Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect.

We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We examine the case of a shifting semi-infinite bad habitat connected to a semi-infinite good habitat. In this case we rigorously establish species persistence (non-persistence) if the habitat shift speed is less (greater) than the asymptotic spreading speed of the species in the good habitat. We also examine the case of a finite shifting patch of hospitable habitat, and find that the habitat shift speed must be less than the asymptotic spreading speed associated with the habitat and there is a critical patch size for species persistence. Spreading speeds and traveling waves are established to address species persistence. Our numerical simulations demonstrate the theoretical results and show the dependence of the critical patch size on the shift speed.

Dynamics of the epidemiological Predator-Prey system in advective environments.

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.

Biological invasion with a porous medium type diffusion in a heterogeneous space.

The knowledge of traveling wave solutions is the main tool in the study of wave propagation. However, in a spatially heterogeneous environment, traveling wave solutions do not exist, and a different approach is needed. In this paper, we study the generation and the propagation of hyperbolic scale singular limits of a KPP-type reaction-diffusion equation when the carrying capacity is spatially heterogeneous and the diffusion is of a porous medium equation type. We show that the interface propagation speed varies according to the carrying capacity.

Genealogical structure changes as range expansions transition from pushed to pulled.

Range expansions accelerate evolution through multiple mechanisms, including gene surfing and genetic drift. The inference and control of these evolutionary processes ultimately rely on the information contained in genealogical trees. Currently, there are two opposing views on how range expansions shape genealogies. In invasion biology, expansions are typically approximated by a series of population bottlenecks producing genealogies with only pairwise mergers between lineages-a process known as the Kingman coalescent. Conversely, traveling wave models predict a coalescent with multiple mergers, known as the Bolthausen-Sznitman coalescent. Here, we unify these two approaches and show that expansions can generate an entire spectrum of coalescent topologies. Specifically, we show that tree topology is controlled by growth dynamics at the front and exhibits large differences between pulled and pushed expansions. These differences are explained by the fluctuations in the total number of descendants left by the early founders. High growth cooperativity leads to a narrow distribution of reproductive values and the Kingman coalescent. Conversely, low growth cooperativity results in a broad distribution, whose exponent controls the merger sizes in the genealogies. These broad distribution and non-Kingman tree topologies emerge due to the fluctuations in the front shape and position and do not occur in quasi-deterministic simulations. Overall, our results show that range expansions provide a robust mechanism for generating different types of multiple mergers, which could be similar to those observed in populations with strong selection or high fecundity. Thus, caution should be exercised in making inferences about the origin of non-Kingman genealogies.

A Symmetrical Quasi-Synchronous Step-Transition Folded Waveguide Slow Wave Structure for 650 GHz Traveling Wave Tubes.

For the purpose of improving performance and reducing the fabrication difficulty of terahertz traveling wave tubes (TWTs), this paper proposes a novel single-section high-gain slow wave structure (SWS), which is named the symmetrical quasi-synchronous step-transition (SQSST) folded waveguide (FW). The SQSST-FW SWS has an artificially designed quasi-synchronous region (QSR) to suppress self-oscillations for sustaining a high gain in an untruncated circuit. Simultaneously, a symmetrical design can improve the efficiency performance to some extent. A prototype of the SQSST-FW SWS for 650 GHz TWTs is designed based on small-signal analysis and numerical simulation. The simulation results indicate that the maximum saturation gain of the designed 650 GHz SQSST-FW TWT is 39.1 dB in a 34.3 mm slow wave circuit, occurring at the 645 GHz point when a 25.4 kV 15 mA electron beam and a 0.43 mW sinusoidal input signal are applied. In addition, a maximum output power exceeding 4 W is observed at the 648 GHz point using the same beam with an increased input power of around 2.8 mW.

A Staggered Vane-Shaped Slot-Line Slow-Wave Structure for W-Band Dual-Sheet Electron-Beam-Traveling Wave Tubes.

A staggered vane-shaped slot-line slow-wave structure (SV-SL SWS) for application in W-band traveling wave tubes (TWTs) is proposed in this article. In contrast to the conventional slot-line SWSs with dielectric substrates, the proposed SWS consists only of a thin metal sheet inscribed with periodic grooves and two half-metal enclosures, which means it can be easily manufactured and assembled and has the potential for mass production. This SWS not only solves the problem of the dielectric loading effect but also improves the heat dissipation capability of such structures. Meanwhile, the SWS design presented here covers a -15 dB S11 frequency range from 87.5 to 95 GHz. The 3-D simulation for a TWT based on the suggested SWS is also investigated. Under dual-electron injection conditions with a total voltage of 17.2 kV and a total current of 0.3 A, the maximum output power at 90 GHz is 200 W, with a 3 dB bandwidth up to 4 GHz. With a good potential for fabrication using microfabrication techniques, this structure can be a good candidate for millimeter-wave TWT applications.

Lumbar multiunit activity power spectrum during air stepping in the spinal cat: evidence for a flexor-dominated rostrocaudally distributed locomotor center.

Clues about the organization of spinal networks responsible for rhythmic motor behaviors have come from the examination of reflex circuitry, lesioning studies, and single-cell recordings. Recently, more attention has been paid to extracellularly recorded multiunit signals thought to represent the general activity of local cellular potentials. Focusing on the gross localization of spinal locomotor networks, we used multiunit signals of the lumbar cord to classify the activation and organization of those networks. We employed power spectral analysis to compare multiunit power across rhythmic conditions and locations and to infer patterns of activation based on coherence and phase measures. We found greater multiunit power in midlumbar segments during stepping, supportive of previous lesioning studies isolating rhythm-generating capabilities to these segments. We also found much greater multiunit power during the flexion phase of stepping than during the extension phase for all lumbar segments. Greater multiunit power at flexion indicates increased neural activity during this phase and is suggestive of previously reported asymmetries between flexor- and extensor-related interneuronal populations of the spinal rhythm-generating network. Finally, the multiunit power showed no phase lag at coherent frequencies throughout the lumbar enlargement indicative of a longitudinal standing wave of neural activation. Our results suggest that the multiunit activity may be representative of the spinal rhythm-generating activity that is distributed in a rostrocaudal gradient. Additionally, our results indicate that this multiunit activity may operate as a flexor-dominant standing wave of activation that is synchronized throughout the rostrocaudal extent of the lumbar enlargement.NEW & NOTEWORTHY We report on the power spectral analysis of multiunit activity (MUA) of lumbar spinal interneurons during a locomotor task. In line with prior studies, we found evidence of greater power at the frequency of locomotion in high lumbar segments and during the flexion phase. Our results also confirm prior observations from our laboratory that the rhythmically active MUA behaves as a longitudinal standing wave of neural activation that is flexor dominant.

Direct pumping of polar fluids with traveling-wave dielectrophoresis.

Efficiently pumping fluids without moving parts in extremely miniaturized formats is challenging. Here, we propose and numerically explore a new type of fluid pump in which a series of electrodes driven at different phases produce a force directly on the molecules of the fluid. This effect is based on traveling-wave dielectrophoresis (twDEP), which has been observed to drive the motion of colloidal particles. Here, we leverage the time needed for fluid molecules with permanent dipoles to align with the applied field to maintain a phase lag between the applied field and the molecular polarization. While requiring operation in the GHz range, this effect is predicted to be efficient due to its ability to directly drive bulk fluid motion. We begin by establishing the foundational equations for this effect and performing finite element simulations to determine its magnitude in a model geometry. By combining theory and a systematic series of calculations, we validate that twDEP pumps should exhibit a fluid flow that scales as the voltage squared divided by the electrode period and that it should increase with the complex permittivity of the fluid and decrease with increasing viscosity. This results in a general equation that predicts the performance of twDEP pumps. Collectively, these computations provide a blueprint for producing twDEP pumps of polar fluids such as water and ethanol. We conclude by noting that the growing interest in high power microwave technology along with metasurfaces to locally tailor phase could provide a path to realizing twDEP pumps in practice.

Semi-autonomous wound invasion via matrix-deposited, haptotactic cues.

Proper wound healing relies on invasion of fibroblasts via directed migration. While the related experimental and mathematical modeling literature has mainly focused on cell migration directed by soluble cues (chemotaxis), there is ample evidence that fibroblast migration is also directed by insoluble, matrix-bound cues (haptotaxis). Furthermore, numerous studies indicate that fibronectin (FN), a haptotactic ligand for fibroblasts, is present and dynamic in the provisional matrix throughout the proliferative phase of wound healing. In the present work, we show the plausibility of a hypothesis that fibroblasts themselves form and maintain haptotactic gradients in a semi-autonomous fashion. As a precursor to this, we examine the positive control scenario where FN is pre-deposited in the wound matrix, and fibroblasts maintain haptotaxis by removing FN at an appropriate rate. After developing conceptual and quantitative understanding of this scenario, we consider two cases in which fibroblasts activate the latent form of a matrix-loaded cytokine, TGFß, which upregulates the fibroblasts' own secretion of FN. In the first of these, the latent cytokine is pre-patterned and released by the fibroblasts. In the second, fibroblasts in the wound produce the latent TGFß, with the presence of the wound providing the only instruction. In all cases, wound invasion is more effective than a negative control model with haptotaxis disabled; however, there is a trade-off between the degree of fibroblast autonomy and the rate of invasion.

Effect of permeability on the initiation of Atherosclerosis modeled as an inflammatory process.

This work presents a mathematical model, based on partial differential equations, that analyzes the inflammatory stage of atherosclerosis. Four leading players are taken into consideration: Low Density Lipoproteins, oxidized Low Density Lipoproteins, immune cells and the inflammatory cytokines. In addition to this, the permeability of the endothelial layer is taken into account in the model. A stability analysis of the fixed points of the kinetic system is presented in details followed by the proof of existence of traveling wave solutions of the system of partial differential equations. The mathematical analysis leads to a biological interpretation. We distinguish three main cases of the disease state that correlate with the permeability of the endothelial layer. In fact, having a low permeability indicates the disease free state since no chronic inflammatory reaction occurs due to the non initiation of the inflammation. With intermediate permeability, a wave propagation corresponding to a chronic inflammatory reaction might occur whether the initial perturbation overcomes a threshold or not. With high permeability, even a small perturbation of the disease free state leads to a chronic inflammatory reaction represented by a wave propagation. We perform numerical simulations of the solutions to illustrate the biological results.

Nonlinear Diffusion for Bacterial Traveling Wave Phenomenon.

The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher-KPP equation. For this reason, the Keller-Segel equations are widely used for bacterial waves. Note that the Keller-Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system.

Forced Traveling Waves in a Reaction-Diffusion Equation with Strong Allee Effect and Shifting Habitat.

We study a reaction-diffusion equation that describes the growth of a population with a strong Allee effect in a bounded habitat which shifts at a speed [Formula: see text]. We demonstrate that the existence of forced positive traveling waves depends on habitat size L, and [Formula: see text], the speed of traveling wave for the corresponding reaction-diffusion equation with the same growth function all over the entire unbounded spatial domain. It is shown that for [Formula: see text] there exists a positive number [Formula: see text] such that for [Formula: see text] there are two positive traveling waves and for [Formula: see text] there is no positive traveling wave. It is also shown if [Formula: see text] for any [Formula: see text] there is no positive traveling wave. The dynamics of the equation are further explored through numerical simulations.

Reaction-Diffusion Modeling of E. coli Colony Growth Based on Nutrient Distribution and Agar Dehydration.

The bacterial colony is a powerful experimental platform for broad biological research, and reaction-diffusion models are widely used to study the mechanisms of its formation process. However, there are still some crucial factors that drastically affect the colony growth but are not considered in the current models, such as the non-homogeneously distributed nutrient within the colony and the substantially decreasing expansion rate caused by agar dehydration. In our study, we propose two plausible reaction-diffusion models (the VN and MVN models) based on the above two factors and validate them against experimental data. Both models provide a plausible description of the non-homogeneously distributed nutrient within the colony and outperform the classical Fisher-Kolmogorov equation and its variation in better describing experimental data. Moreover, by accounting for agar dehydration, the MVN model captures how a colony's expansion slows down and the change of a colony's height profile over time. Furthermore, we demonstrate the existence of a traveling wave solution for the VN model.

Demonstration of a 263-GHz Traveling Wave Tube for Electron Paramagnetic Resonance Spectroscopy.

In this letter, a 263 GHz traveling wave tube for electron paramagnetic resonance spectroscopy is designed, fabricated and tested. A periodic permanent magnet focused pencil beam electron optical system is adopted. A folded waveguide slow-wave structure with modified serpentine bends is optimized to provide high-power wideband performance and stable operation. An experiment has been performed to verify the analysis results and confirm the amplifier stability. The device provides a maximum 11.9 W saturation output power and 25.5 dB saturation gain. Although the available solid-state signal source is unable to drive the amplifier to saturation beyond 260 - 264 GHz, 10 W output power over 5.6 GHz bandwidth has been measured.

Pile Damage Detection Using Machine Learning with the Multipoint Traveling Wave Decomposition Method.

The in-hole multipoint traveling wave decomposition (MPTWD) method is developed for detecting and characterizing the damage of cast in situ reinforced concrete (RC) piles. Compared with the results of MPTWD, the results of the in-hole MPTWD reconstruction technique are found ideal for evaluating the lower-part pile integrity and are further utilized to establish a data-driven machine-learning framework to detect and quantify the degree of damage. Considering the relatively small number of field test samples of the in-hole MPTWD method at this stage, an analytical solution is employed to generate sufficient samples to verify the feasibility and optimize the performance of the machine learning modeling framework. Two types of features extracted by the distributed sampling and statistical and signal processing techniques are applied to three machine-learning classifiers, i.e., logistic regression (LR), extreme gradient boosting (XGBoost) and multilayer perceptron (MLP). The performance of the data-driven machine-learning framework is then evaluated through a specific case study. The results demonstrate that all three classifiers perform better when employing the statistical and signal processing techniques, and the total of 24 extracted features are sufficient for the machine-learning algorithms.

A Novel Staggered Double-Segmented Grating Slow-Wave Structure for 340 GHz Traveling-Wave Tube.

In this paper, a novel staggered double-segmented grating slow-wave structure (SDSG-SWS) is developed for wide-band high-power submillimeter wave traveling-wave tubes (TWTs). The SDSG-SWS can be considered as a combination of the sine waveguide (SW) SWS and the staggered double-grating (SDG) SWS; that is, it is obtained by introducing the rectangular geometric ridges of the SDG-SWS into the SW-SWS. Thus, the SDSG-SWS has the advantages of the wide operating band, high interaction impedance, low ohmic loss, low reflection, and ease of fabrication. The analysis for high-frequency characteristics shows that, compared with the SW-SWS, the SDSG-SWS has higher interaction impedance when their dispersions are at the same level, while the ohmic loss for the two SWSs remains basically unchanged. Furthermore, the calculation results of beam-wave interaction show that the output power is above 16.4 W for the TWT using the SDSG-SWS in the range of 316 GHz-405 GHz with a maximum power of 32.8 W occurring at 340 GHz, whose corresponding maximum electron efficiency is 2.84%, when the operating voltage is 19.2 kV and the current is 60 mA.

Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model.

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the 'go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

Cross Laminar Traveling Components of Field Potentials due to Volume Conduction of Non-Traveling Neuronal Activity in Macaque Sensory Cortices.

Field potentials (FPs) reflect neuronal activities in the brain, and often exhibit traveling peaks across recording sites. While traveling FPs are interpreted as propagation of neuronal activity, not all studies directly reveal such propagating patterns of neuronal activation. Neuronal activity is associated with transmembrane currents that form dipoles and produce negative and positive fields. Thereby, FP components reverse polarity between those fields and have minimal amplitudes at the center of dipoles. Although their amplitudes could be smaller, FPs are never flat even around these reversals. What occurs around the reversal has not been addressed explicitly, although those are rationally in the middle of active neurons. We show that sensory FPs around the reversal appeared with peaks traveling across cortical laminae in macaque sensory cortices. Interestingly, analyses of current source density did not depict traveling patterns but lamina-delimited current sinks and sources. We simulated FPs produced by volume conduction of a simplified 2 dipoles' model mimicking sensory cortical laminar current source density components. While FPs generated by single dipoles followed the temporal patterns of the dipole moments without traveling peaks, FPs generated by concurrently active dipole moments appeared with traveling components in the vicinity of dipoles by superimposition of individually non-traveling FPs generated by single dipoles. These results indicate that not all traveling FP are generated by traveling neuronal activity, and that recording positions need to be taken into account to describe FP peak components around active neuronal populations.SIGNIFICANCE STATEMENT Field potentials (FPs) generated by neuronal activity in the brain occur with fields of opposite polarity. Likewise, in the cerebral cortices, they have mirror-imaged waveforms in upper and lower layers. We show that FPs appear like traveling across the cortical layers. Interestingly, the traveling FPs occur without traveling components of current source density, which represents transmembrane currents associated with neuronal activity. These seemingly odd findings are explained using current source density models of multiple dipoles. Concurrently active, non-traveling dipoles produce FPs as mixtures of FPs produced by individual dipoles, and result in traveling FP waveforms as the mixing ratio depends on the distances from those dipoles. The results suggest that not all traveling FP components are associated with propagating neuronal activity.

Traveling Wave Ion Mobility-Derived Collision Cross Section Database for Plant Specialized Metabolites: An Application to Ventilago harmandiana Pierre.

The combination of ion mobility mass spectrometry (IM-MS) and chromatography is a valuable tool for identifying compounds in natural products. In this study, using an ultra-performance liquid chromatography system coupled to a high-resolution quadrupole/traveling wave ion mobility spectrometry/time-of-flight MS (UPLC-TWIMS-QTOF), we have established and validated a comprehensive TWCCSN2 and MS database for 112 plant specialized metabolites. The database included 15 compounds that were isolated and purified in-house and are not commercially available. We obtained accurate m/z, retention times, fragment ions, and TWIMS-derived CCS (TWCCSN2) values for 207 adducts (ESI+ and ESI-). The database included novel 158 TWCCSN2 values from 79 specialized metabolites. In the presence of plant matrix, the CCS measurement was reproducible and robust. Finally, we demonstrated the application of the database to extend the metabolite coverage of Ventilago harmandiana Pierre. In addition to pyranonaphthoquinones, a group of known specialized metabolites in V. harmandiana, we identified flavonoids, xanthone, naphthofuran, and protocatechuic acid for the first time through targeted analysis. Interestingly, further investigation using IM-MS of unknown features suggested the presence of organonitrogen compounds and lipid and lipid-like molecules, which is also reported for the first time. Data are available on the MassIVE (https://massive.ucsd.edu, data set identifier MSV000090213).

A novel approach on designing ultrahigh burnup metallic TWR fuels: Upsetting the current technological limits.

Abstract: The grand challenge of "net-zero carbon" emission calls for technological breakthroughs in energy production. The traveling wave reactor (TWR) is designed to provide economical and safe nuclear power and solve imminent problems, including limited uranium resources and radiotoxicity burdens from back-end fuel reprocessing/disposal. However, qualification of fuels and materials for TWR remains challenging and it sets an "end of the road" mark on the route of R&D of this technology. In this article, a novel approach is proposed to maneuver reactor operations and utilize high-temperature transients to mitigate the challenges raised by envisioned TWR service environment. Annular U-50Zr fuel and oxidation dispersion strengthened (ODS) steels are proposed to be used instead of the current U-10Zr and HT-9 ferritic/martensitic steels. In addition, irradiation-accelerated transport of Mn and Cr to the cladding surface to form a protective oxide layer as a self-repairing mechanism was discovered and is believed capable of mitigating long-term corrosion. This work represents an attempt to disruptively overcome current technological limits in the TWR fuels. Impact statement: After the Fukushima accident in 2011, the entire nuclear industry calls for a major technological breakthrough that addresses the following three fundamental issues: (1) Reducing spent nuclear fuel reprocessing demands, (2) reducing the probability of a severe accident, and (3) reducing the energy production cost per kilowatt-hour. An inherently safe and ultralong life fast neutron reactor fuel form can be such one stone that kills the three birds. In light of the recent development findings on U-50Zr fuels, we hereby propose a disruptive, conceptual metallic fuel design that can serve the following purposes at the same time: (1) Reaching ultrahigh burnup of above 40% FIMA, (2) possessing strong inherent safety features, and (3) extending current limits on fast neutron irradiation dose to be far beyond 200 dpa. We believe that this technology will be able to bring about revolutionary changes to the nuclear industry by significantly lowering the operational costs as well as improving the reactor system safety to a large extent. Supplementary information: The online version contains supplementary material available at 10.1557/s43577-022-00420-4.