an entire exponential dimension of efficiency. The triangle method is a first attempt at realizing the exponential potential of deep networks. Instead of randomly setting weights, we force pairs of neurons in each layer learn to build triangles (i.e. functions from [0,1] -> [0,1] that look like triangles). This is a very efficient pattern for generating lots of linear pieces because composing two triangular functions doubles the number of pieces with each composition. The triangle method is more than just a different initialization, it is a new paradigm of training. Instead of making direct updates to the matrix weights, we do an extra step of backpropagation to collect the derivatives of the loss function with respect to the shapes of the triangles, training them to tilt left or right. This process essentially holds the networks hand throughout the loss landscape and forces it to always use depth effectively by producing triangular shapes internally. This can produce several orders of magnitude of improvement on convex one-dimensional regression problems. Much more theoretical work is needed to realize its full potential beyond this context, but the implementation in this repository will still work in arbitrary numbers of dimensions. The file Triangle_Method.py is a generalized form of the method that will build each neuron its own custom 1-d convex activation function (with exponential efficiency). Example usage on one dimensional problems can be found in Example_Usage.ipynb and an example of using this in a real neural network can be found in Example_VGG16_CIFAR10.ipynb.
Milkert, Max [National Renewable Energy Laboratory↗
Link statistics of dislocation network during strain hardening
Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.
Crystal plasticity↗
Generalized master equation for particle transport in binary random media with renewal statistics
Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.
Fluctuations & noise↗
Beam energy dependence of net-hyperon yield and its implication on baryon transport mechanism
In the constituent quark model, each quark inside a baryon carries 1/3 unit of the baryon number. An alternative picture exists where the center of a Y-shaped topology of gluon fields, called the baryon junction, carries a unit baryon number. Studying baryon transport over a large rapidity gap (δy) in nuclear collisions provides a possible tool to distinguish these two pictures. A recent analysis of global data on net-proton yield at mid-rapidity in Au+Au collisions showed an exponential dependence on δy and the exponential slope does not vary with event centrality, favoring the baryon junction picture. Since junctions are flavor blind, hyperons – baryons containing valence strange quarks – are expected to exhibit a similar behavior as the proton. This study aims to test this prediction by analyzing hyperon yields in Au+Au collisions at various energies. We observe that net-hyperon yields, after correcting for the strangeness production suppression, adhere to the expected exponential form. The extracted slope parameters for net-Λ, net-$Ξ$ and net-Ω are consistent with each other and with those of net-proton within uncertainties, and exhibit no centrality dependence. Various implementations of the PYTHIA event generator, primarily based on valence quarks for baryon transport, are unable to simultaneously describe the slope parameters for all baryons.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Multioutput Convolutional Neural Network for Improved Parameter Extraction in Time-Resolved Electrostatic Force Microscopy Data
Time-resolved scanning probe microscopy methods, like time-resolved electrostatic force microscopy (trEFM), enable imaging of dynamic processes ranging from ion motion in batteries to electronic dynamics in microstructured thin film semiconductors for solar cells. Reconstructing the underlying physical dynamics from these techniques can be challenging due to the interplay of cantilever physics with the actual transient kinetics of interest in the resulting signal. Previously, quantitative trEFM used empirical calibration of the cantilever or feed-forward neural networks trained on simulated data to extract the physical dynamics of interest. Both these approaches are limited by interpreting the underlying signal as a single exponential function, which serves as an approximation but does not adequately reflect many realistic systems. Here, we present a multi-branched, multi-output convolutional neural network (CNN) that uses the trEFM signal in addition to the physical cantilever parameters as input. The trained CNN accurately extracts parameters describing both single-exponential and bi-exponential underlying functions, and more accurately reconstructs real experimental data in the presence of noise. This article demonstrates an application of physics-informed machine learning to complex signal processing tasks, enabling more efficient and accurate analysis of trEFM.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Particle Markov Chain Monte Carlo Approach to Inference in Transient Surface Kinetics
Here, in this work, we develop a novel Bayesian approach to study the adsorption and desorption of CO onto a Pd(111) surface, a process of great importance in natural sciences. The motivation for this work comes from the recent availability of time-resolved infrared spectroscopy data and the need for model interpretability and uncertainty quantification in chemical processes. The objective is to learn the relevant parameters that characterize the process: coverage with time, rate constants, activation energies, and pre-exponential factors. Our approach consists of three main schemes: (i) a problem design and probabilistic model for the whole system, (ii) a particle Markov chain Monte Carlo sampler to learn the hidden coverages and rate constant parameters, and (iii) two Bayesian formulations to infer the activation energies and pre-exponential factors. The flexibility of the Bayesian framework allows for uncertainty quantification where possible and integration of mathematical constraints in the model to reflect the system physically. We found that our results for the activation energies and pre-exponential factor are in agreement with those reported in the experimental literature, independently, and we provide discussions on the advantages and disadvantages as well as applicability to other systems.
36 MATERIALS SCIENCE↗
Certifying almost all quantum states with few single-qubit measurements
Certifying that an n -qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n -qubit target states, including those with exponential circuit complexity, can be certified from only O ( n 2 ) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O ( n 3 ) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.
information theory and computation↗
An enzyme-based approach for highly efficient self-replication of DNA origami dimers
Self-replication and exponential growth are essential to all living things, the driving force for Darwinian evolution, and potentially useful in nanotechnology for large-scale production of nanoscopic materials. An artificial (nonliving) self-replication system has been shown to exhibit exponential growth and selection using DNA monomer origami tiles templated on a dimer seed. That system purposefully avoided the use of enzymes to get a hint of how self-replication might have evolved in a prebiotic world by using CNV K and UV light to crosslink complementary DNA single strands. For further investigations into competition and extinction and for potential applications involving biocompatibility, we wanted to investigate enzymatic ligation to replace the chemical photo crosslinking step. Here, we present a system which uses thermotolerant T4 DNA ligase and no UV. This system has several additional advantages including a much faster cycling time, yielding 2,000,000 amplifications in 12 h. We also introduce competition to study the possibility of Darwinian-like evolution. Two pairs of DNA origami tiles compete for the same connection strands and show different growth rates under different connection strand concentrations. This system has the potential to combine with other enzymes, such as RNA polymerase to support feedback, allowing us to fine-tune replication dynamics and achieve sophisticated, life-like behaviors. The highly efficient self-replication and exponential growth of DNA origami dimers demonstrated in this work not only enhances our understanding of Darwinian evolution in nature but also opens the door to applications ranging from synthetic biology to smart materials.
Science & Technology - Other Topics↗
Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem
Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight 𝑤. For sufficiently small values of 𝑤 and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of 𝑤 values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.
computation↗
Efficient Unitary Designs from Random Sums and Permutations
A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.
algebra↗
Investigations on the Thermal Stability and Kinetics of Biolubricants Synthesized from Different Types of Vegetable Oils
Petroleum-based lubricants raise environmental concerns due to their non-biodegradability and toxicity, whereas biobased lubricants underperform owing to low thermal stability. This study examined and compared three vegetable oils, along with their chemically modified versions, to better understand their suitability as biolubricants. High oleic soybean oil (HOSOY), regular soybean oil (RSOY), and waste cooking oil (WCO) were subjected to chemical modification, where isopropyl groups were attached to the fatty acid chains of the oils to produce branched oils, i.e., b-HOSOY, b-RSOY, and b-WCO. The detailed kinetic study of each regular and modified sample was investigated using thermogravimetric analysis. The kinetic parameters, such as the activation energies, reaction rate, and pre-exponential factor, were generated via Friedman methods. The differential thermal gravimetric (DTG) analysis showed low volatilization at the onset temperature in each modified oil as compared with the unmodified samples under an oxidative environment. Furthermore, the comparative kinetic studies demonstrated the enhanced thermoxidative stability of the modified products relative to their unaltered counterparts. Among the tested oils, the b-RSOY showed an average activation energy of 325 kJ/mol, followed by the b-WCO: 300 kJ/mol and the b-HOSOY: 251 kJ/mol, indicating the most stable modified product under an oxidative environment. For all the samples, the pre-exponential factors were in good agreement with the activation energies, which validates that finding the pre-exponential components is crucial to the kinetic analysis.
Sarker, Majher I. (ORCID:0000000299509274)↗