Smooth Interaction Research Articles

The design and evolution of TurboTurtle, a collaborative microworld for exploring Newtonian physics

TurboTurtle is a dynamicmulti-usermicroworld for the exploration of Newtonian physics. With TurboTurtle, students can alter the attributes of the simulation environment, such as gravity, friction, and presence or absence of walls. Students explore the microworld by manipulating a variety of parameters, and learn concepts by studying the behaviours and interactions that occur. TurboTurtle has evolved into a “group-aware” system where several students, each on their own computer, can simultaneously control the microworld and gesture around the shared display. TurboTurtle's design rationale includes concepts such as equal opportunity controls, simulation timing, concrete vs. abstract controls, recoverability, and how strictly views should be shared between students. Teachers can also add structure to the group's activities by setting the simulation environment to an interesting state, which includes a set of problems and questions. Observations of pairs of young children using TurboTurtle highlight extremes in collaboration styles, from conflict to smooth interaction. Finally, the technical work in making TurboTurtle group-aware is slight, primarily because it was built with a groupware toolkit called GroupKit.

Solvation forces between rough surfaces

We investigate the role of surface roughness on solvation forces and solvation free energies. Roughness is introduced by dividing a surface into an array of square tiles that are then randomly displaced in the direction perpendicular to the wall. The integrated wall strength of these tiled surfaces is independent of the surface roughness and hence this class of rough walls is ideally suited for isolating roughness effects. We use grand canonical Monte Carlo simulations of a Lennard-Jones fluid confined in a slit pore with rough walls to generate the solvation interactions as a function of roughness, tile size, and surface area. The simulation data are compared to a simple superposition approximation of smooth wall solvation interactions (obtained from simulation or density functional theory), based on a distribution of wall separations. We find that this approximation provides a surprisingly accurate route to the solvation interaction of rough surfaces. In general, increased roughness leads to a reduction of oscillations in the solvation forces and surface free energies. However, nonmonotonic behavior of the oscillation amplitude with roughness can be observed for finite surfaces. The washing out of the oscillations found for large surface roughness produces a solvation force that exhibits a broad repulsive peak with separation. The broad repulsion is a consequence of the resistance to squeezing out fluid from the smallest gaps between two opposing rough surfaces. It is as much a reflection of packing effects as are the solvation oscillations for perfectly smooth pores. In addition, we present results for patterned and undulating surfaces produced by an analogous modification of the one-body external field for smooth walls. Finally, we discuss the implications of our results for a number of experimental systems including self-assembled monolayers, microporous materials, protein solutions, and DNA crystals.

A barrier to clinical effectiveness: the etiquette of district nursing

Objectives the following paper addresses the etique tte of district nursing, which, it is argued, is a manifestation of the profession's non-challenging occupational culture and a barrier to clinical effectiveness. Etiquette describes courtesy rules that are applied, often unthinkingly, to facilitate smooth social interaction. Although good working relationships are essential to ‘teamwork’, there are circumstances under which patient care can suffer if politeness becomes an overriding aim. Design the data for this paper are taken from a larger ethnographic study of district nursing work. Participant observation spanned 13 days, and 50 semi-structured interviews were conducted. Setting three community trusts in North West England. Participants 37 district nurses, grades G, H and one F, were observed and interviewed. Analysis the data were analysed by constant comparative analysis until no new themes arose. Findings the findings presented here address the problem faced by the nurses of perceiving that a colleague's care was out of date, or otherwise inappropriate, and of how they dealt with this. In such circumstances, the rule of etiquette was usually that the patient's care would not be challenged, although whether the issue would be subsequently raised with the nurse concerned was attributed to a number of factors. The implications of etiquette in the workplace are addressed. Conclusions the paper concludes by suggesting that a more formal set up for clinical peer review may be a useful platform to move discussion about patient care onto a more professional footing.

Spinodal Decomposition in Binary Gases

We carried out three-dimensional simulations, with about $1.4\ifmmode\times\else\texttimes\fi{}{10}^{6}$ particles, of phase segregation in a low density binary fluid mixture, described mesoscopically by energy and momentum conserving Boltzmann-Vlasov equations. Using a combination of direct simulation Monte Carlo for the short range collisions and a version of particle-in-cell evolution for the smooth long range interaction, we found dynamical scaling after the ratio of the interface thickness to the domain size is less than $\ensuremath{\sim}0.1$. The scaling length $R(t)$ grows at late times like ${t}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ for critical quenches and $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{3}$ for off-critical ones. We also measured the variation of temperature, total particle density, and hydrodynamic velocity during the segregation process.

Dietary Lipid Source Alters Murine Macrophage/Vascular Smooth Muscle Cell Interactions in Vitro

This study was conducted to compare the impact of dietary lipids on the ability of macrophages to modulate vascular smooth muscle cell (SMC) DNA synthesis in vitro. C57BL/6 female mice were fed six different diets (6 mice/diet) containing 10% fat from corn oil (CO), borage oil (BO), primrose oil (PO), fish-corn oil mix (FC, 9:1, w/w), fish-borage oil mix (FB, 1:3, w/w), or fish-primrose oil mix (FP, 1:3, w/w) for 2 wk. Peritoneal macrophages were isolated from these mice, stimulated with zymosan or vehicle, and subsequently co-cultured with naive mouse aortic SMC in the presence of 3H-thymidine to measure SMC DNA synthesis. In this co-culture system, macrophages were seeded on 25-mm culture inserts (upper chamber) and SMC were seeded on 35-mm culture dishes (lower chamber). The two cell types were separated by a semipermeable membrane with a 30-kD cut-off. When quiescent SMC were co-cultured with macrophages, only the PO and FP diet groups had significantly (P < 0.05) lower SMC DNA synthesis compared with the control CO group whose diet contained no γ-linolenic acid (GLA) or (n-3) polyunsaturated fatty acids (PUFA). In contrast, when cycling SMC were co-cultured with dietmodulated macrophages, all dietary groups except for those fed FC had significantly lower (P < 0.05) SMC DNA synthesis relative to the CO group. Although the level of GLA in PO and BO diets was different (11.5 and 22.3 g/100 g fatty acids, respectively), these treatments exerted comparable inhibitory effects on SMC DNA synthesis. The FP treatment consistently exhibited the lowest SMC DNA synthetic profile among the six dietary groups irrespective of SMC growth conditions. These data suggest that BO and PO alone or in combination with fish oil influence macrophage/smooth muscle cell interactions in a manner consistent with favorable modulation of the atherogenic process.

Gonadotropin-releasing hormone (GnRH) and GnRH receptor gene expression in human myometrium and leiomyomata and the direct action of GnRH analogs on myometrial smooth muscle cells and interaction with ovarian steroids in vitro

Gonadotropin-releasing hormone (GnRH) and GnRH receptor gene expression in human myometrium and leiomyomata and the direct action of GnRH analogs on myometrial smooth muscle cells and interaction with ovarian steroids in vitro

Gonadotropin-releasing hormone (GnRH) and GnRH receptor gene expression in human myometrium and leiomyomata and the direct action of GnRH analogs on myometrial smooth muscle cells and interaction with ovarian steroids in vitro.

The objective of the present study was to determine whether GnRH and GnRH receptor are expressed in myometrium and leiomyomata, and if GnRH analogs alone or in the presence of ovarian steroids can modulate the rate of DNA synthesis, proliferation, and transforming growth factor-beta 1 (TGF beta 1) production in myometrial smooth muscle cells in vitro. Reverse transcription-PCR revealed that leiomyomata, unaffected myometrium, and isolated myometrial smooth muscle cells express GnRH and GnRH receptor messenger ribonucleic acid. Furthermore, in a dose-dependent manner, GnRH agonist (leuprolide acetate) inhibited, but GnRH antagonist [D-pGlu1,D-Phe2,D-Trp3.6] (GnRH-Ant1) stimulated, the rate of [3H]thymidine incorporation into myometrial smooth muscle cells (P < 0.05), whereas GnRH-Ant2 (Ac-D-P-Cl-Phe1.2,D-Trp3,D-Arg6,D-Ala10) had no effect. 17 beta-Estradiol (E2) medroxyprogesterone acetate (MPA), and E2 plus MPA (1 micromol/L) stimulated the rate of DNA synthesis by smooth muscle cells (P < 0.05), which was inhibited by GnRH analogs used at 5 micromol/L (P < 0.05). GnRH analogs had no significant effect on myometrial smooth muscle cell proliferation, with the exception of GnRH-Ant1; however, they inhibited the stimulatory action of E2, MPA, and E2 plus MPA in a time-dependent manner (P < 0.05). These cells also synthesized and released approximately 1.32 +/- 0.02 ng/mL total (active plus latent) TGF beta 1, of which 0.73 +/- 0.02 ng/mL was in an active form. E2, MPA, E2 plus MPA, and GnRH analog treatments resulted in an increase in total TGF beta 1 production, whereas GnRH agonist and GnRH-Ant2, but not GnRH-An1, inhibited active TGF beta 1 (P < 0.05). GnRH analogs also inhibited the action of E2 plus MPA on total and active TGF beta 1 production, whereas GnRH-Ant1 further stimulated E2, MPA, or E2 plus MPA action on active TGF beta 1 production (P < 0.05). The data demonstrate for the first time that GnRH and GnRH receptor messenger ribonucleic acid are expressed in myometrium, leiomyomata, and myometrial smooth muscle cells. The local expression of GnRH and receptor along with the direct action of GnRH analogs on the smooth muscle cell DNA synthesis and TGF beta 1 production suggest an autocrine/paracrine role for GnRH in these tissues, a mechanism that may be involved in leiomyomata regression in women receiving GnRH agonist therapy.

Regulation of myosin phosphatase by Rho and Rho-associated kinase (Rho-kinase)

The small guanosine triphosphatase Rho is implicated in myosin light chain (MLC) phosphorylation, which results in contraction of smooth muscle and interaction of actin and myosin in nonmuscle cells. The guanosine triphosphate (GTP)-bound, active form of RhoA (GTP.RhoA) specifically interacted with the myosin-binding subunit (MBS) of myosin phosphatase, which regulates the extent of phosphorylation of MLC. Rho-associated kinase (Rho-kinase), which is activated by GTP.RhoA, phosphorylated MBS and consequently inactivated myosin phosphatase. Overexpression of RhoA or activated RhoA in NIH 3T3 cells increased phosphorylation of MBS and MLC. Thus, Rho appears to inhibit myosin phosphatase through the action of Rho-kinase.

Smooth muscle-epithelial interactions in normal and neoplastic prostatic development.

A hypothesis is proposed that unifies prostatic developmental biology and carcinogenesis. The foundation of this hypothesis is the reciprocal interaction of epithelium and mesenchyme during prostatic development followed thereafter by a reciprocal homeostatic interaction of epithelium and smooth muscle in adulthood. This smooth muscle-epithelial cell interaction is perturbed during prostatic carcinogenesis with adverse sequelae for both epithelium and smooth muscle. The following sequence of events is proposed to occur: (1) Under the influence of androgens, urogenital sinus mesenchyme (UGM) induces urogenital sinus epithelium to undergo prostatic ductal morphogenesis and differentiation. (2) As prostatic epithelium differentiates, it in turn signals the UGM to differentiate into smooth muscle cells that closely surround the epithelial ducts. Differentiation of prostatic smooth muscle requires both an inductive signal from epithelium and androgens. (3) Once formed, prostatic smooth muscle participates in reciprocal homeostatic interactions. We propose that prostatic smooth muscle under the influence of androgens signals to prostatic epithelium to maintain epithelial differentiation and to repress epithelial proliferation, while prostatic epithelium signals to prostatic smooth muscle to maintain smooth muscle differentiation. In adulthood, homeostasis is maintained through reciprocal interactions between smooth muscle and epithelial cells with minimal proliferation of either cell type. Prostatic carcinogenesis, which is initiated following genetic damage to prostatic epithelium, is surmised to involve a sequential disruption in these reciprocal homeostatic interactions with ensuing dedifferentiation of both the emerging prostatic carcinoma cells and smooth muscle. Thus, following genetic insult to prostatic epithelium the epithelium fails to signal appropriately to the smooth muscle, which then begins to dedifferentiate. As smooth muscle differentiation begins to deviate, signaling from prostatic smooth muscle to prostatic epithelium becomes anomalous resulting in progressive loss of control over epithelial differentiation and proliferation. During progression of prostatic carcinogenesis a vicious cycle is established in which both prostatic epithelium and smooth muscle dedifferentiate. This hypothesis is based on the ontogeny of prostatic smooth muscle differentiation during development and by the fact that the amount of smooth muscle progressively diminishes in human prostatic adenocarcinomas during progression from low- to high-grade cancers. Finally, in experimental tissue recombinants in which various normal or neoplastic prostatic epithelia were grown in combination with embryonic rat UGM, only normal (non-neoplastic) epithelia were capable of inducing differentiation of prostatic smooth muscle in UGM. Based on several lines of evidence, it is now apparent that smooth muscle-epithelial interactions are the operative cell-cell interaction in the postnatal prostate which plays a key role in regulating epithelial differentiation, proliferation and carcinogenesis.

Human vascular smooth muscle cell-monocyte interactions and metalloproteinase secretion in culture.

Degradation of the atherosclerotic plaque extracellular matrix could destabilize the lesion, rendering it more prone to rupture. Both macrophages and vascular smooth muscle cells (SMCs) are potential sources of matrix metalloproteinases (MMPs), secreted enzymes that can digest vascular matrix. We explored interactions between human vascular SMCs and human monocytes that result in the secretion of interstitial collagenase (MMP-1) and stromelysin (MMP-3). Monocytes alone or those treated with SMC-conditioned media did not secrete these metalloproteinases as detectable by Western blot analysis. SMCs increased secretion of both MMP-1 and MMP-3 greater than 20-fold when cocultured with monocytes or when treated with monocyte-conditioned media. Addition of macrophage colony stimulating factor (< or = 1000 U/mL) to cocultures of monocytes and SMCs did not affect metalloproteinase secretion. Recombinant interleukin (IL)-1 receptor antagonist inhibited MMP-1 and MMP-3 induction in SMC cultures treated with monocyte-conditioned media (94% and 96% reduction, respectively), while a neutralizing antibody to tumor necrosis factor-alpha had no significant effect on metalloproteinase secretion. In contrast to the induction by monocyte-conditioned media of MMP-1 and MMP-3 secretion by SMCs, monocyte-conditioned media did not increase secretion of 72-kD gelatinase (MMP-2). Thus, monocytes induce MMP-1 and MMP-3 secretion by vascular SMCs through an IL-1-dependent mechanism. This response of SMCs to a defined macrophage product may contribute to plaque destabilization by mononuclear phagocytes in the lesion.

Why Does Behavioral Confirmation Occur? A Functional Perspective on the Role of the Target

The authors performed a functional analysis of the target's role in behavioral confirmation to determine the motivational function(s) being served by the target. Perceivers engaged in getting-acquainted telephone conversations with targets believed to be either obese or of normal weight. Targets were given standard instructions (i.e., no motivation explicitly engaged), adjustive-function instructions (i.e., ensure a smooth and pleasing interaction by being responsive to one's partner's interpersonal style), or knowledge-function instructions (i.e., acquire stable and predictable impressions through interaction). In the standard condition and adjustive-function condition, targets behaviorally confirmed perceivers' erroneous beliefs. However, in the knowledge-function condition, behavioral confirmation was attenuated. These results suggest that targets' interactional activities are performed in the service of an adjustive function when targets behaviorally confirm perceivers' beliefs.

Dietary γ-Linolenic Acid Modulates Macrophage–Vascular Smooth Muscle Cell Interactions

Macrophages and smooth muscle cells (SMCs) are two of the major reactive cell types in atherosclerosis, a disease characterized by uncontrolled proliferation of SMCs. The present study was designed to determine how dietary oils containing gamma-linolenic acid (GLA) (primrose oil [PO]) and long-chain n-3 fatty acids (fish oil) influence the ability of macrophages to modulate SMC DNA synthesis in vitro. Mice were fed one of four diets containing 10% (wt/wt) corn oil (CO), PO, fish oil-CO mix (FC; 9:1, wt/wt), or fish oil-PO mix (FP; 1:3, wt/wt) for 2 weeks. Resident peritoneal macrophages were isolated from these mice and seeded on a semipermeable membrane with a 30-kDa cutoff. Macrophages were preincubated with or without 50 mumol/L indomethacin (a cyclooxygenase inhibitor) or 50 mumol/L L655,238 (a 5-lipoxygenase inhibitor) for 30 minutes and subsequently cocultured with naive murine aortic SMCs grown on culture dishes. DNA synthesis in SMCs and prostaglandin formation in coculture supernatants were measured at the end of a 39-hour incubation period. SMC DNA synthesis was inhibited by 28% and 60% in PO and FP diets containing 10.1% and 8.2% GLA, respectively, relative to the control CO diet containing no GLA or long-chain n-3 fatty acid. A fourfold increase in the levels of PGE1, a potent antiproliferative eicosanoid derived from GLA, was observed in the PO and FP groups relative to the control CO group.(ABSTRACT TRUNCATED AT 250 WORDS)

T Cell—Vascular Smooth Muscle Cell Interactions: Antigen-Specific Activation and Cell Cycle Blockade of T Helper Clones by Cloned Vascular Smooth Muscle Cells

Histological observations have demonstrated the presence of T lymphocytes in atherosclerotic plaques, often in close association with vascular smooth muscle cells (VSMC). We have examined the interaction occurring between cloned murine VSMC and histocompatibitity-matched, antigen-specific Th1 and Th2 cell lines. Incubation of either Th1 or Th2 cells with antigen-pulsed VSMC resulted in the formation of T cell-VSMC conjugates accompanied by morphological changes in both cell types. This interaction resulted in an antigen-dependent activation of IL-2 receptor expression by the Th cells, demonstrating the ability of cloned VSMC to process and present antigen through the exogenous pathway. However, although the T cells were activated to express IL-2 receptors by antigen-pulsed VSMC, they were unable to progress through cell cycle. The secretion of an inhibitory mediator by VSMC was suggested by the observations that (1) fixation of the VSMC's eliminated the inhibitory signal and (2) the supernatants of IFNγ-primed VSMC displayed similar inhibitory activity. The inhibitory effect could not be abrogated with indomethacin or an inhibitor of the generation of reactive nitrogen intermediates, indicating that prostaglandin synthesis and/or nitric oxide production are not solely responsible for the inhibition of proliferation. Flow cytometric cell cycle analysis revealed that VSMC delivered signals resulting in a late G1 blockade of T cell cycle progression. Mitogen responses of purified primary T cells are also dramatically inhibited by IFNγ-treated VSMC, despite significant IL-2 production. Our data depict a complex and intimate T cell-VSMC interaction and suggest that mutual activation events may occur.

The Hospitality Service Encounter: the Role of Communication

Communication in the service encounter is an important determinant of a smooth and effective interaction between hotel service staff and customers. This study investigated 579 hotel service providers and 326 customers to provide empirical data on roles of service providers, topics of conversation, perceived control, forms of address, and gender differences. Factor analysis and MANOVA were performed to identify dimensionality and compare service providers and customers. The results demonstrated communication comprises two roles within the service encounter: task and process. Further, conversation within the service encounter was found to comprise role related, personal, and small talk topics. Significant effects were found for service providers and customers on most items with service providers consistently rating items more highly than customers. In addition, sex of subject was significant with females rating the items more highly than their male counterparts. The study assists in understanding the dyna...

Pulmonary reflexes: neural mechanisms of pulmonary defense.

In his 1954 Harvey lecture on the functions of the lung, Comroe divided pulmonary reflexes into regulatory and defensive or protective (18). Char­ acteristically, regulatory reflexes are subject to a continuous input from low-threshold afferent endings whose impulse frequency waxes and wanes as their effective stimulus (e.g. volume or pressure) varies around a control or resting setpoint. Reflexes of this type exert a continuous control of ventilatory events (11) and promote the smooth interaction of the ventilatory and cardiovascular systems (13), their predominant function being to main­ tain the status quo. Defensive reflexes are a broader constellation of reflex responses evoked by stimuli that threaten lung function. These reflexes are the subject of the present review. Both regulatory and defensive reflexes are mediated predominantly by afferent fibers traveling to the medullary centers in the vagus nerves. The sensory innervation of the lower airways includes a component whose cell bodies are in the upper thoracic dorsal root ganglia and whose fibers travel to the spinal cord with branches of the sympathetic nerves. However, these so-called sympathetic afferents appear to play a relatively minor part in pulmonary defensive reflexes, and even powerful chemical stimuli applied to their endings cause little more than a brief disturbance of breathing (14, 19). Pulmonary defensive reflexes (or effects indistinguishable from them) are not only triggered by extrinsic agents such as irritant gases that pose a threat to the airways, but can be

Stability and single-particle properties of bosonized Fermi liquids.

We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth non-singular Fermi liquid interactions we obtain Shankar's renormalization- group flows and reproduce well known results for quasi-particle lifetimes. We demonstrate by explicit calculation that spin-charge separation does not occur when the Fermi liquid interactions are regular. We also explore the relationship between quantized bosonic excitations and zero sound modes and present a concise derivation of both the spin and the charge collective mode equations. Finally we discuss some aspects of singular Fermi liquid interactions.

Smooth muscle calponin-caltropin interaction: effect on biological activity and stability of calponin.

Calponin inhibits actomyosin Mg2+ ATPase and is proposed to regulate smooth muscle contraction; however, the mechanism by which it exerts its effect and the regulation of its behavior is still under investigation. The proposed methods by which calponin regulation is effected include reversible phosphorylation of calponin which would allow contraction to occur and regulation by interaction with calcium-calmodulin. However, several investigators have been unable to find evidence of in vivo phosphorylation of calponin, and the affinity between calponin and calmodulin is not high enough to suggest that this interaction is biologically significant. In this paper, we present an alternative method of calponin regulation via calcium-caltropin and describe the calponin-caltropin complex for the first time. Caltropin, a calcium-binding protein isolated from smooth muscle, is a dimer under native conditions and interacts with calponin in a calcium-dependent fashion in the ratio of 2 mol of dimer: 1 mol of calponin. The formation of this complex can be monitored by following the fluorescence of an acrylodan label on cysteine 273 of calponin, which undergoes a 35-nm blue shift in wavelength peak from 505 to 470 nm when calponin becomes complexed with caltropin. This fluorescence change when titrated with calcium indicates that the concentration of calcium required for complex formation is approximately 10(-5) M, corresponding to the low-affinity calcium-binding sites of caltropin. This complex was further characterized by circular dichroism (CD).(ABSTRACT TRUNCATED AT 250 WORDS)

Electromagnetically pumped free-electron laser in the scheme of separate interaction space from pump wave generator

The theory of an electromagnetically pumped free-electron laser in the scheme of a separate interaction space from the pump wave generator is developed, taking into account the transverse inhomogeneity of incident and scattered waves, and the presence of a magnetic field of 20 kG focusing the particles. The nonlinear computation results, including the coupling coefficients, the excitation curves, powers and efficiency, etc., are obtained on a set of input parameters of our recently established accelerator and FEL system with a pulse high-current relativistic electron beam (600 kV, 3 kA, 70 ns). An experiment is demonstrated in which the relativistic backward wave corrugation oscillator provides a TM/sub 01/ pump wave with the power of 100 MW at 3 cm wavelength and connects with a smooth tube interaction section to produce stimulated scattering radiation with integral power of 1 MW at 38 mm wavelengths. Also, the numerical and the measured results are compared and discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Physiological aspects of vascular endothelial cell interactions in hypertension and atherosclerosis.

Hypertension causes a number of alterations of the coronary circulation which may influence the outcome of anaesthesia and surgery. These include changes in the architecture of the coronary vasculature, and impairments in coronary reserve and autoregulatory ability of the coronary microvasculature during decreases in perfusion pressure. Chronic hypertension may also alter endothelial regulation of vascular control. Many of the vasodilators used to treat hypertension may have unique effects on the coronary circulation which may become modified by chronic hypertension and cardiac hypertrophy. In this review, each of these areas are considered together with some unique aspects of endothelial/vascular smooth muscle interactions as they relate to acute and chronic hypertension, and to the pharmacological agents used in the treatment of hypertension.

The collision-frequency and reaction rate

The collision-frequencies between pairs of particles in a steady state for both smooth rigid elastic and Coulomb interaction are obtained by a uniform method. In addition, the results for smooth rigid elastic interaction are the same as that obtained previously [S. Champman and T. C. Cowling, in The Mathematical Theory of Non-Uniform Gas (Cambridge U.P., Cambridge, 1970), Chap. 5]. A momentum change distribution for collision frequency is obtained. It cannot only be used as an exact means for the description of Coulomb collision frequency but can also be used for calculating reaction rates. In the case of smooth rigid elastic interaction, the reaction rate proved to be of Arrhenius formula [D. H. Charles and G. A. Rayford, Fundamentals of Chemical Reaction Engineering (Prentice–Hall, Englewood Cliffs, NJ, 1979), Chap. 12]. For Coulomb interaction, a formula for the fusion reaction rate between deuterium and tritium as 〈σvDT〉 = 0.24T−3/2Γ(−1, 17.3/T) cm3/sec (with T in keV) is obtained, which is in agreement with the empirical data over a large temperature region (10 keV&amp;lt;T&amp;lt;1000 keV).