Transverse Channel Research Articles

Synthesis of hierarchical porous carbon particles by hollow polymer microsphere template

Carbon particles with hierarchical pore structure are prepared from resol-type phenol–formaldehyde resin using hollow polymer microspheres as template. The template microspheres have a polystyrene shell with transverse hydrophilic channels connecting to the interior cavity. They are stable and permeable, so a crosslinking catalyst can be previously loaded into the cavity reservoir. Following the incorporation of resol phenol–formaldehyde resin, the aggregates of resin and hollow microspheres have been achieved. Porous carbon particles are derived from carbonization of the composite particles. The structures of carbon materials can be tuned from open wall to closed wall by varying the resol/template weight ratio. The carbon particles are comprised of a series of pores with broad size distribution: from micropore, mesopore to macropore. The porosity development in the carbon materials has been investigated by electron micrograph and N 2 adsorption.

Growth of folds in a deep-water setting

Regional 3D seismic data of the deep-water area offshore NW Borneo provide a detailed picture of the interaction between sedimentary processes on a continental slope and the growth of major folds over a time period of ca. 3.5–5 Ma. In the deep-water area, the estimated rates of fold propagation of tens of mm/yr−1, shortening rates of mm/yr−1, and fold segment lengths of tens of kilometers indicate the studied folds are similar in scale and deformation rate to folds in orogenic belts such as the Zagros Mountains and Himalayas. Feedbacks between sediment dispersal patterns, anticline growth, and structural style are manifested in many ways, and are enhanced by the presence of weak, poorly lithified, synkinematic sediments at fold crests that undergo mass wasting as the fold grows. As folds tighten they range in geometry through simple folds—folds affected by crestal normal faults, folds with crestal normal faults and rotational slides, and folds with forelimb degradation complexes and pronounced erosional unconformities. The unconformity surfaces are either elongate parallel to the fold axes (related to local mass wasting) or perpendicular (related to flows crossing the anticlines). Mass wasting processes in the study area that are large in scale compared with folds (i.e., giant landslides) have modified anticline shape by erosion, and are little affected by anticline topography. More commonly, gravity flows are relatively small compared with the anticlines, and transport pathways are influenced by anticline surface topography. The factors influencing sediment pathway changes during anticline growth include: proximal to distal propagation of folds, lateral propagation of folds, and changing locations of fold growth with time. Assuming an overall consistency in sediment supply, local relative changes in sediment supply to individual piggyback basins are defined by relative changes in sediment supply (generally increasing with time) with respect to growth in anticline amplitude. Such changes may be due to sediment infilling of depressions farther updip and prograding downslope with time or to changes in rate of deformation with time. Initial sediment pathways were predominantly subparallel to growing faults. As folds matured, canyons and channels exploited low points (e.g., fold linkage or intersection points) or weak points (e.g., mud pipes) on folds to initiate transverse channel systems. At a late stage, transverse channels carved up the once long and linear surface ridges into isolated segments.

A synthesis of morphological evolutions and Holocene stratigraphy of a wave-dominated estuary: The Arcachon lagoon, SW France

This work presents the first synthesis of secular to millenary morphological evolutions and stratigraphy of a wave-dominated estuary, the Arcachon lagoon, from a combination of unpublished bathymetric maps (1865 and 2001), core results and high-resolution seismic profiles recorded for the first time in this lagoon. The Arcachon lagoon is located on the Atlantic coast of France, facing the wave-dominated shelf of the Bay of Biscay. It is a mesotidal semi-enclosed environment of about 160 km 2. The sediment budget of the Arcachon lagoon was computed by subtracting the 1865 bathymetric map from that of 2001. The computed volume difference is low (−9.9±35×10 6 m 3 in 136 yrs) and is the result of the balance between erosion and accretion that occurs within tidal channels and tidal flats, respectively. This morphological evolution pattern is explained by low sediment supply and also by the tidal distortion resulting from the morphology of the lagoon. Deep channels connected to the inlet are dominated by ebb currents inducing erosion. Tidal flats and transverse channels display weak or flood-dominated tidal currents leading to the deposition of silts. The areas of tidal flat siltation locally correlate with the presence of oyster farms, suggesting the influence of Man on the lagoon sediment-fill. Transverse channel-infill is related to weak tidal currents resulting from the hydraulically inefficient orientation of these channels which served as an ancient drainage network. Evidence for tidal channel-infill and channel abandonment are also provided by seismic profiling and cores. The upper stratigraphic succession of the lagoon (about 10 m thick) includes four main stratigraphic units dominated by channel-fills. The two lower units (around 7500–2800 yrs BP) display tabular-shape sandy channels interpreted to be records of the open estuarine phase of the Arcachon lagoon. The two upper units (around 2800 yrs BP to present-day) display U-shaped mixed sand-and-mud channel-fills interpreted to be records of the closure of the lagoon. Given that the basal estuarine units are transgressive and the upper lagoonal units are regressive, the main stratigraphic change at around 2800 yrs BP is interpreted as being the maximum flooding surface (MFS). This late MFS is explained by the low sediment supply. It is proposed that the transition from the estuarine to the lagoonal phase is related to the development of the Cap-Ferret spit in response to an increase in the ratio between wave power to tide power. This change in wave-to-tide ratio may be triggered by wave power increase following the Subboreal/Subatlantic climate instability or a decrease in tide power following a decrease in tidal prism related to the lagoon sediment-fill. Thus, the evolution of the Arcachon lagoon over the last millenaries was mainly controlled by its spit development, leading to a wave-dominated estuary in terms of its geomorphology. Once it was partially closed, extensive mud flats developed in the lagoon which became ebb-dominated.

Pionic transparency in semi-exclusive electroproduction off nuclei

We investigate the early onset of pionic color transparency ({pi}CT) observed at Jefferson Laboratory (JLAB) in semi-exclusive pion electroproduction reaction A(e,e{sup '}{pi}{sup +}) off nuclei. In the present description the primary {gamma}*p{yields}{pi}{sup +}n interaction is described very well both for the longitudinal and the transverse polarizations. For the final state interactions a coupled-channel treatment of the interactions of transmitted hadrons allows to go beyond the Glauber approximation. We show that a proper distinction between the soft hadronic and hard partonic components of the electroproduction amplitude is essential for a quantitative description of the measured nuclear transparency. The data are well reproduced if one assumes that point-like configurations are produced in the regime of hard deep-inelastic scattering (DIS) off partons and dominate the transverse channel.

Effective mapping of spin-1 chains onto integrable fermionic models. A study of string and Néel correlation functions

We derive the dominant contribution to the large-distance decay laws of correlation functions towards their asymptotic limits for a spin chain model that exhibits both Haldane and Néel phases in its ground-state phase diagram. The analytic results are obtained by means of an approximate mapping between a spin-1 anisotropic Hamiltonian onto a fermionic model of noninteracting Bogoliubov quasiparticles related in turn (via Jordan–Wigner transformation) to the XY spin-1/2 chain in a transverse field. This approach allows us to express the spin-1 string operators in terms of fermionic operators so that the dominant contribution to the string correlators at large distances can be computed using the technique of Toeplitz determinants. As expected, we find long-range string order both in the longitudinal and in the transverse channel in the Haldane phase, while in the Néel phase only the longitudinal order survives. In this way, the long-range string order can be explicitly related to the components of the magnetization of the XY model. Moreover, apart from the critical line, where the decay is algebraic, we find that in the gapped phases the decay is governed by an exponential tail multiplied by power-law factors. As regards the usual two points correlation functions, we show that the longitudinal one behaves in a ‘dual’ fashion with respect to the transverse string correlator, namely both the asymptotic values and the decay laws exchange when the transition line is crossed. For the transverse spin–spin correlator, we always find a finite characteristic length which is an unexpected feature at the critical point. The results of this analysis prove some conjectures put forward in the past. We also comment briefly on the entanglement features of the original system versus those of the effective model. The goodness of the approximation and the analytical predictions are checked versus density-matrix renormalization group calculations.

Crossover fromhc/etohc/2ecurrent oscillations in rings ofs-wave superconductors

We analyze the crossover from an $hc/e$ periodicity of the persistent current in flux-threaded clean metallic rings toward an $hc/2e$-flux periodicity of the supercurrent upon entering the superconducting state. On the basis of a model calculation for a one-dimensional ring we identify the underlying mechanism, which balances the $hc/e$ versus the $hc/2e$ periodic components of the current density. When the ring circumference exceeds the coherence length of the superconductor, the flux dependence is strictly $hc/2e$ periodic. Further, we develop a multichannel model which reduces the Bogoliubov--de Gennes equations to a one-dimensional differential equation for the radial component of the wave function. The discretization of this differential equation introduces transverse channels whose number scales with the thickness of the ring. The periodicity crossover is analyzed close the critical temperature.

Dendritic vascularization for countering intense heating from the side

This paper is a proposal to vascularize a solid wall with transverse tree-shaped channels with fluid flow from side to side. The purpose of the fluid flow is to intercept in counterflow the solid heat conduction caused by an intense heat flux that lands on the exit plane of the wall. Tree architectures with 1–4 levels of bifurcation are simulated numerically, as a conjugate (convection and conduction) heat flow phenomenon in three dimensions. The effect of local pressure losses at junctions and entrances is included. The numerical work covers the Reynolds number range 10–550, svelteness number range 2.2–11.5, wall porosity range 0.01–0.1, and pressure drop number range 3 × 10 5–10 10. The objective of the tree flow is to keep down the peaks of hot spot temperatures and the fraction of the volume occupied by high temperatures while using minimum pumping power. It is shown that the tree design is very effective, and that there is an optimal number of bifurcation levels for a specified porosity and pressure drop number. Tree designs are more effective than designs with parallel channels when the pressure drop number and the porosity are sufficiently large.

Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

The Wiedemann-Franz law relates the low temperature (T) limit of the ratio W ≡ κ/(σT) of the thermal (κ) and electrical (σ) conductivities of metals to the universal Lorenz number L0 = (π 2 /3)(kB/e) 2 . This remarkable relationship is independent of the strength of the interactions between the electrons, relates macroscopic transport properties to fundamental constants of nature, and depends only upon the Fermi statistics and charge of the elementary quasiparticle excitations of the metal. It has been experimentally verified to high precision in a wide range of metals [1], and realizes a sensitive macroscopic test of the quantum statistics of the charge carriers. It is interesting to note the value of the WiedemannFranz ratio in some other important strongly interacting quantum systems. In superconductors, which have low energy bosonic quasiparticle excitations, σ is infinite for a range of T > 0, while κ is finite in the presence of impurities [2], and so W = 0. At quantum phase transitions described by relativistic field theories, such as the superfluid-insulator transition in the Bose Hubbard model, the low energy excitations are strongly coupled and quasiparticles are not well defined; in such theories the conservation of the relativistic stress-energy tensor implies that κ is infinite, and so W = ∞ [3]. Li and Orignac [4] computed W in disordered Luttinger liquids, and found deviations from L0, and found a non-zero universal value for W at the metal-insulator transition for spinless fermions. The present paper will focus on the quantum phase transition between a superconductor and a metal (a SMT). We will consider quasi-one dimensional nanowires with a large number of transverse channels (so that the electronic localization length is much larger than the mean free path (l)) which can model numerous recent experiments [5, 6, 7, 8, 9, 10, 11, 12, 13]. We will describe universal deviations in the value of W from L0, which can serve as sensitive tests of the theory in future experiments. The mean-field theory for the SMT goes back to the early work [14] of Abrikosov and Gorkov (AG): in one of the earliest discussions of a quantum phase transition, they showed that a large enough concentration of magnetic impurities could induce a SMT at T = 0. It has since been shown that such a theory applies in a large variety of situations with ‘pair-breaking’ perturbations: anisotropic superconductors with non-magnetic impurities [15], lower-dimensional superconductors with magnetic fields oriented in a direction parallel to the Cooper pair motion [16], and s-wave superconductors with inhomogeneity in the strength of the attractive BCS interaction [17]. Indeed, it is expected that pair-breaking is present in any experimentally realizable SMT at T = 0: in the nanowire experiments, explicit evidence for pairbreaking magnetic moments on the wire surface was presented recently by Rogachev et al. [13].

Multichannel atomic scattering and confinement-induced resonances in waveguides

We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\ensuremath{\omega}$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.

Decoheringd-dimensional quantum resistance

The Landauer scattering approach to four-probe resistance is revisited for the case of a $d$-dimensional disordered resistor in the presence of decoherence. Our treatment is based on an invariant-embedding equation for the evolution of the coherent reflection amplitude coefficient in the length of a one-dimensional disordered conductor, where decoherence is introduced at par with the disorder through an outcoupling, or stochastic absorption, of the wave amplitude into side (transverse) channels, and its subsequent incoherent reinjection into the conductor. This is essentially in the spirit of B\"uttiker's reservoir-induced decoherence. The resulting evolution equation for the probability density of the four-probe resistance in the presence of decoherence is then generalized from the one-dimensional to the $d$-dimensional case following an anisotropic Migdal-Kadanoff-type procedure and analyzed. The anisotropy, namely, that the disorder evolves in one arbitrarily chosen direction only, is the main approximation here that makes the analytical treatment possible. A qualitative result is that arbitrarily small decoherence reduces the localization-delocalization transition to a crossover making resistance moments of all orders finite.

Nonperturbative interaction effects in the thermodynamics of disordered wires

We study nonperturbative interaction corrections to the thermodynamic quantities of multichannel disordered wires in the presence of the Coulomb interactions. Within the replica nonlinear $\sigma$-model (NL$\sigma$M) formalism, they arise from nonperturbative soliton saddle points of the NL$\sigma$M action. The problem is reduced to evaluating the partition function of a replicated classical one dimensional Coulomb gas. The state of the latter depends on two parameters: the number of transverse channels in the wire, N_{ch}, and the dimensionless conductance, G(L_T), of a wire segment of length equal to the thermal diffusion length, L_T. At relatively high temperatures, $G(L_T) \gtrsim \ln N_{ch} $, the gas is dimerized, i.e. consists of bound neutral pairs. At lower temperatures, $\ln N_{ch} \gtrsim G(L_T) \gtrsim 1$, the pairs overlap and form a Coulomb plasma. The crossover between the two regimes occurs at a parametrically large conductance $G(L_T) \sim \ln N_{ch}$, and may be studied independently from the perturbative effects. Specializing to the high temperature regime, we obtain the leading nonperturbative correction to the wire heat capacity. Its ratio to the heat capacity for noninteracting electrons, C_0, is $\delta C/C_0\sim N_{ch}G^2(L_T)e^{-2G(L_T)}$.

Numerical analysis of heat transfer in a manifold microchannel heat sink with high efficient copper heat spreader

A manifold microchannel heat sink integrated with a high efficient copper heat spreader is presented. A series analysis of three-dimensional fluid flow and heat transfer performance in this mirochannel heat sink and conventional structure are performed by CFX commercial software package. The temperature difference along the flow direction in the new microchannel heat sink is less than that of the conventional microchannel heat sink due to effect of the transverse channel arrays. The maximum heat flux input of the new microchannel heat sink increases 75% more than the conventional structure with the flow rate of 1 m/s. The new design has better heat transfer characteristics than conventional one for the full range of flow rates considered.

Continuous-Flow Particle Separation by 3D Insulative Dielectrophoresis Using Coherently Shaped, dc-Biased, ac Electric Fields

We present the development of a continuous-flow, "dielectrophoretic spectrometer" based on insulative DEP techniques and three-dimensional geometric design. Hot-embossed thermoplastic devices allow for high-throughput analysis and geometric control of electric fields via ridged microstructures patterned in a high width-to-depth aspect ratio (250:1) channel. We manipulate particles with dc-biased, ac electric fields and generate continuous-output streams of particles with a transverse outlet position specified by linear and nonlinear particle mobilities. We show, with simulation and experiment, that characteristic shape factors can be defined that capture the effects of constrictions in channel depth and that modulating the angle of these constrictions changes the resulting local DEP force. Microdevices are fabricated with an insulative constriction in channel depth, whose angle of incidence with the direction of flow varies continuously across the channel width. The resulting electric field gradients enable demonstration of a dielectrophoretic spectrometer that separates particles and controls their transverse channel position.

Case Study: Promoting the Stability of the Óbidos Lagoon Inlet

The stabilization of tidal inlets by jetties interrupts the littoral drift and has negative visual impacts. This paper proposes an innovative solution to improve the stability of a tidal inlet (the Obidos Lagoon, Portugal) and minimize maintenance dredging, while avoiding the disadvantages of the traditional solution. The new solution has two key features. First, transverse channels are dredged over the tidal flats to promote ebb dominance, thereby improving the ability of the lagoon to flush out incoming sediments. Second, a partially submerged guiding wall near the southern shoreline, together with the existing guiding wall in the northern shore, prevents the movement of the inlet channel and concentrates the ebb flow in the channel. Analyses with empirical, numerical, and analytical models indicate that the solution improves the stability of the tidal inlet and reduces the accretion in the system.

Investigation on influence of sodium- or strontium-modification on corrosion-resistance of Al–11.7%Si alloy

Weight loss test in 4% sulfuric acid aqueous solution bath and salt spray test with 5% NaCl aqueous solution were used to evaluate the corrosion resistance of Al–11.7 wt%Si alloys with no modification, sodium modification, or strontium modification. SEM and optical microscopy were used to, respectively, observe the surface and depth corrosion morphologies of the alloys. The results showed that the corrosion-resistance of the alloy with no modification was the best, followed by the Sr-modified alloy, with the Na-modified alloy showing the worst results. Up to 360 h duration in 4% sulfuric acid aqueous solution bath, all the three alloys showed uniform corrosion characteristics. However, after 360 h duration, pitting corrosion became the typical characteristic of the modified alloys and it resulted in a considerable increase in percentage weight loss. After 480 h, the depth of the pitting holes in the Sr-modified alloy was larger than that in the Na-modified alloy, but the transverse corrosion channels in the former were far less than those in the latter. After this duration, the well-developed transverse corrosion channels in the Na-modified alloy became interconnected inch by inch, which led to severe exfoliation corrosion, so the percentage weight loss of the Na-modified alloy rose abruptly.

Constraining the origin and evolution of confined turbidite systems: southern Cretan margin, Eastern Mediterranean Sea (34°30–36°N)

Bathymetric, 9.5-kHz long-range sidescan sonar (OKEAN), seismic reflection and sediment-core data are used in the analysis of two tectonic troughs south of Crete, Eastern Mediterranean Sea. Here, up to 1.2 s two-way travel time (TWTT) of strata have accumulated since the Middle Miocene in association with extension in the South Aegean region. The study area comprises >100-km- long by >25-km-wide basins filled by sediments subdivided into two seismic units: (1) an upper Unit 1 deposited in sub-basins which follow the present-day configuration of the southern Cretan margin; (2) a basal Unit 2, more than 500 ms (TWTT) thick, accumulated in deeper half-graben/grabens distinct from the present-day depocentres. Both units overlap a locally stratified Unit 3 comprising the pre-Neogene core complex of Crete and Gavdos. In this work, the interpreted seismic units are correlated with the onshore stratigraphy, demonstrating that denudation processes occurring on Crete and Gavdos in response to major tectonic events have been responsible for high sedimentation rates along the proximal southern Cretan margin. Consequently, topographically confined sedimentary units have been deposited south of Crete in the last 12 Ma, including turbidites and other mass-flow deposits fed by evolving transverse and axial channel systems. Surface processes controlling facies distribution include the direct inflow of sediment from alluvial-fan systems and incising mountain rivers onto the Cretan slope, where significant sediment instability processes occur at present. In this setting, seismic profiles reveal eight different types of stratigraphic contacts on basin-margin highs, and basinal areas show evidence of halokinesis and/or fluid escape. The acquired data also show that significant changes to the margin’s configuration occurred in association with the post-Alpine tectonic and eustatic episodes affecting the Eastern Mediterranean.

Porous Gelatin Hydrogels: 2. In Vitro Cell Interaction Study

We report on the feasibility of applying porous gelatin hydrogels, prepared by a novel and controlled cryogenic treatment, as cell-interactive scaffolds for tissue engineering applications. Despite the large number of publications on gelatin as a biomaterial, a detailed study of screening a limited number of gelatin scaffolds for their interaction with a panel of human cells has, to the best of our knowledge, not yet been published. In the present work, we have evaluated two types of porous gelatin scaffolds that differ in their pore geometry and pore size. Type I hydrogels contained top-to-bottom transverse channels (i.e. cones) with a decreasing diameter from the top (330 microm) to the bottom (20-30 microm). Type II hydrogels contained spherical pores with a diameter of 135 microm. Both types of scaffolds were evaluated by confocal laser scanning microscopy in terms of adhesion, spreading, and proliferation of human cells (endothelial, epithelial, fibroblast, glial, and osteoblast) by visualizing cells using calcein-acetoxy methyl ester as a vital stain. The results indicated that cells attached, spread, and proliferated on both types of hydrogels. In addition, the scaffolds developed can be used for the long-term culturing of human cells.

String predictions for near future colliders from one-loop scattering amplitudes around D-brane worlds

We derive compact expressions for one-loop scattering amplitudes of four open-string vector bosons around supersymmetric configurations with intersecting or magnetized D-branes on toroidal orbifolds. We check the validity of our formulae against the structure of their singularities and their behaviour under modular transformations to the transverse channel, exposing closed string exchange. We then specialize to the case of forward scattering and compute the total cross section for two massless open string vector bosons on the brane to decay into closed strings in the bulk, relying on the optical theorem. Although not directly related to collider signatures our predictions represent a step forward towards unveiling phenomenological implications of open and unoriented superstrings

Characterization of Transverse Channel Concentration Profiles Obtainable with a Class of Microfluidic Networks

We analyze mathematically a previously reported class of passive microfluidic mixing networks. The networks produce nonhomogeneous concentrations in the output channel, resulting in diverse concentration profiles. We formally prove that all profiles obtainable with this class of networks can be described as polynomials of degree no higher than the number of input channels less one. We derive explicit formulas for the calculation of resultant output concentration profiles and conversely for the calculation of input concentrations needed to obtain set output profiles.

Effect of transverse gap-junction channels on transverse propagation in an enlarged PSpice model of cardiac muscle.

BackgroundIn previous PSpice modeling studies of simulated action potentials (APs) in parallel chains of cardiac muscle, it was found that transverse propagation could occur between adjacent chains in the absence of gap-junction (gj) channels, presumably by the electric field (EF) generated in the narrow interstitial space between the chains. Transverse propagation was sometimes erratic, the more distal chains firing out of order.MethodsIn the present study, the propagation of complete APs was studied in a 2-dimensional network of 100 cardiac muscle cells (10 × 10 model). Various numbers of gj-channels (assumed to be 100 pS each) were inserted across the junctions between the longitudinal cells of each chain and between adjacent chains (only at the end cells of each chain). The shunt resistance produced by the gj-channels (Rgj) was varied from 100,000 MΩ (0 gj-channels) to 1,000 MΩ (10 channels), 100 MΩ (100 channels) and 10 MΩ (1,000 channels). Total propagation time (TPT) was measured as the difference between the times when the AP rising phase of the first cell (cell # A1) and the last cell (in the J chain) crossed 0 mV. When there were no gj-channels, the excitation was transmitted between cells by the EF, i.e., the negative potential generated in the narrow junctional clefts (e.g., 100 Å) when the prejunctional membrane fired an AP. For the EF mechanism to work, the prejunctional membrane must fire a fraction of a millisecond before the adjacent surface membrane. When there were many gj-channels (e.g., 100 or 1,000), the excitation was transmitted by local-circuit current flow from one cell to the next through these channels.ResultsTPT was measured as a function of four different numbers of transverse gj-channels, namely 0, 10, 100 and 1,000, and four different numbers of longitudinal gj-channels, namely 0, 10, 100 and 1,000. Thus, 16 different measurements were made. It was found that increasing the number of transverse channels had no effect on TPT when the number of longitudinal channels was low (i.e., 0 or 10). In contrast, when the number of longitudinal gj-channels was high (e.g., 100 or 1,000), then increasing the number of transverse channels decreased TPT markedly.ConclusionThus, complete APs could propagate along a network of 100 cardiac muscle cells even when no gj-channels were present between the cells. Insertion of transverse gj-channels greatly speeded propagation through the 10 × 10 network when there were also many longitudinal gj-channels.